Input:
Find x and y such that
8x + 6y = -466/5
7x + 6y = -464/5

Output:
8x + 6y = -466/5
7x + 6y = -464/5

Using elimination
7*(8x + 6y = -466/5)
8*(7x + 6y = -464/5)
56x + 42y = -3262/5
56x + 48y = -3712/5
Subtract equations
-6y = 90
y = 90/-6
y = -15

Substitute y
8x + 6(-15) = -466/5
8x = -16/5
x = -16/5/8
x = -2/5


Input:
Solve simultaneously:
1x + 6y = -1/5
5x + 8y = 9/2

Output:
1x + 6y = -1/5
5x + 8y = 9/2

Using elimination
5*(1x + 6y = -1/5)
1*(5x + 8y = 9/2)
5x + 30y = -1
5x + 8y = 9/2
Subtract equations
22y = -11/2
y = -11/2/22
y = -1/4

Substitute y
1x + 6(-1/4) = -1/5
1x = 13/10
x = 13/10/1
x = 13/10


Input:
Find x and y such that
10x + 7y = -143/4
6x + 4y = -21

Output:
10x + 7y = -143/4
6x + 4y = -21

Using elimination
6*(10x + 7y = -143/4)
10*(6x + 4y = -21)
60x + 42y = -429/2
60x + 40y = -210
Subtract equations
2y = -9/2
y = -9/2/2
y = -9/4

Substitute y
10x + 7(-9/4) = -143/4
10x = -20
x = -20/10
x = -2


Input:
Solve the equations:
8x + 4y = 48/5
3x + 2y = 24/5

Output:
8x + 4y = 48/5
3x + 2y = 24/5

Using elimination
3*(8x + 4y = 48/5)
8*(3x + 2y = 24/5)
24x + 12y = 144/5
24x + 16y = 192/5
Subtract equations
-4y = -48/5
y = -48/5/-4
y = 12/5

Substitute y
8x + 4(12/5) = 48/5
8x = 0
x = 0/8
x = 0


Input: Solve 8x + 112/5 = 0

Output:
8x + 112/5 = 0
8x = -112/5
x = -112/5 / 8
x = -14/5


Input: Solve x^2 - 41/8x + 5/8 = 0

Output:
x^2 - 41/8x + 5/8 = 0
(x - 1/8)(x - 5) = 0
x - 1/8 = 0  or  x - 5 = 0
x = 1/8
x = 5


Input:
Solve the system:
2x + 3y = 213/35
5x + 2y = 90/7

Output:
2x + 3y = 213/35
5x + 2y = 90/7

Using elimination
5*(2x + 3y = 213/35)
2*(5x + 2y = 90/7)
10x + 15y = 213/7
10x + 4y = 180/7
Subtract equations
11y = 33/7
y = 33/7/11
y = 3/7

Substitute y
2x + 3(3/7) = 213/35
2x = 24/5
x = 24/5/2
x = 12/5


Input:
Solve the system:
5x + 2y = -17/2
2x + 9y = -15/2

Output:
5x + 2y = -17/2
2x + 9y = -15/2

Using elimination
2*(5x + 2y = -17/2)
5*(2x + 9y = -15/2)
10x + 4y = -17
10x + 45y = -75/2
Subtract equations
-41y = 41/2
y = 41/2/-41
y = -1/2

Substitute y
5x + 2(-1/2) = -17/2
5x = -15/2
x = -15/2/5
x = -3/2


Input: Find x for x^3 + 143/40x^2 - 65/16x + 9/20 = 0

Output:
x^3 + 143/40x^2 - 65/16x + 9/20 = 0
(x - -9/2)(x - 1/8)(x - 4/5) = 0
x - -9/2 = 0
x - 1/8 = 0
x - 4/5 = 0
x = -9/2
x = 1/8
x = 4/5


Input: Find x in x^2 + 1x - 5/16 = 0

Output:
x^2 + 1x - 5/16 = 0
(x - -5/4)(x - 1/4) = 0
x - -5/4 = 0  or  x - 1/4 = 0
x = -5/4
x = 1/4


Input:
Solve simultaneously:
1x + 6y = 34/3
6x + 6y = 3

Output:
1x + 6y = 34/3
6x + 6y = 3

Using elimination
6*(1x + 6y = 34/3)
1*(6x + 6y = 3)
6x + 36y = 68
6x + 6y = 3
Subtract equations
30y = 65
y = 65/30
y = 13/6

Substitute y
1x + 6(13/6) = 34/3
1x = -5/3
x = -5/3/1
x = -5/3


Input: Find x for x^2 + 49/10x + 51/10 = 0

Output:
x^2 + 49/10x + 51/10 = 0
(x - -3/2)(x - -17/5) = 0
x - -3/2 = 0  or  x - -17/5 = 0
x = -3/2
x = -17/5


Input: Find the solution to x^2 + 27/2x - 7 = 0

Output:
x^2 + 27/2x - 7 = 0
(x - 1/2)(x - -14) = 0
x - 1/2 = 0  or  x - -14 = 0
x = 1/2
x = -14


Input:
Find x and y such that
8x + 2y = -4
4x + 8y = 40

Output:
8x + 2y = -4
4x + 8y = 40

Using elimination
4*(8x + 2y = -4)
8*(4x + 8y = 40)
32x + 8y = -16
32x + 64y = 320
Subtract equations
-56y = -336
y = -336/-56
y = 6

Substitute y
8x + 2(6) = -4
8x = -16
x = -16/8
x = -2


Input: Solve quickly: 10x - 36 = 0

Output:
10x - 36 = 0
10x = 36
x = 36 / 10
x = 18/5


Input: Find x in x^3 - 124/7x^2 + 467/7x - 494/7 = 0

Output:
x^3 - 124/7x^2 + 467/7x - 494/7 = 0
(x - 2)(x - 19/7)(x - 13) = 0
x - 2 = 0
x - 19/7 = 0
x - 13 = 0
x = 2
x = 19/7
x = 13


Input: Find the solution to x^3 - 6/5x^2 - 53/20x + 21/10 = 0

Output:
x^3 - 6/5x^2 - 53/20x + 21/10 = 0
(x - -3/2)(x - 7/10)(x - 2) = 0
x - -3/2 = 0
x - 7/10 = 0
x - 2 = 0
x = -3/2
x = 7/10
x = 2


Input:
Solve the equations:
10x + 7y = -397/9
1x + 9y = -82/5

Output:
10x + 7y = -397/9
1x + 9y = -82/5

Using elimination
1*(10x + 7y = -397/9)
10*(1x + 9y = -82/5)
10x + 7y = -397/9
10x + 90y = -164
Subtract equations
-83y = 1079/9
y = 1079/9/-83
y = -13/9

Substitute y
10x + 7(-13/9) = -397/9
10x = -34
x = -34/10
x = -17/5


Input:
Find x and y such that
2x + 9y = -440/3
1x + 8y = -388/3

Output:
2x + 9y = -440/3
1x + 8y = -388/3

Using elimination
1*(2x + 9y = -440/3)
2*(1x + 8y = -388/3)
2x + 9y = -440/3
2x + 16y = -776/3
Subtract equations
-7y = 112
y = 112/-7
y = -16

Substitute y
2x + 9(-16) = -440/3
2x = -8/3
x = -8/3/2
x = -4/3


Input: Determine x in 10x + 30 = 0

Output:
10x + 30 = 0
10x = -30
x = -30 / 10
x = -3


Input: Compute the solution of x^3 - 971/126x^2 + 2399/126x - 136/9 = 0

Output:
x^3 - 971/126x^2 + 2399/126x - 136/9 = 0
(x - 7/2)(x - 17/7)(x - 16/9) = 0
x - 7/2 = 0
x - 17/7 = 0
x - 16/9 = 0
x = 7/2
x = 17/7
x = 16/9


Input: Solve 4x - 26/5 = 0

Output:
4x - 26/5 = 0
4x = 26/5
x = 26/5 / 4
x = 13/10


Input: Find the solution to x^3 + 31/3x^2 + 379/12x + 55/2 = 0

Output:
x^3 + 31/3x^2 + 379/12x + 55/2 = 0
(x - -3/2)(x - -11/2)(x - -10/3) = 0
x - -3/2 = 0
x - -11/2 = 0
x - -10/3 = 0
x = -3/2
x = -11/2
x = -10/3


Input: Solve the equation 7x - 133/4 = 0

Output:
7x - 133/4 = 0
7x = 133/4
x = 133/4 / 7
x = 19/4


Input: Solve x^2 - 21/5x + 98/25 = 0

Output:
x^2 - 21/5x + 98/25 = 0
(x - 7/5)(x - 14/5) = 0
x - 7/5 = 0  or  x - 14/5 = 0
x = 7/5
x = 14/5


Input: Determine x in x^3 - 99/35x^2 - 42/5x + 104/7 = 0

Output:
x^3 - 99/35x^2 - 42/5x + 104/7 = 0
(x - 4)(x - -13/5)(x - 10/7) = 0
x - 4 = 0
x - -13/5 = 0
x - 10/7 = 0
x = 4
x = -13/5
x = 10/7


Input: Find the solution to x^2 - 48/5x - 4 = 0

Output:
x^2 - 48/5x - 4 = 0
(x - -2/5)(x - 10) = 0
x - -2/5 = 0  or  x - 10 = 0
x = -2/5
x = 10


Input: Solve the equation x^2 - 50/3x - 24 = 0

Output:
x^2 - 50/3x - 24 = 0
(x - 18)(x - -4/3) = 0
x - 18 = 0  or  x - -4/3 = 0
x = 18
x = -4/3


Input: What value of x satisfies x^2 - 109/30x + 7/3 = 0

Output:
x^2 - 109/30x + 7/3 = 0
(x - 14/5)(x - 5/6) = 0
x - 14/5 = 0  or  x - 5/6 = 0
x = 14/5
x = 5/6


Input: Find x for 8x - 28 = 0

Output:
8x - 28 = 0
8x = 28
x = 28 / 8
x = 7/2


Input:
Solve the system:
6x + 9y = -243/7
2x + 5y = -121/7

Output:
6x + 9y = -243/7
2x + 5y = -121/7

Using elimination
2*(6x + 9y = -243/7)
6*(2x + 5y = -121/7)
12x + 18y = -486/7
12x + 30y = -726/7
Subtract equations
-12y = 240/7
y = 240/7/-12
y = -20/7

Substitute y
6x + 9(-20/7) = -243/7
6x = -9
x = -9/6
x = -3/2


Input:
Solve the system:
7x + 2y = -197/6
9x + 8y = -275/6

Output:
7x + 2y = -197/6
9x + 8y = -275/6

Using elimination
9*(7x + 2y = -197/6)
7*(9x + 8y = -275/6)
63x + 18y = -591/2
63x + 56y = -1925/6
Subtract equations
-38y = 76/3
y = 76/3/-38
y = -2/3

Substitute y
7x + 2(-2/3) = -197/6
7x = -63/2
x = -63/2/7
x = -9/2


Input: Solve quickly: 7x - 70 = 0

Output:
7x - 70 = 0
7x = 70
x = 70 / 7
x = 10


Input: Solve the equation x^3 + 1865/252x^2 + 1103/84x + 323/126 = 0

Output:
x^3 + 1865/252x^2 + 1103/84x + 323/126 = 0
(x - -17/7)(x - -19/4)(x - -2/9) = 0
x - -17/7 = 0
x - -19/4 = 0
x - -2/9 = 0
x = -17/7
x = -19/4
x = -2/9


Input:
Solve the equations:
10x + 1y = -47/9
6x + 6y = -13/3

Output:
10x + 1y = -47/9
6x + 6y = -13/3

Using elimination
6*(10x + 1y = -47/9)
10*(6x + 6y = -13/3)
60x + 6y = -94/3
60x + 60y = -130/3
Subtract equations
-54y = 12
y = 12/-54
y = -2/9

Substitute y
10x + 1(-2/9) = -47/9
10x = -5
x = -5/10
x = -1/2


Input: Compute the solution of 1x  = 0

Output:
1x  = 0
1x = 0
x = 0 / 1
x = 0


Input: Solve 10x + 6 = 0

Output:
10x + 6 = 0
10x = -6
x = -6 / 10
x = -3/5


Input: What value of x satisfies x^2 - 7/5x - 34/5 = 0

Output:
x^2 - 7/5x - 34/5 = 0
(x - 17/5)(x - -2) = 0
x - 17/5 = 0  or  x - -2 = 0
x = 17/5
x = -2


Input: Solve the equation x^2 - 67/72x + 5/24 = 0

Output:
x^2 - 67/72x + 5/24 = 0
(x - 3/8)(x - 5/9) = 0
x - 3/8 = 0  or  x - 5/9 = 0
x = 3/8
x = 5/9


Input: Solve x^2 - 13/3x + 4 = 0

Output:
x^2 - 13/3x + 4 = 0
(x - 3)(x - 4/3) = 0
x - 3 = 0  or  x - 4/3 = 0
x = 3
x = 4/3


Input:
Find x and y such that
8x + 6y = -50
7x + 8y = -41

Output:
8x + 6y = -50
7x + 8y = -41

Using elimination
7*(8x + 6y = -50)
8*(7x + 8y = -41)
56x + 42y = -350
56x + 64y = -328
Subtract equations
-22y = -22
y = -22/-22
y = 1

Substitute y
8x + 6(1) = -50
8x = -56
x = -56/8
x = -7


Input:
Solve simultaneously:
10x + 9y = -38/7
9x + 10y = -152/35

Output:
10x + 9y = -38/7
9x + 10y = -152/35

Using elimination
9*(10x + 9y = -38/7)
10*(9x + 10y = -152/35)
90x + 81y = -342/7
90x + 100y = -304/7
Subtract equations
-19y = -38/7
y = -38/7/-19
y = 2/7

Substitute y
10x + 9(2/7) = -38/7
10x = -8
x = -8/10
x = -4/5


Input:
Solve the equations:
1x + 3y = 169/15
9x + 1y = 221/5

Output:
1x + 3y = 169/15
9x + 1y = 221/5

Using elimination
9*(1x + 3y = 169/15)
1*(9x + 1y = 221/5)
9x + 27y = 507/5
9x + 1y = 221/5
Subtract equations
26y = 286/5
y = 286/5/26
y = 11/5

Substitute y
1x + 3(11/5) = 169/15
1x = 14/3
x = 14/3/1
x = 14/3


Input:
Solve the system:
1x + 2y = 31/10
8x + 9y = 103/5

Output:
1x + 2y = 31/10
8x + 9y = 103/5

Using elimination
8*(1x + 2y = 31/10)
1*(8x + 9y = 103/5)
8x + 16y = 124/5
8x + 9y = 103/5
Subtract equations
7y = 21/5
y = 21/5/7
y = 3/5

Substitute y
1x + 2(3/5) = 31/10
1x = 19/10
x = 19/10/1
x = 19/10


Input: Determine x in x^3 - 11/8x^2 - 41/16x + 21/8 = 0

Output:
x^3 - 11/8x^2 - 41/16x + 21/8 = 0
(x - 2)(x - -3/2)(x - 7/8) = 0
x - 2 = 0
x - -3/2 = 0
x - 7/8 = 0
x = 2
x = -3/2
x = 7/8


Input:
Solve the equations:
5x + 6y = 281/6
1x + 4y = 247/18

Output:
5x + 6y = 281/6
1x + 4y = 247/18

Using elimination
1*(5x + 6y = 281/6)
5*(1x + 4y = 247/18)
5x + 6y = 281/6
5x + 20y = 1235/18
Subtract equations
-14y = -196/9
y = -196/9/-14
y = 14/9

Substitute y
5x + 6(14/9) = 281/6
5x = 75/2
x = 75/2/5
x = 15/2


Input: Determine x in x^2 - 26/5x - 24/5 = 0

Output:
x^2 - 26/5x - 24/5 = 0
(x - 6)(x - -4/5) = 0
x - 6 = 0  or  x - -4/5 = 0
x = 6
x = -4/5


Input: Find the solution to 1x - 18/7 = 0

Output:
1x - 18/7 = 0
1x = 18/7
x = 18/7 / 1
x = 18/7


Input:
Solve the equations:
9x + 9y = 63/2
10x + 8y = 31

Output:
9x + 9y = 63/2
10x + 8y = 31

Using elimination
10*(9x + 9y = 63/2)
9*(10x + 8y = 31)
90x + 90y = 315
90x + 72y = 279
Subtract equations
18y = 36
y = 36/18
y = 2

Substitute y
9x + 9(2) = 63/2
9x = 27/2
x = 27/2/9
x = 3/2


Input: Solve the equation x^3 + 233/168x^2 - 10/21x - 25/42 = 0

Output:
x^3 + 233/168x^2 - 10/21x - 25/42 = 0
(x - -10/7)(x - -5/8)(x - 2/3) = 0
x - -10/7 = 0
x - -5/8 = 0
x - 2/3 = 0
x = -10/7
x = -5/8
x = 2/3


Input: Find x in 7x - 49/6 = 0

Output:
7x - 49/6 = 0
7x = 49/6
x = 49/6 / 7
x = 7/6


Input: Find x in x^3 - 59/10x^2 + 49/18x + 8/5 = 0

Output:
x^3 - 59/10x^2 + 49/18x + 8/5 = 0
(x - -1/3)(x - 9/10)(x - 16/3) = 0
x - -1/3 = 0
x - 9/10 = 0
x - 16/3 = 0
x = -1/3
x = 9/10
x = 16/3


Input:
Solve simultaneously:
5x + 8y = -88
10x + 5y = -110

Output:
5x + 8y = -88
10x + 5y = -110

Using elimination
10*(5x + 8y = -88)
5*(10x + 5y = -110)
50x + 80y = -880
50x + 25y = -550
Subtract equations
55y = -330
y = -330/55
y = -6

Substitute y
5x + 8(-6) = -88
5x = -40
x = -40/5
x = -8


Input:
Solve the system:
9x + 5y = -1697/36
1x + 5y = -473/36

Output:
9x + 5y = -1697/36
1x + 5y = -473/36

Using elimination
1*(9x + 5y = -1697/36)
9*(1x + 5y = -473/36)
9x + 5y = -1697/36
9x + 45y = -473/4
Subtract equations
-40y = 640/9
y = 640/9/-40
y = -16/9

Substitute y
9x + 5(-16/9) = -1697/36
9x = -153/4
x = -153/4/9
x = -17/4


Input:
Solve simultaneously:
3x + 7y = 88/5
1x + 7y = 56/5

Output:
3x + 7y = 88/5
1x + 7y = 56/5

Using elimination
1*(3x + 7y = 88/5)
3*(1x + 7y = 56/5)
3x + 7y = 88/5
3x + 21y = 168/5
Subtract equations
-14y = -16
y = -16/-14
y = 8/7

Substitute y
3x + 7(8/7) = 88/5
3x = 48/5
x = 48/5/3
x = 16/5


Input: Determine x in 8x + 16 = 0

Output:
8x + 16 = 0
8x = -16
x = -16 / 8
x = -2


Input:
Solve the system:
10x + 3y = -49/2
9x + 5y = -191/12

Output:
10x + 3y = -49/2
9x + 5y = -191/12

Using elimination
9*(10x + 3y = -49/2)
10*(9x + 5y = -191/12)
90x + 27y = -441/2
90x + 50y = -955/6
Subtract equations
-23y = -184/3
y = -184/3/-23
y = 8/3

Substitute y
10x + 3(8/3) = -49/2
10x = -65/2
x = -65/2/10
x = -13/4


Input: Determine x in x^2 - 2/5x - 33/20 = 0

Output:
x^2 - 2/5x - 33/20 = 0
(x - -11/10)(x - 3/2) = 0
x - -11/10 = 0  or  x - 3/2 = 0
x = -11/10
x = 3/2


Input: What value of x satisfies x^3 + 21/8x^2 - 27/4x - 5 = 0

Output:
x^3 + 21/8x^2 - 27/4x - 5 = 0
(x - -5/8)(x - -4)(x - 2) = 0
x - -5/8 = 0
x - -4 = 0
x - 2 = 0
x = -5/8
x = -4
x = 2


Input: Solve the equation 4x - 28 = 0

Output:
4x - 28 = 0
4x = 28
x = 28 / 4
x = 7


Input: Solve x^3 + 73/6x^2 + 95/4x - 361/24 = 0

Output:
x^3 + 73/6x^2 + 95/4x - 361/24 = 0
(x - -19/2)(x - 1/2)(x - -19/6) = 0
x - -19/2 = 0
x - 1/2 = 0
x - -19/6 = 0
x = -19/2
x = 1/2
x = -19/6


Input:
Solve simultaneously:
7x + 3y = -153/4
10x + 7y = -131/2

Output:
7x + 3y = -153/4
10x + 7y = -131/2

Using elimination
10*(7x + 3y = -153/4)
7*(10x + 7y = -131/2)
70x + 30y = -765/2
70x + 49y = -917/2
Subtract equations
-19y = 76
y = 76/-19
y = -4

Substitute y
7x + 3(-4) = -153/4
7x = -105/4
x = -105/4/7
x = -15/4


Input: What value of x satisfies x^2 - 40/9x + 16/9 = 0

Output:
x^2 - 40/9x + 16/9 = 0
(x - 4/9)(x - 4) = 0
x - 4/9 = 0  or  x - 4 = 0
x = 4/9
x = 4


Input: Determine x in 5x + 15/4 = 0

Output:
5x + 15/4 = 0
5x = -15/4
x = -15/4 / 5
x = -3/4


Input: Compute the solution of x^2 + 31/5x - 28/5 = 0

Output:
x^2 + 31/5x - 28/5 = 0
(x - -7)(x - 4/5) = 0
x - -7 = 0  or  x - 4/5 = 0
x = -7
x = 4/5


Input: Find x for x^3 + 26/45x^2 - 1/135x - 4/135 = 0

Output:
x^3 + 26/45x^2 - 1/135x - 4/135 = 0
(x - 1/5)(x - -1/3)(x - -4/9) = 0
x - 1/5 = 0
x - -1/3 = 0
x - -4/9 = 0
x = 1/5
x = -1/3
x = -4/9


Input: Solve 1x + 1 = 0

Output:
1x + 1 = 0
1x = -1
x = -1 / 1
x = -1


Input: Solve quickly: x^3 - 16/21x^2 - 71/21x - 34/21 = 0

Output:
x^3 - 16/21x^2 - 71/21x - 34/21 = 0
(x - -1)(x - 17/7)(x - -2/3) = 0
x - -1 = 0
x - 17/7 = 0
x - -2/3 = 0
x = -1
x = 17/7
x = -2/3


Input: Find the solution to x^3 + 7/3x^2 - 58/3x + 16 = 0

Output:
x^3 + 7/3x^2 - 58/3x + 16 = 0
(x - -6)(x - 1)(x - 8/3) = 0
x - -6 = 0
x - 1 = 0
x - 8/3 = 0
x = -6
x = 1
x = 8/3


Input: Determine x in x^3 + 17/3x^2 - 103/3x - 39 = 0

Output:
x^3 + 17/3x^2 - 103/3x - 39 = 0
(x - -9)(x - 13/3)(x - -1) = 0
x - -9 = 0
x - 13/3 = 0
x - -1 = 0
x = -9
x = 13/3
x = -1


Input: Solve the equation 10x - 32 = 0

Output:
10x - 32 = 0
10x = 32
x = 32 / 10
x = 16/5


Input: Solve the equation x^2 + 4x - 32 = 0

Output:
x^2 + 4x - 32 = 0
(x - -8)(x - 4) = 0
x - -8 = 0  or  x - 4 = 0
x = -8
x = 4


Input:
Solve the equations:
6x + 7y = 68
7x + 3y = 197/6

Output:
6x + 7y = 68
7x + 3y = 197/6

Using elimination
7*(6x + 7y = 68)
6*(7x + 3y = 197/6)
42x + 49y = 476
42x + 18y = 197
Subtract equations
31y = 279
y = 279/31
y = 9

Substitute y
6x + 7(9) = 68
6x = 5
x = 5/6
x = 5/6


Input: Solve quickly: 8x + 4 = 0

Output:
8x + 4 = 0
8x = -4
x = -4 / 8
x = -1/2


Input: Find x for x^2 + 118/15x + 8 = 0

Output:
x^2 + 118/15x + 8 = 0
(x - -6/5)(x - -20/3) = 0
x - -6/5 = 0  or  x - -20/3 = 0
x = -6/5
x = -20/3


Input: Determine x in 8x - 120 = 0

Output:
8x - 120 = 0
8x = 120
x = 120 / 8
x = 15


Input:
Solve the equations:
2x + 7y = -217/6
4x + 5y = -263/6

Output:
2x + 7y = -217/6
4x + 5y = -263/6

Using elimination
4*(2x + 7y = -217/6)
2*(4x + 5y = -263/6)
8x + 28y = -434/3
8x + 10y = -263/3
Subtract equations
18y = -57
y = -57/18
y = -19/6

Substitute y
2x + 7(-19/6) = -217/6
2x = -14
x = -14/2
x = -7


Input:
Solve simultaneously:
10x + 6y = -16/7
2x + 3y = 22/7

Output:
10x + 6y = -16/7
2x + 3y = 22/7

Using elimination
2*(10x + 6y = -16/7)
10*(2x + 3y = 22/7)
20x + 12y = -32/7
20x + 30y = 220/7
Subtract equations
-18y = -36
y = -36/-18
y = 2

Substitute y
10x + 6(2) = -16/7
10x = -100/7
x = -100/7/10
x = -10/7


Input: Solve 2x - 11/4 = 0

Output:
2x - 11/4 = 0
2x = 11/4
x = 11/4 / 2
x = 11/8


Input:
Find x and y such that
6x + 10y = -61/4
4x + 4y = -15/2

Output:
6x + 10y = -61/4
4x + 4y = -15/2

Using elimination
4*(6x + 10y = -61/4)
6*(4x + 4y = -15/2)
24x + 40y = -61
24x + 24y = -45
Subtract equations
16y = -16
y = -16/16
y = -1

Substitute y
6x + 10(-1) = -61/4
6x = -21/4
x = -21/4/6
x = -7/8


Input: Compute the solution of 6x - 19 = 0

Output:
6x - 19 = 0
6x = 19
x = 19 / 6
x = 19/6


Input: What value of x satisfies 3x - 9/7 = 0

Output:
3x - 9/7 = 0
3x = 9/7
x = 9/7 / 3
x = 3/7


Input: Find the solution to x^2 - 14/9x + 16/27 = 0

Output:
x^2 - 14/9x + 16/27 = 0
(x - 8/9)(x - 2/3) = 0
x - 8/9 = 0  or  x - 2/3 = 0
x = 8/9
x = 2/3


Input: Find x in x^3 + 12x^2 + 29x + 18 = 0

Output:
x^3 + 12x^2 + 29x + 18 = 0
(x - -9)(x - -2)(x - -1) = 0
x - -9 = 0
x - -2 = 0
x - -1 = 0
x = -9
x = -2
x = -1


Input: Compute the solution of x^3 + 122/15x^2 + 19/5x - 722/15 = 0

Output:
x^3 + 122/15x^2 + 19/5x - 722/15 = 0
(x - 2)(x - -19/5)(x - -19/3) = 0
x - 2 = 0
x - -19/5 = 0
x - -19/3 = 0
x = 2
x = -19/5
x = -19/3


Input: Determine x in 4x - 22 = 0

Output:
4x - 22 = 0
4x = 22
x = 22 / 4
x = 11/2


Input:
Solve simultaneously:
6x + 4y = 67/10
9x + 10y = 131/20

Output:
6x + 4y = 67/10
9x + 10y = 131/20

Using elimination
9*(6x + 4y = 67/10)
6*(9x + 10y = 131/20)
54x + 36y = 603/10
54x + 60y = 393/10
Subtract equations
-24y = 21
y = 21/-24
y = -7/8

Substitute y
6x + 4(-7/8) = 67/10
6x = 51/5
x = 51/5/6
x = 17/10


Input: Solve quickly: x^2 - 23/3x + 76/9 = 0

Output:
x^2 - 23/3x + 76/9 = 0
(x - 19/3)(x - 4/3) = 0
x - 19/3 = 0  or  x - 4/3 = 0
x = 19/3
x = 4/3


Input:
Solve the equations:
10x + 2y = -10
9x + 1y = -43/3

Output:
10x + 2y = -10
9x + 1y = -43/3

Using elimination
9*(10x + 2y = -10)
10*(9x + 1y = -43/3)
90x + 18y = -90
90x + 10y = -430/3
Subtract equations
8y = 160/3
y = 160/3/8
y = 20/3

Substitute y
10x + 2(20/3) = -10
10x = -70/3
x = -70/3/10
x = -7/3


Input: Find x for x^2 + 7/2x + 3 = 0

Output:
x^2 + 7/2x + 3 = 0
(x - -3/2)(x - -2) = 0
x - -3/2 = 0  or  x - -2 = 0
x = -3/2
x = -2


Input: Compute the solution of x^2 + 22/5x - 9/20 = 0

Output:
x^2 + 22/5x - 9/20 = 0
(x - 1/10)(x - -9/2) = 0
x - 1/10 = 0  or  x - -9/2 = 0
x = 1/10
x = -9/2


Input: Solve quickly: x^2 + 323/72x + 361/72 = 0

Output:
x^2 + 323/72x + 361/72 = 0
(x - -19/9)(x - -19/8) = 0
x - -19/9 = 0  or  x - -19/8 = 0
x = -19/9
x = -19/8


Input: Find x for 4x + 14/5 = 0

Output:
4x + 14/5 = 0
4x = -14/5
x = -14/5 / 4
x = -7/10


Input: Find x for x^2 + 14/5x - 19/5 = 0

Output:
x^2 + 14/5x - 19/5 = 0
(x - 1)(x - -19/5) = 0
x - 1 = 0  or  x - -19/5 = 0
x = 1
x = -19/5


Input: Determine x in 8x - 24 = 0

Output:
8x - 24 = 0
8x = 24
x = 24 / 8
x = 3


Input: What value of x satisfies x^3 - 127/10x^2 + 88/5x + 121/10 = 0

Output:
x^3 - 127/10x^2 + 88/5x + 121/10 = 0
(x - 11/5)(x - 11)(x - -1/2) = 0
x - 11/5 = 0
x - 11 = 0
x - -1/2 = 0
x = 11/5
x = 11
x = -1/2


Input: Compute the solution of x^3 + 7/3x^2 - 245/12x + 19/2 = 0

Output:
x^3 + 7/3x^2 - 245/12x + 19/2 = 0
(x - 19/6)(x - -6)(x - 1/2) = 0
x - 19/6 = 0
x - -6 = 0
x - 1/2 = 0
x = 19/6
x = -6
x = 1/2


Input: Determine x in x^3 + 133/40x^2 - 281/80x - 13/4 = 0

Output:
x^3 + 133/40x^2 - 281/80x - 13/4 = 0
(x - 13/10)(x - -5/8)(x - -4) = 0
x - 13/10 = 0
x - -5/8 = 0
x - -4 = 0
x = 13/10
x = -5/8
x = -4


Input: Find x for 1x + 7/9 = 0

Output:
1x + 7/9 = 0
1x = -7/9
x = -7/9 / 1
x = -7/9


Input:
Solve the system:
4x + 6y = -106
2x + 6y = -98

Output:
4x + 6y = -106
2x + 6y = -98

Using elimination
2*(4x + 6y = -106)
4*(2x + 6y = -98)
8x + 12y = -212
8x + 24y = -392
Subtract equations
-12y = 180
y = 180/-12
y = -15

Substitute y
4x + 6(-15) = -106
4x = -16
x = -16/4
x = -4


Input: Compute the solution of x^3 + 481/280x^2 - 97/56x - 57/140 = 0

Output:
x^3 + 481/280x^2 - 97/56x - 57/140 = 0
(x - -19/8)(x - -1/5)(x - 6/7) = 0
x - -19/8 = 0
x - -1/5 = 0
x - 6/7 = 0
x = -19/8
x = -1/5
x = 6/7


Input: Find x for x^2 + 2/3x - 133/3 = 0

Output:
x^2 + 2/3x - 133/3 = 0
(x - 19/3)(x - -7) = 0
x - 19/3 = 0  or  x - -7 = 0
x = 19/3
x = -7


Input: Determine x in x^3 + 23/5x^2 - 101/5x - 119/5 = 0

Output:
x^3 + 23/5x^2 - 101/5x - 119/5 = 0
(x - -7)(x - 17/5)(x - -1) = 0
x - -7 = 0
x - 17/5 = 0
x - -1 = 0
x = -7
x = 17/5
x = -1


Input:
Find x and y such that
6x + 10y = 668/21
8x + 4y = 1076/63

Output:
6x + 10y = 668/21
8x + 4y = 1076/63

Using elimination
8*(6x + 10y = 668/21)
6*(8x + 4y = 1076/63)
48x + 80y = 5344/21
48x + 24y = 2152/21
Subtract equations
56y = 152
y = 152/56
y = 19/7

Substitute y
6x + 10(19/7) = 668/21
6x = 14/3
x = 14/3/6
x = 7/9


Input: Find x in x^3 + 29/28x^2 - 15/14x - 27/28 = 0

Output:
x^3 + 29/28x^2 - 15/14x - 27/28 = 0
(x - -9/7)(x - 1)(x - -3/4) = 0
x - -9/7 = 0
x - 1 = 0
x - -3/4 = 0
x = -9/7
x = 1
x = -3/4


Input: Solve x^2 + 7/8x - 9/4 = 0

Output:
x^2 + 7/8x - 9/4 = 0
(x - 9/8)(x - -2) = 0
x - 9/8 = 0  or  x - -2 = 0
x = 9/8
x = -2


Input: Solve the equation 3x + 24/5 = 0

Output:
3x + 24/5 = 0
3x = -24/5
x = -24/5 / 3
x = -8/5


Input: Determine x in x^3 - 7/120x^2 - 49/120x + 1/20 = 0

Output:
x^3 - 7/120x^2 - 49/120x + 1/20 = 0
(x - 1/8)(x - -2/3)(x - 3/5) = 0
x - 1/8 = 0
x - -2/3 = 0
x - 3/5 = 0
x = 1/8
x = -2/3
x = 3/5


Input: Find x in x^2 - 23/10x + 9/10 = 0

Output:
x^2 - 23/10x + 9/10 = 0
(x - 1/2)(x - 9/5) = 0
x - 1/2 = 0  or  x - 9/5 = 0
x = 1/2
x = 9/5


Input: Solve the equation x^2 + 22/5x + 21/5 = 0

Output:
x^2 + 22/5x + 21/5 = 0
(x - -3)(x - -7/5) = 0
x - -3 = 0  or  x - -7/5 = 0
x = -3
x = -7/5


Input: Find the solution to 9x - 27/4 = 0

Output:
9x - 27/4 = 0
9x = 27/4
x = 27/4 / 9
x = 3/4


Input: Compute the solution of x^2 - 29/4x + 51/4 = 0

Output:
x^2 - 29/4x + 51/4 = 0
(x - 3)(x - 17/4) = 0
x - 3 = 0  or  x - 17/4 = 0
x = 3
x = 17/4


Input: Solve 6x + 24/7 = 0

Output:
6x + 24/7 = 0
6x = -24/7
x = -24/7 / 6
x = -4/7


Input:
Solve simultaneously:
3x + 9y = 197/10
8x + 5y = 167/6

Output:
3x + 9y = 197/10
8x + 5y = 167/6

Using elimination
8*(3x + 9y = 197/10)
3*(8x + 5y = 167/6)
24x + 72y = 788/5
24x + 15y = 167/2
Subtract equations
57y = 741/10
y = 741/10/57
y = 13/10

Substitute y
3x + 9(13/10) = 197/10
3x = 8
x = 8/3
x = 8/3


Input: Find x in x^3 - 41/6x^2 - 185/6x + 425/3 = 0

Output:
x^3 - 41/6x^2 - 185/6x + 425/3 = 0
(x - -5)(x - 10/3)(x - 17/2) = 0
x - -5 = 0
x - 10/3 = 0
x - 17/2 = 0
x = -5
x = 10/3
x = 17/2


Input: Solve quickly: 8x + 36 = 0

Output:
8x + 36 = 0
8x = -36
x = -36 / 8
x = -9/2


Input: Find the solution to x^3 - 23/10x^2 - 1/2x  = 0

Output:
x^3 - 23/10x^2 - 1/2x  = 0
(x - 0)(x - 5/2)(x - -1/5) = 0
x - 0 = 0
x - 5/2 = 0
x - -1/5 = 0
x = 0
x = 5/2
x = -1/5


Input: Determine x in 1x + 19/7 = 0

Output:
1x + 19/7 = 0
1x = -19/7
x = -19/7 / 1
x = -19/7


Input: Solve x^2 - 2x + 1 = 0

Output:
x^2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
x - 1 = 0  or  x - 1 = 0
x = 1
x = 1


Input: Find x in x^2 - 157/40x + 63/20 = 0

Output:
x^2 - 157/40x + 63/20 = 0
(x - 9/8)(x - 14/5) = 0
x - 9/8 = 0  or  x - 14/5 = 0
x = 9/8
x = 14/5


Input: What value of x satisfies 1x + 7/4 = 0

Output:
1x + 7/4 = 0
1x = -7/4
x = -7/4 / 1
x = -7/4


Input: Determine x in 6x - 18/5 = 0

Output:
6x - 18/5 = 0
6x = 18/5
x = 18/5 / 6
x = 3/5


Input: Solve the equation x^3 + 7/10x^2 - 173/80x - 91/160 = 0

Output:
x^3 + 7/10x^2 - 173/80x - 91/160 = 0
(x - -7/4)(x - -1/4)(x - 13/10) = 0
x - -7/4 = 0
x - -1/4 = 0
x - 13/10 = 0
x = -7/4
x = -1/4
x = 13/10


Input: Compute the solution of 1x - 2 = 0

Output:
1x - 2 = 0
1x = 2
x = 2 / 1
x = 2


Input:
Find x and y such that
6x + 5y = 87/5
10x + 7y = 137/5

Output:
6x + 5y = 87/5
10x + 7y = 137/5

Using elimination
10*(6x + 5y = 87/5)
6*(10x + 7y = 137/5)
60x + 50y = 174
60x + 42y = 822/5
Subtract equations
8y = 48/5
y = 48/5/8
y = 6/5

Substitute y
6x + 5(6/5) = 87/5
6x = 57/5
x = 57/5/6
x = 19/10


Input: Solve the equation 4x + 8/7 = 0

Output:
4x + 8/7 = 0
4x = -8/7
x = -8/7 / 4
x = -2/7


Input: Find x for x^3 - 59/56x^2 - 211/98x + 195/98 = 0

Output:
x^3 - 59/56x^2 - 211/98x + 195/98 = 0
(x - 6/7)(x - 13/8)(x - -10/7) = 0
x - 6/7 = 0
x - 13/8 = 0
x - -10/7 = 0
x = 6/7
x = 13/8
x = -10/7


Input:
Solve simultaneously:
1x + 7y = 31/28
7x + 8y = 18

Output:
1x + 7y = 31/28
7x + 8y = 18

Using elimination
7*(1x + 7y = 31/28)
1*(7x + 8y = 18)
7x + 49y = 31/4
7x + 8y = 18
Subtract equations
41y = -41/4
y = -41/4/41
y = -1/4

Substitute y
1x + 7(-1/4) = 31/28
1x = 20/7
x = 20/7/1
x = 20/7


Input: Find x for 1x - 19/5 = 0

Output:
1x - 19/5 = 0
1x = 19/5
x = 19/5 / 1
x = 19/5


Input: Solve the equation x^3 - 18/5x^2 + 253/180x - 19/180 = 0

Output:
x^3 - 18/5x^2 + 253/180x - 19/180 = 0
(x - 1/3)(x - 19/6)(x - 1/10) = 0
x - 1/3 = 0
x - 19/6 = 0
x - 1/10 = 0
x = 1/3
x = 19/6
x = 1/10


Input: Solve 9x + 42 = 0

Output:
9x + 42 = 0
9x = -42
x = -42 / 9
x = -14/3


Input: Find the solution to 3x - 54/7 = 0

Output:
3x - 54/7 = 0
3x = 54/7
x = 54/7 / 3
x = 18/7


Input:
Solve the system:
7x + 8y = -115/3
5x + 3y = -91/6

Output:
7x + 8y = -115/3
5x + 3y = -91/6

Using elimination
5*(7x + 8y = -115/3)
7*(5x + 3y = -91/6)
35x + 40y = -575/3
35x + 21y = -637/6
Subtract equations
19y = -171/2
y = -171/2/19
y = -9/2

Substitute y
7x + 8(-9/2) = -115/3
7x = -7/3
x = -7/3/7
x = -1/3


Input:
Find x and y such that
3x + 10y = 17
9x + 1y = -7

Output:
3x + 10y = 17
9x + 1y = -7

Using elimination
9*(3x + 10y = 17)
3*(9x + 1y = -7)
27x + 90y = 153
27x + 3y = -21
Subtract equations
87y = 174
y = 174/87
y = 2

Substitute y
3x + 10(2) = 17
3x = -3
x = -3/3
x = -1


Input: Determine x in x^2 - 2/3x - 16/3 = 0

Output:
x^2 - 2/3x - 16/3 = 0
(x - 8/3)(x - -2) = 0
x - 8/3 = 0  or  x - -2 = 0
x = 8/3
x = -2


Input: Find the solution to x^3 - 67/9x^2 + 428/27x - 224/27 = 0

Output:
x^3 - 67/9x^2 + 428/27x - 224/27 = 0
(x - 4)(x - 7/9)(x - 8/3) = 0
x - 4 = 0
x - 7/9 = 0
x - 8/3 = 0
x = 4
x = 7/9
x = 8/3


Input: Determine x in x^2 - 1/4x - 5/4 = 0

Output:
x^2 - 1/4x - 5/4 = 0
(x - -1)(x - 5/4) = 0
x - -1 = 0  or  x - 5/4 = 0
x = -1
x = 5/4


Input:
Solve the system:
7x + 7y = -763/12
2x + 6y = -79/2

Output:
7x + 7y = -763/12
2x + 6y = -79/2

Using elimination
2*(7x + 7y = -763/12)
7*(2x + 6y = -79/2)
14x + 14y = -763/6
14x + 42y = -553/2
Subtract equations
-28y = 448/3
y = 448/3/-28
y = -16/3

Substitute y
7x + 7(-16/3) = -763/12
7x = -105/4
x = -105/4/7
x = -15/4


Input:
Solve the equations:
5x + 3y = 191/28
8x + 5y = 293/28

Output:
5x + 3y = 191/28
8x + 5y = 293/28

Using elimination
8*(5x + 3y = 191/28)
5*(8x + 5y = 293/28)
40x + 24y = 382/7
40x + 25y = 1465/28
Subtract equations
-1y = 9/4
y = 9/4/-1
y = -9/4

Substitute y
5x + 3(-9/4) = 191/28
5x = 95/7
x = 95/7/5
x = 19/7


Input:
Solve the equations:
5x + 5y = -650/21
3x + 4y = -481/21

Output:
5x + 5y = -650/21
3x + 4y = -481/21

Using elimination
3*(5x + 5y = -650/21)
5*(3x + 4y = -481/21)
15x + 15y = -650/7
15x + 20y = -2405/21
Subtract equations
-5y = 65/3
y = 65/3/-5
y = -13/3

Substitute y
5x + 5(-13/3) = -650/21
5x = -65/7
x = -65/7/5
x = -13/7


Input: Solve the equation 9x + 126 = 0

Output:
9x + 126 = 0
9x = -126
x = -126 / 9
x = -14


Input:
Solve simultaneously:
9x + 2y = 15/8
9x + 3y = -9/8

Output:
9x + 2y = 15/8
9x + 3y = -9/8

Using elimination
9*(9x + 2y = 15/8)
9*(9x + 3y = -9/8)
81x + 18y = 135/8
81x + 27y = -81/8
Subtract equations
-9y = 27
y = 27/-9
y = -3

Substitute y
9x + 2(-3) = 15/8
9x = 63/8
x = 63/8/9
x = 7/8


Input: Solve 4x + 56/5 = 0

Output:
4x + 56/5 = 0
4x = -56/5
x = -56/5 / 4
x = -14/5


Input:
Solve the system:
6x + 4y = 23/2
9x + 1y = 19/4

Output:
6x + 4y = 23/2
9x + 1y = 19/4

Using elimination
9*(6x + 4y = 23/2)
6*(9x + 1y = 19/4)
54x + 36y = 207/2
54x + 6y = 57/2
Subtract equations
30y = 75
y = 75/30
y = 5/2

Substitute y
6x + 4(5/2) = 23/2
6x = 3/2
x = 3/2/6
x = 1/4


Input:
Solve the system:
4x + 3y = -3/2
1x + 10y = -5

Output:
4x + 3y = -3/2
1x + 10y = -5

Using elimination
1*(4x + 3y = -3/2)
4*(1x + 10y = -5)
4x + 3y = -3/2
4x + 40y = -20
Subtract equations
-37y = 37/2
y = 37/2/-37
y = -1/2

Substitute y
4x + 3(-1/2) = -3/2
4x = 0
x = 0/4
x = 0


Input: Solve 5x - 100/3 = 0

Output:
5x - 100/3 = 0
5x = 100/3
x = 100/3 / 5
x = 20/3


Input:
Solve the system:
6x + 4y = 16/3
3x + 9y = 22/3

Output:
6x + 4y = 16/3
3x + 9y = 22/3

Using elimination
3*(6x + 4y = 16/3)
6*(3x + 9y = 22/3)
18x + 12y = 16
18x + 54y = 44
Subtract equations
-42y = -28
y = -28/-42
y = 2/3

Substitute y
6x + 4(2/3) = 16/3
6x = 8/3
x = 8/3/6
x = 4/9


Input: What value of x satisfies x^2 + 4x + 3 = 0

Output:
x^2 + 4x + 3 = 0
(x - -3)(x - -1) = 0
x - -3 = 0  or  x - -1 = 0
x = -3
x = -1


Input: Solve quickly: x^2 + 42/5x + 49/5 = 0

Output:
x^2 + 42/5x + 49/5 = 0
(x - -7/5)(x - -7) = 0
x - -7/5 = 0  or  x - -7 = 0
x = -7/5
x = -7


Input: Solve the equation x^3 - 95/18x^2 + 37/54x + 38/3 = 0

Output:
x^3 - 95/18x^2 + 37/54x + 38/3 = 0
(x - -4/3)(x - 9/2)(x - 19/9) = 0
x - -4/3 = 0
x - 9/2 = 0
x - 19/9 = 0
x = -4/3
x = 9/2
x = 19/9


Input: Solve the equation 9x - 21 = 0

Output:
9x - 21 = 0
9x = 21
x = 21 / 9
x = 7/3


Input:
Solve the equations:
8x + 5y = -263/12
6x + 3y = -59/4

Output:
8x + 5y = -263/12
6x + 3y = -59/4

Using elimination
6*(8x + 5y = -263/12)
8*(6x + 3y = -59/4)
48x + 30y = -263/2
48x + 24y = -118
Subtract equations
6y = -27/2
y = -27/2/6
y = -9/4

Substitute y
8x + 5(-9/4) = -263/12
8x = -32/3
x = -32/3/8
x = -4/3


Input: Find x for x^3 - 202/15x^2 - 341/15x - 4 = 0

Output:
x^3 - 202/15x^2 - 341/15x - 4 = 0
(x - -4/3)(x - 15)(x - -1/5) = 0
x - -4/3 = 0
x - 15 = 0
x - -1/5 = 0
x = -4/3
x = 15
x = -1/5


Input: Solve quickly: x^3 - 16/5x^2 - 5x + 36/5 = 0

Output:
x^3 - 16/5x^2 - 5x + 36/5 = 0
(x - 4)(x - -9/5)(x - 1) = 0
x - 4 = 0
x - -9/5 = 0
x - 1 = 0
x = 4
x = -9/5
x = 1


Input: Solve x^2  - 36 = 0

Output:
x^2  - 36 = 0
(x - -6)(x - 6) = 0
x - -6 = 0  or  x - 6 = 0
x = -6
x = 6


Input: Find x in x^3 - 96/5x^2 + 907/20x + 468/5 = 0

Output:
x^3 - 96/5x^2 + 907/20x + 468/5 = 0
(x - 16)(x - 9/2)(x - -13/10) = 0
x - 16 = 0
x - 9/2 = 0
x - -13/10 = 0
x = 16
x = 9/2
x = -13/10


Input: Find the solution to 3x - 27/7 = 0

Output:
3x - 27/7 = 0
3x = 27/7
x = 27/7 / 3
x = 9/7


Input: What value of x satisfies x^2 + 7/9x + 4/27 = 0

Output:
x^2 + 7/9x + 4/27 = 0
(x - -4/9)(x - -1/3) = 0
x - -4/9 = 0  or  x - -1/3 = 0
x = -4/9
x = -1/3


Input: Solve quickly: 6x - 18/5 = 0

Output:
6x - 18/5 = 0
6x = 18/5
x = 18/5 / 6
x = 3/5


Input: Solve quickly: 10x - 10/3 = 0

Output:
10x - 10/3 = 0
10x = 10/3
x = 10/3 / 10
x = 1/3


Input: Determine x in x^2 + 59/10x + 17/2 = 0

Output:
x^2 + 59/10x + 17/2 = 0
(x - -17/5)(x - -5/2) = 0
x - -17/5 = 0  or  x - -5/2 = 0
x = -17/5
x = -5/2


Input: Solve the equation x^3 - 7/6x^2 - 28/3x + 19/2 = 0

Output:
x^3 - 7/6x^2 - 28/3x + 19/2 = 0
(x - 19/6)(x - 1)(x - -3) = 0
x - 19/6 = 0
x - 1 = 0
x - -3 = 0
x = 19/6
x = 1
x = -3


Input: Determine x in 8x + 8/3 = 0

Output:
8x + 8/3 = 0
8x = -8/3
x = -8/3 / 8
x = -1/3


Input: Solve the equation x^2 - 36/5x - 28 = 0

Output:
x^2 - 36/5x - 28 = 0
(x - 10)(x - -14/5) = 0
x - 10 = 0  or  x - -14/5 = 0
x = 10
x = -14/5


Input: Find x in x^3 - 65/14x^2 + 39/14x + 45/7 = 0

Output:
x^3 - 65/14x^2 + 39/14x + 45/7 = 0
(x - 3)(x - 5/2)(x - -6/7) = 0
x - 3 = 0
x - 5/2 = 0
x - -6/7 = 0
x = 3
x = 5/2
x = -6/7


Input: Determine x in x^3 - 41/9x^2 + 523/81x - 665/243 = 0

Output:
x^3 - 41/9x^2 + 523/81x - 665/243 = 0
(x - 7/9)(x - 5/3)(x - 19/9) = 0
x - 7/9 = 0
x - 5/3 = 0
x - 19/9 = 0
x = 7/9
x = 5/3
x = 19/9


Input:
Solve the equations:
7x + 2y = 34/3
6x + 5y = 16/3

Output:
7x + 2y = 34/3
6x + 5y = 16/3

Using elimination
6*(7x + 2y = 34/3)
7*(6x + 5y = 16/3)
42x + 12y = 68
42x + 35y = 112/3
Subtract equations
-23y = 92/3
y = 92/3/-23
y = -4/3

Substitute y
7x + 2(-4/3) = 34/3
7x = 14
x = 14/7
x = 2


Input: Find x for 1x + 17/5 = 0

Output:
1x + 17/5 = 0
1x = -17/5
x = -17/5 / 1
x = -17/5


Input:
Solve simultaneously:
4x + 8y = -140
6x + 8y = -130

Output:
4x + 8y = -140
6x + 8y = -130

Using elimination
6*(4x + 8y = -140)
4*(6x + 8y = -130)
24x + 48y = -840
24x + 32y = -520
Subtract equations
16y = -320
y = -320/16
y = -20

Substitute y
4x + 8(-20) = -140
4x = 20
x = 20/4
x = 5


Input:
Find x and y such that
3x + 10y = -20
8x + 5y = -85/2

Output:
3x + 10y = -20
8x + 5y = -85/2

Using elimination
8*(3x + 10y = -20)
3*(8x + 5y = -85/2)
24x + 80y = -160
24x + 15y = -255/2
Subtract equations
65y = -65/2
y = -65/2/65
y = -1/2

Substitute y
3x + 10(-1/2) = -20
3x = -15
x = -15/3
x = -5


Input:
Solve the equations:
5x + 6y = -1
3x + 4y = -1/5

Output:
5x + 6y = -1
3x + 4y = -1/5

Using elimination
3*(5x + 6y = -1)
5*(3x + 4y = -1/5)
15x + 18y = -3
15x + 20y = -1
Subtract equations
-2y = -2
y = -2/-2
y = 1

Substitute y
5x + 6(1) = -1
5x = -7
x = -7/5
x = -7/5


Input:
Solve the equations:
9x + 8y = 547/20
5x + 5y = 59/4

Output:
9x + 8y = 547/20
5x + 5y = 59/4

Using elimination
5*(9x + 8y = 547/20)
9*(5x + 5y = 59/4)
45x + 40y = 547/4
45x + 45y = 531/4
Subtract equations
-5y = 4
y = 4/-5
y = -4/5

Substitute y
9x + 8(-4/5) = 547/20
9x = 135/4
x = 135/4/9
x = 15/4


Input: Find x in x^3 - 43/14x^2 - 45/7x  = 0

Output:
x^3 - 43/14x^2 - 45/7x  = 0
(x - 9/2)(x - 0)(x - -10/7) = 0
x - 9/2 = 0
x - 0 = 0
x - -10/7 = 0
x = 9/2
x = 0
x = -10/7


Input:
Find x and y such that
2x + 7y = -50/3
3x + 1y = 13

Output:
2x + 7y = -50/3
3x + 1y = 13

Using elimination
3*(2x + 7y = -50/3)
2*(3x + 1y = 13)
6x + 21y = -50
6x + 2y = 26
Subtract equations
19y = -76
y = -76/19
y = -4

Substitute y
2x + 7(-4) = -50/3
2x = 34/3
x = 34/3/2
x = 17/3


Input: Find x for x^3 - 115/14x^2 - 159/14x + 270/7 = 0

Output:
x^3 - 115/14x^2 - 159/14x + 270/7 = 0
(x - 9)(x - 12/7)(x - -5/2) = 0
x - 9 = 0
x - 12/7 = 0
x - -5/2 = 0
x = 9
x = 12/7
x = -5/2


Input:
Solve the system:
9x + 8y = 40
5x + 10y = 100/3

Output:
9x + 8y = 40
5x + 10y = 100/3

Using elimination
5*(9x + 8y = 40)
9*(5x + 10y = 100/3)
45x + 40y = 200
45x + 90y = 300
Subtract equations
-50y = -100
y = -100/-50
y = 2

Substitute y
9x + 8(2) = 40
9x = 24
x = 24/9
x = 8/3


Input: Find x in x^2 + 16/5x - 16/5 = 0

Output:
x^2 + 16/5x - 16/5 = 0
(x - 4/5)(x - -4) = 0
x - 4/5 = 0  or  x - -4 = 0
x = 4/5
x = -4


Input: Find the solution to x^2 + 11/30x - 34/15 = 0

Output:
x^2 + 11/30x - 34/15 = 0
(x - -17/10)(x - 4/3) = 0
x - -17/10 = 0  or  x - 4/3 = 0
x = -17/10
x = 4/3


Input:
Solve simultaneously:
2x + 2y = -43/14
7x + 9y = -77/4

Output:
2x + 2y = -43/14
7x + 9y = -77/4

Using elimination
7*(2x + 2y = -43/14)
2*(7x + 9y = -77/4)
14x + 14y = -43/2
14x + 18y = -77/2
Subtract equations
-4y = 17
y = 17/-4
y = -17/4

Substitute y
2x + 2(-17/4) = -43/14
2x = 38/7
x = 38/7/2
x = 19/7


Input:
Solve simultaneously:
3x + 9y = 43/2
6x + 1y = 35/2

Output:
3x + 9y = 43/2
6x + 1y = 35/2

Using elimination
6*(3x + 9y = 43/2)
3*(6x + 1y = 35/2)
18x + 54y = 129
18x + 3y = 105/2
Subtract equations
51y = 153/2
y = 153/2/51
y = 3/2

Substitute y
3x + 9(3/2) = 43/2
3x = 8
x = 8/3
x = 8/3


Input: Solve the equation x^3 + 27/2x^2 - 537/50x - 1309/25 = 0

Output:
x^3 + 27/2x^2 - 537/50x - 1309/25 = 0
(x - -17/10)(x - 11/5)(x - -14) = 0
x - -17/10 = 0
x - 11/5 = 0
x - -14 = 0
x = -17/10
x = 11/5
x = -14


Input: Solve the equation 9x - 117/4 = 0

Output:
9x - 117/4 = 0
9x = 117/4
x = 117/4 / 9
x = 13/4


Input: Find x in x^2 + 5/6x - 1 = 0

Output:
x^2 + 5/6x - 1 = 0
(x - 2/3)(x - -3/2) = 0
x - 2/3 = 0  or  x - -3/2 = 0
x = 2/3
x = -3/2


Input: Find the solution to 10x - 35 = 0

Output:
10x - 35 = 0
10x = 35
x = 35 / 10
x = 7/2


Input: What value of x satisfies x^3 - 83/30x^2 + 11/5x - 8/15 = 0

Output:
x^3 - 83/30x^2 + 11/5x - 8/15 = 0
(x - 1/2)(x - 8/5)(x - 2/3) = 0
x - 1/2 = 0
x - 8/5 = 0
x - 2/3 = 0
x = 1/2
x = 8/5
x = 2/3


Input: Solve quickly: 5x + 5 = 0

Output:
5x + 5 = 0
5x = -5
x = -5 / 5
x = -1


Input:
Solve the system:
5x + 10y = -1
2x + 6y = -6/5

Output:
5x + 10y = -1
2x + 6y = -6/5

Using elimination
2*(5x + 10y = -1)
5*(2x + 6y = -6/5)
10x + 20y = -2
10x + 30y = -6
Subtract equations
-10y = 4
y = 4/-10
y = -2/5

Substitute y
5x + 10(-2/5) = -1
5x = 3
x = 3/5
x = 3/5


Input: Determine x in 5x - 30 = 0

Output:
5x - 30 = 0
5x = 30
x = 30 / 5
x = 6


Input: Find x in x^3 - 28/5x^2 - 1076/45x + 112 = 0

Output:
x^3 - 28/5x^2 - 1076/45x + 112 = 0
(x - 20/3)(x - 18/5)(x - -14/3) = 0
x - 20/3 = 0
x - 18/5 = 0
x - -14/3 = 0
x = 20/3
x = 18/5
x = -14/3


Input: Find x in x^3 - 4/3x^2 + 1/3x  = 0

Output:
x^3 - 4/3x^2 + 1/3x  = 0
(x - 1)(x - 1/3)(x - 0) = 0
x - 1 = 0
x - 1/3 = 0
x - 0 = 0
x = 1
x = 1/3
x = 0


Input: Compute the solution of x^3 + 443/20x^2 + 437/10x + 14 = 0

Output:
x^3 + 443/20x^2 + 437/10x + 14 = 0
(x - -7/4)(x - -2/5)(x - -20) = 0
x - -7/4 = 0
x - -2/5 = 0
x - -20 = 0
x = -7/4
x = -2/5
x = -20


Input:
Solve the equations:
10x + 7y = -89/10
7x + 6y = -24/5

Output:
10x + 7y = -89/10
7x + 6y = -24/5

Using elimination
7*(10x + 7y = -89/10)
10*(7x + 6y = -24/5)
70x + 49y = -623/10
70x + 60y = -48
Subtract equations
-11y = -143/10
y = -143/10/-11
y = 13/10

Substitute y
10x + 7(13/10) = -89/10
10x = -18
x = -18/10
x = -9/5


Input:
Solve the system:
8x + 7y = -48/5
6x + 1y = -104/5

Output:
8x + 7y = -48/5
6x + 1y = -104/5

Using elimination
6*(8x + 7y = -48/5)
8*(6x + 1y = -104/5)
48x + 42y = -288/5
48x + 8y = -832/5
Subtract equations
34y = 544/5
y = 544/5/34
y = 16/5

Substitute y
8x + 7(16/5) = -48/5
8x = -32
x = -32/8
x = -4


Input: Find x for x^2 + 19/12x + 5/12 = 0

Output:
x^2 + 19/12x + 5/12 = 0
(x - -5/4)(x - -1/3) = 0
x - -5/4 = 0  or  x - -1/3 = 0
x = -5/4
x = -1/3


Input:
Solve the system:
5x + 9y = -35
8x + 10y = -45

Output:
5x + 9y = -35
8x + 10y = -45

Using elimination
8*(5x + 9y = -35)
5*(8x + 10y = -45)
40x + 72y = -280
40x + 50y = -225
Subtract equations
22y = -55
y = -55/22
y = -5/2

Substitute y
5x + 9(-5/2) = -35
5x = -25/2
x = -25/2/5
x = -5/2


Input:
Solve the system:
8x + 8y = 32
2x + 5y = -13

Output:
8x + 8y = 32
2x + 5y = -13

Using elimination
2*(8x + 8y = 32)
8*(2x + 5y = -13)
16x + 16y = 64
16x + 40y = -104
Subtract equations
-24y = 168
y = 168/-24
y = -7

Substitute y
8x + 8(-7) = 32
8x = 88
x = 88/8
x = 11


Input:
Solve the equations:
9x + 8y = -94/5
2x + 9y = -57/5

Output:
9x + 8y = -94/5
2x + 9y = -57/5

Using elimination
2*(9x + 8y = -94/5)
9*(2x + 9y = -57/5)
18x + 16y = -188/5
18x + 81y = -513/5
Subtract equations
-65y = 65
y = 65/-65
y = -1

Substitute y
9x + 8(-1) = -94/5
9x = -54/5
x = -54/5/9
x = -6/5


Input: Find x in 1x - 1 = 0

Output:
1x - 1 = 0
1x = 1
x = 1 / 1
x = 1


Input: What value of x satisfies x^2 - 23/18x - 1/3 = 0

Output:
x^2 - 23/18x - 1/3 = 0
(x - -2/9)(x - 3/2) = 0
x - -2/9 = 0  or  x - 3/2 = 0
x = -2/9
x = 3/2


Input: Find x in x^2 + 145/24x - 25/6 = 0

Output:
x^2 + 145/24x - 25/6 = 0
(x - 5/8)(x - -20/3) = 0
x - 5/8 = 0  or  x - -20/3 = 0
x = 5/8
x = -20/3


Input: Compute the solution of x^3 - 151/10x^2 - 178/5x + 561/10 = 0

Output:
x^3 - 151/10x^2 - 178/5x + 561/10 = 0
(x - -3)(x - 11/10)(x - 17) = 0
x - -3 = 0
x - 11/10 = 0
x - 17 = 0
x = -3
x = 11/10
x = 17


Input:
Solve the equations:
5x + 7y = -197/8
7x + 9y = -263/8

Output:
5x + 7y = -197/8
7x + 9y = -263/8

Using elimination
7*(5x + 7y = -197/8)
5*(7x + 9y = -263/8)
35x + 49y = -1379/8
35x + 45y = -1315/8
Subtract equations
4y = -8
y = -8/4
y = -2

Substitute y
5x + 7(-2) = -197/8
5x = -85/8
x = -85/8/5
x = -17/8


Input: What value of x satisfies x^3 - 175/12x^2 + 127/2x - 260/3 = 0

Output:
x^3 - 175/12x^2 + 127/2x - 260/3 = 0
(x - 10/3)(x - 13/4)(x - 8) = 0
x - 10/3 = 0
x - 13/4 = 0
x - 8 = 0
x = 10/3
x = 13/4
x = 8


Input:
Solve the equations:
4x + 2y = 32/7
6x + 1y = 16/7

Output:
4x + 2y = 32/7
6x + 1y = 16/7

Using elimination
6*(4x + 2y = 32/7)
4*(6x + 1y = 16/7)
24x + 12y = 192/7
24x + 4y = 64/7
Subtract equations
8y = 128/7
y = 128/7/8
y = 16/7

Substitute y
4x + 2(16/7) = 32/7
4x = 0
x = 0/4
x = 0


Input: Compute the solution of x^3 - 87/20x^2 - 267/100x + 1463/400 = 0

Output:
x^3 - 87/20x^2 - 267/100x + 1463/400 = 0
(x - -11/10)(x - 7/10)(x - 19/4) = 0
x - -11/10 = 0
x - 7/10 = 0
x - 19/4 = 0
x = -11/10
x = 7/10
x = 19/4


Input: Find the solution to 5x - 95/8 = 0

Output:
5x - 95/8 = 0
5x = 95/8
x = 95/8 / 5
x = 19/8


Input:
Find x and y such that
4x + 8y = 8/3
8x + 4y = 16/3

Output:
4x + 8y = 8/3
8x + 4y = 16/3

Using elimination
8*(4x + 8y = 8/3)
4*(8x + 4y = 16/3)
32x + 64y = 64/3
32x + 16y = 64/3
Subtract equations
48y = 0
y = 0/48
y = 0

Substitute y
4x + 8(0) = 8/3
4x = 8/3
x = 8/3/4
x = 2/3


Input: Find x in 4x - 8/3 = 0

Output:
4x - 8/3 = 0
4x = 8/3
x = 8/3 / 4
x = 2/3


Input: Determine x in x^3 + 2/9x^2 - 71/81x - 8/81 = 0

Output:
x^3 + 2/9x^2 - 71/81x - 8/81 = 0
(x - 8/9)(x - -1)(x - -1/9) = 0
x - 8/9 = 0
x - -1 = 0
x - -1/9 = 0
x = 8/9
x = -1
x = -1/9


Input: Find x for x^3 + 11/6x^2 - 13/2x - 7/3 = 0

Output:
x^3 + 11/6x^2 - 13/2x - 7/3 = 0
(x - -1/3)(x - -7/2)(x - 2) = 0
x - -1/3 = 0
x - -7/2 = 0
x - 2 = 0
x = -1/3
x = -7/2
x = 2


Input: Solve quickly: 3x - 10/3 = 0

Output:
3x - 10/3 = 0
3x = 10/3
x = 10/3 / 3
x = 10/9


Input: Determine x in x^2 - 1/12x - 65/6 = 0

Output:
x^2 - 1/12x - 65/6 = 0
(x - -13/4)(x - 10/3) = 0
x - -13/4 = 0  or  x - 10/3 = 0
x = -13/4
x = 10/3


Input:
Find x and y such that
1x + 10y = 11/2
9x + 6y = 99/2

Output:
1x + 10y = 11/2
9x + 6y = 99/2

Using elimination
9*(1x + 10y = 11/2)
1*(9x + 6y = 99/2)
9x + 90y = 99/2
9x + 6y = 99/2
Subtract equations
84y = 0
y = 0/84
y = 0

Substitute y
1x + 10(0) = 11/2
1x = 11/2
x = 11/2/1
x = 11/2


Input: Compute the solution of 2x + 2 = 0

Output:
2x + 2 = 0
2x = -2
x = -2 / 2
x = -1


Input:
Find x and y such that
6x + 7y = -23
1x + 4y = -37/3

Output:
6x + 7y = -23
1x + 4y = -37/3

Using elimination
1*(6x + 7y = -23)
6*(1x + 4y = -37/3)
6x + 7y = -23
6x + 24y = -74
Subtract equations
-17y = 51
y = 51/-17
y = -3

Substitute y
6x + 7(-3) = -23
6x = -2
x = -2/6
x = -1/3


Input: What value of x satisfies 3x - 21/4 = 0

Output:
3x - 21/4 = 0
3x = 21/4
x = 21/4 / 3
x = 7/4


Input: Solve quickly: x^3 - 149/6x^2 + 445/3x - 1547/6 = 0

Output:
x^3 - 149/6x^2 + 445/3x - 1547/6 = 0
(x - 7/2)(x - 17)(x - 13/3) = 0
x - 7/2 = 0
x - 17 = 0
x - 13/3 = 0
x = 7/2
x = 17
x = 13/3


Input:
Find x and y such that
3x + 4y = -46
7x + 8y = -94

Output:
3x + 4y = -46
7x + 8y = -94

Using elimination
7*(3x + 4y = -46)
3*(7x + 8y = -94)
21x + 28y = -322
21x + 24y = -282
Subtract equations
4y = -40
y = -40/4
y = -10

Substitute y
3x + 4(-10) = -46
3x = -6
x = -6/3
x = -2


Input: Find x in 5x - 55/4 = 0

Output:
5x - 55/4 = 0
5x = 55/4
x = 55/4 / 5
x = 11/4


Input: Find x in x^3 + 19/5x^2 + 127/45x - 7/5 = 0

Output:
x^3 + 19/5x^2 + 127/45x - 7/5 = 0
(x - -9/5)(x - 1/3)(x - -7/3) = 0
x - -9/5 = 0
x - 1/3 = 0
x - -7/3 = 0
x = -9/5
x = 1/3
x = -7/3


Input: Determine x in x^3 - 9/35x^2 - 36/7x  = 0

Output:
x^3 - 9/35x^2 - 36/7x  = 0
(x - -15/7)(x - 0)(x - 12/5) = 0
x - -15/7 = 0
x - 0 = 0
x - 12/5 = 0
x = -15/7
x = 0
x = 12/5


Input:
Find x and y such that
8x + 7y = 148/5
9x + 3y = 147/5

Output:
8x + 7y = 148/5
9x + 3y = 147/5

Using elimination
9*(8x + 7y = 148/5)
8*(9x + 3y = 147/5)
72x + 63y = 1332/5
72x + 24y = 1176/5
Subtract equations
39y = 156/5
y = 156/5/39
y = 4/5

Substitute y
8x + 7(4/5) = 148/5
8x = 24
x = 24/8
x = 3


Input: Find x in x^2 + 51/40x - 19/16 = 0

Output:
x^2 + 51/40x - 19/16 = 0
(x - -19/10)(x - 5/8) = 0
x - -19/10 = 0  or  x - 5/8 = 0
x = -19/10
x = 5/8


Input:
Solve the system:
2x + 4y = 14
3x + 3y = 12

Output:
2x + 4y = 14
3x + 3y = 12

Using elimination
3*(2x + 4y = 14)
2*(3x + 3y = 12)
6x + 12y = 42
6x + 6y = 24
Subtract equations
6y = 18
y = 18/6
y = 3

Substitute y
2x + 4(3) = 14
2x = 2
x = 2/2
x = 1


Input: Find x in 4x - 4/9 = 0

Output:
4x - 4/9 = 0
4x = 4/9
x = 4/9 / 4
x = 1/9


Input: Determine x in 6x + 18 = 0

Output:
6x + 18 = 0
6x = -18
x = -18 / 6
x = -3


Input: Compute the solution of x^2 + 33/7x + 20/7 = 0

Output:
x^2 + 33/7x + 20/7 = 0
(x - -5/7)(x - -4) = 0
x - -5/7 = 0  or  x - -4 = 0
x = -5/7
x = -4


Input:
Find x and y such that
3x + 3y = 27/2
5x + 3y = 17/2

Output:
3x + 3y = 27/2
5x + 3y = 17/2

Using elimination
5*(3x + 3y = 27/2)
3*(5x + 3y = 17/2)
15x + 15y = 135/2
15x + 9y = 51/2
Subtract equations
6y = 42
y = 42/6
y = 7

Substitute y
3x + 3(7) = 27/2
3x = -15/2
x = -15/2/3
x = -5/2


Input: Solve the equation 10x + 110/3 = 0

Output:
10x + 110/3 = 0
10x = -110/3
x = -110/3 / 10
x = -11/3


Input:
Solve the system:
3x + 7y = 134
6x + 7y = 142

Output:
3x + 7y = 134
6x + 7y = 142

Using elimination
6*(3x + 7y = 134)
3*(6x + 7y = 142)
18x + 42y = 804
18x + 21y = 426
Subtract equations
21y = 378
y = 378/21
y = 18

Substitute y
3x + 7(18) = 134
3x = 8
x = 8/3
x = 8/3


Input: Find x in x^3 + 43/2x^2 + 108x + 315/2 = 0

Output:
x^3 + 43/2x^2 + 108x + 315/2 = 0
(x - -7/2)(x - -3)(x - -15) = 0
x - -7/2 = 0
x - -3 = 0
x - -15 = 0
x = -7/2
x = -3
x = -15


Input: Find the solution to x^2 - 15/4x - 1 = 0

Output:
x^2 - 15/4x - 1 = 0
(x - -1/4)(x - 4) = 0
x - -1/4 = 0  or  x - 4 = 0
x = -1/4
x = 4


Input: Find x in x^3 - 57/14x^2 + 55/14x  = 0

Output:
x^3 - 57/14x^2 + 55/14x  = 0
(x - 11/7)(x - 0)(x - 5/2) = 0
x - 11/7 = 0
x - 0 = 0
x - 5/2 = 0
x = 11/7
x = 0
x = 5/2


Input: Compute the solution of x^3 - 131/180x^2 - 203/30x + 392/45 = 0

Output:
x^3 - 131/180x^2 - 203/30x + 392/45 = 0
(x - 7/4)(x - -14/5)(x - 16/9) = 0
x - 7/4 = 0
x - -14/5 = 0
x - 16/9 = 0
x = 7/4
x = -14/5
x = 16/9


Input: Determine x in x^3 - 13/6x^2 - 107/192x + 19/128 = 0

Output:
x^3 - 13/6x^2 - 107/192x + 19/128 = 0
(x - -3/8)(x - 1/6)(x - 19/8) = 0
x - -3/8 = 0
x - 1/6 = 0
x - 19/8 = 0
x = -3/8
x = 1/6
x = 19/8


Input: Solve x^3 + 77/8x^2 + 29x + 26 = 0

Output:
x^3 + 77/8x^2 + 29x + 26 = 0
(x - -4)(x - -4)(x - -13/8) = 0
x - -4 = 0
x - -4 = 0
x - -13/8 = 0
x = -4
x = -4
x = -13/8


Input: Find the solution to x^2 + 1/8x - 39/16 = 0

Output:
x^2 + 1/8x - 39/16 = 0
(x - 3/2)(x - -13/8) = 0
x - 3/2 = 0  or  x - -13/8 = 0
x = 3/2
x = -13/8


Input: Compute the solution of x^2 - 54/35x - 72/35 = 0

Output:
x^2 - 54/35x - 72/35 = 0
(x - 12/5)(x - -6/7) = 0
x - 12/5 = 0  or  x - -6/7 = 0
x = 12/5
x = -6/7


Input:
Solve the system:
9x + 1y = 71/8
9x + 6y = -249/8

Output:
9x + 1y = 71/8
9x + 6y = -249/8

Using elimination
9*(9x + 1y = 71/8)
9*(9x + 6y = -249/8)
81x + 9y = 639/8
81x + 54y = -2241/8
Subtract equations
-45y = 360
y = 360/-45
y = -8

Substitute y
9x + 1(-8) = 71/8
9x = 135/8
x = 135/8/9
x = 15/8


Input:
Find x and y such that
9x + 5y = 19/2
3x + 4y = -5

Output:
9x + 5y = 19/2
3x + 4y = -5

Using elimination
3*(9x + 5y = 19/2)
9*(3x + 4y = -5)
27x + 15y = 57/2
27x + 36y = -45
Subtract equations
-21y = 147/2
y = 147/2/-21
y = -7/2

Substitute y
9x + 5(-7/2) = 19/2
9x = 27
x = 27/9
x = 3


Input: What value of x satisfies x^3 - 293/63x^2 + 170/63x - 8/21 = 0

Output:
x^3 - 293/63x^2 + 170/63x - 8/21 = 0
(x - 3/7)(x - 2/9)(x - 4) = 0
x - 3/7 = 0
x - 2/9 = 0
x - 4 = 0
x = 3/7
x = 2/9
x = 4


Input: Determine x in 8x + 16 = 0

Output:
8x + 16 = 0
8x = -16
x = -16 / 8
x = -2


Input: What value of x satisfies x^2 + 5/4x + 1/4 = 0

Output:
x^2 + 5/4x + 1/4 = 0
(x - -1/4)(x - -1) = 0
x - -1/4 = 0  or  x - -1 = 0
x = -1/4
x = -1


Input: Solve quickly: x^3 - 28/15x^2 - 7x + 22/15 = 0

Output:
x^3 - 28/15x^2 - 7x + 22/15 = 0
(x - 11/3)(x - 1/5)(x - -2) = 0
x - 11/3 = 0
x - 1/5 = 0
x - -2 = 0
x = 11/3
x = 1/5
x = -2


Input:
Solve the equations:
7x + 3y = 127/2
6x + 6y = 123

Output:
7x + 3y = 127/2
6x + 6y = 123

Using elimination
6*(7x + 3y = 127/2)
7*(6x + 6y = 123)
42x + 18y = 381
42x + 42y = 861
Subtract equations
-24y = -480
y = -480/-24
y = 20

Substitute y
7x + 3(20) = 127/2
7x = 7/2
x = 7/2/7
x = 1/2


Input: Solve the equation x^3 - 9/70x^2 - 1632/175x + 3179/350 = 0

Output:
x^3 - 9/70x^2 - 1632/175x + 3179/350 = 0
(x - 17/7)(x - -17/5)(x - 11/10) = 0
x - 17/7 = 0
x - -17/5 = 0
x - 11/10 = 0
x = 17/7
x = -17/5
x = 11/10


Input: Compute the solution of x^3 - 113/18x^2 + 187/48x + 2299/144 = 0

Output:
x^3 - 113/18x^2 + 187/48x + 2299/144 = 0
(x - 11/4)(x - 19/4)(x - -11/9) = 0
x - 11/4 = 0
x - 19/4 = 0
x - -11/9 = 0
x = 11/4
x = 19/4
x = -11/9


Input: Solve quickly: x^2 - 34/3x + 21 = 0

Output:
x^2 - 34/3x + 21 = 0
(x - 9)(x - 7/3) = 0
x - 9 = 0  or  x - 7/3 = 0
x = 9
x = 7/3


Input:
Solve simultaneously:
1x + 6y = -97/20
5x + 7y = -439/20

Output:
1x + 6y = -97/20
5x + 7y = -439/20

Using elimination
5*(1x + 6y = -97/20)
1*(5x + 7y = -439/20)
5x + 30y = -97/4
5x + 7y = -439/20
Subtract equations
23y = -23/10
y = -23/10/23
y = -1/10

Substitute y
1x + 6(-1/10) = -97/20
1x = -17/4
x = -17/4/1
x = -17/4


Input: Compute the solution of 9x + 9/2 = 0

Output:
9x + 9/2 = 0
9x = -9/2
x = -9/2 / 9
x = -1/2


Input: What value of x satisfies x^2 - 64/21x + 19/21 = 0

Output:
x^2 - 64/21x + 19/21 = 0
(x - 19/7)(x - 1/3) = 0
x - 19/7 = 0  or  x - 1/3 = 0
x = 19/7
x = 1/3


Input: What value of x satisfies x^2 - 15/7x  = 0

Output:
x^2 - 15/7x  = 0
(x - 0)(x - 15/7) = 0
x - 0 = 0  or  x - 15/7 = 0
x = 0
x = 15/7


Input: Find x in x^3 - 55/6x^2 + 3/2x  = 0

Output:
x^3 - 55/6x^2 + 3/2x  = 0
(x - 1/6)(x - 9)(x - 0) = 0
x - 1/6 = 0
x - 9 = 0
x - 0 = 0
x = 1/6
x = 9
x = 0


Input: Determine x in x^3 - 182/15x^2 - 637/15x - 8 = 0

Output:
x^3 - 182/15x^2 - 637/15x - 8 = 0
(x - -8/3)(x - 15)(x - -1/5) = 0
x - -8/3 = 0
x - 15 = 0
x - -1/5 = 0
x = -8/3
x = 15
x = -1/5


Input: Compute the solution of x^3 - 1037/140x^2 + 2249/140x - 627/70 = 0

Output:
x^3 - 1037/140x^2 + 2249/140x - 627/70 = 0
(x - 11/4)(x - 6/7)(x - 19/5) = 0
x - 11/4 = 0
x - 6/7 = 0
x - 19/5 = 0
x = 11/4
x = 6/7
x = 19/5


Input: Solve 9x + 57/2 = 0

Output:
9x + 57/2 = 0
9x = -57/2
x = -57/2 / 9
x = -19/6


Input: Solve 10x + 55/3 = 0

Output:
10x + 55/3 = 0
10x = -55/3
x = -55/3 / 10
x = -11/6


Input: What value of x satisfies x^2 - 67/35x - 76/35 = 0

Output:
x^2 - 67/35x - 76/35 = 0
(x - -4/5)(x - 19/7) = 0
x - -4/5 = 0  or  x - 19/7 = 0
x = -4/5
x = 19/7


Input: What value of x satisfies x^2 + 5/2x - 44 = 0

Output:
x^2 + 5/2x - 44 = 0
(x - -8)(x - 11/2) = 0
x - -8 = 0  or  x - 11/2 = 0
x = -8
x = 11/2


Input: Find x in x^3 - 47/10x^2 + 128/25x + 14/25 = 0

Output:
x^3 - 47/10x^2 + 128/25x + 14/25 = 0
(x - -1/10)(x - 14/5)(x - 2) = 0
x - -1/10 = 0
x - 14/5 = 0
x - 2 = 0
x = -1/10
x = 14/5
x = 2


Input: Find x in x^3 - 127/6x^2 + 1043/18x - 17 = 0

Output:
x^3 - 127/6x^2 + 1043/18x - 17 = 0
(x - 18)(x - 1/3)(x - 17/6) = 0
x - 18 = 0
x - 1/3 = 0
x - 17/6 = 0
x = 18
x = 1/3
x = 17/6


Input:
Solve the equations:
3x + 6y = 25/3
10x + 2y = 160/9

Output:
3x + 6y = 25/3
10x + 2y = 160/9

Using elimination
10*(3x + 6y = 25/3)
3*(10x + 2y = 160/9)
30x + 60y = 250/3
30x + 6y = 160/3
Subtract equations
54y = 30
y = 30/54
y = 5/9

Substitute y
3x + 6(5/9) = 25/3
3x = 5
x = 5/3
x = 5/3


Input: Solve x^2 - 8x - 9 = 0

Output:
x^2 - 8x - 9 = 0
(x - -1)(x - 9) = 0
x - -1 = 0  or  x - 9 = 0
x = -1
x = 9


Input: Solve quickly: 3x + 27/10 = 0

Output:
3x + 27/10 = 0
3x = -27/10
x = -27/10 / 3
x = -9/10


Input: Compute the solution of x^2 - 20/3x  = 0

Output:
x^2 - 20/3x  = 0
(x - 0)(x - 20/3) = 0
x - 0 = 0  or  x - 20/3 = 0
x = 0
x = 20/3


Input:
Solve simultaneously:
6x + 10y = -80/3
10x + 10y = -100/3

Output:
6x + 10y = -80/3
10x + 10y = -100/3

Using elimination
10*(6x + 10y = -80/3)
6*(10x + 10y = -100/3)
60x + 100y = -800/3
60x + 60y = -200
Subtract equations
40y = -200/3
y = -200/3/40
y = -5/3

Substitute y
6x + 10(-5/3) = -80/3
6x = -10
x = -10/6
x = -5/3


Input: Compute the solution of x^3 + 116/15x^2 - 65/3x + 10 = 0

Output:
x^3 + 116/15x^2 - 65/3x + 10 = 0
(x - 5/3)(x - 3/5)(x - -10) = 0
x - 5/3 = 0
x - 3/5 = 0
x - -10 = 0
x = 5/3
x = 3/5
x = -10


Input: What value of x satisfies x^2 - 31/9x + 26/9 = 0

Output:
x^2 - 31/9x + 26/9 = 0
(x - 2)(x - 13/9) = 0
x - 2 = 0  or  x - 13/9 = 0
x = 2
x = 13/9


Input: Determine x in 3x  = 0

Output:
3x  = 0
3x = 0
x = 0 / 3
x = 0


Input:
Solve simultaneously:
4x + 10y = 83
6x + 4y = 73/2

Output:
4x + 10y = 83
6x + 4y = 73/2

Using elimination
6*(4x + 10y = 83)
4*(6x + 4y = 73/2)
24x + 60y = 498
24x + 16y = 146
Subtract equations
44y = 352
y = 352/44
y = 8

Substitute y
4x + 10(8) = 83
4x = 3
x = 3/4
x = 3/4


Input: Find the solution to 10x + 11 = 0

Output:
10x + 11 = 0
10x = -11
x = -11 / 10
x = -11/10


Input: Solve x^3 + 9/4x^2 + 127/200x - 21/50 = 0

Output:
x^3 + 9/4x^2 + 127/200x - 21/50 = 0
(x - -4/5)(x - 3/10)(x - -7/4) = 0
x - -4/5 = 0
x - 3/10 = 0
x - -7/4 = 0
x = -4/5
x = 3/10
x = -7/4


Input: Find x for x^3 - 757/120x^2 + 1361/120x - 19/4 = 0

Output:
x^3 - 757/120x^2 + 1361/120x - 19/4 = 0
(x - 19/8)(x - 10/3)(x - 3/5) = 0
x - 19/8 = 0
x - 10/3 = 0
x - 3/5 = 0
x = 19/8
x = 10/3
x = 3/5


Input: Find x for x^3 - 5x^2 + 21/4x  = 0

Output:
x^3 - 5x^2 + 21/4x  = 0
(x - 0)(x - 7/2)(x - 3/2) = 0
x - 0 = 0
x - 7/2 = 0
x - 3/2 = 0
x = 0
x = 7/2
x = 3/2


Input:
Solve simultaneously:
2x + 5y = -58/3
2x + 4y = -103/6

Output:
2x + 5y = -58/3
2x + 4y = -103/6

Using elimination
2*(2x + 5y = -58/3)
2*(2x + 4y = -103/6)
4x + 10y = -116/3
4x + 8y = -103/3
Subtract equations
2y = -13/3
y = -13/3/2
y = -13/6

Substitute y
2x + 5(-13/6) = -58/3
2x = -17/2
x = -17/2/2
x = -17/4


Input:
Solve simultaneously:
9x + 1y = 37/70
4x + 5y = 236/35

Output:
9x + 1y = 37/70
4x + 5y = 236/35

Using elimination
4*(9x + 1y = 37/70)
9*(4x + 5y = 236/35)
36x + 4y = 74/35
36x + 45y = 2124/35
Subtract equations
-41y = -410/7
y = -410/7/-41
y = 10/7

Substitute y
9x + 1(10/7) = 37/70
9x = -9/10
x = -9/10/9
x = -1/10


Input: Solve 1x - 6/5 = 0

Output:
1x - 6/5 = 0
1x = 6/5
x = 6/5 / 1
x = 6/5


Input: Solve 9x + 117/2 = 0

Output:
9x + 117/2 = 0
9x = -117/2
x = -117/2 / 9
x = -13/2


Input: Compute the solution of x^3 + 35/3x^2 + 38/3x - 40 = 0

Output:
x^3 + 35/3x^2 + 38/3x - 40 = 0
(x - 4/3)(x - -10)(x - -3) = 0
x - 4/3 = 0
x - -10 = 0
x - -3 = 0
x = 4/3
x = -10
x = -3


Input: Determine x in 2x + 12 = 0

Output:
2x + 12 = 0
2x = -12
x = -12 / 2
x = -6


Input: Compute the solution of x^2 + 29/10x + 19/10 = 0

Output:
x^2 + 29/10x + 19/10 = 0
(x - -19/10)(x - -1) = 0
x - -19/10 = 0  or  x - -1 = 0
x = -19/10
x = -1


Input: Find the solution to 9x - 27 = 0

Output:
9x - 27 = 0
9x = 27
x = 27 / 9
x = 3


Input: Solve x^3 - 26/7x^2 + 29/7x - 10/7 = 0

Output:
x^3 - 26/7x^2 + 29/7x - 10/7 = 0
(x - 1)(x - 2)(x - 5/7) = 0
x - 1 = 0
x - 2 = 0
x - 5/7 = 0
x = 1
x = 2
x = 5/7


Input:
Solve the equations:
8x + 4y = 124/3
5x + 8y = 358/3

Output:
8x + 4y = 124/3
5x + 8y = 358/3

Using elimination
5*(8x + 4y = 124/3)
8*(5x + 8y = 358/3)
40x + 20y = 620/3
40x + 64y = 2864/3
Subtract equations
-44y = -748
y = -748/-44
y = 17

Substitute y
8x + 4(17) = 124/3
8x = -80/3
x = -80/3/8
x = -10/3


Input: Compute the solution of x^2 - 59/12x + 6 = 0

Output:
x^2 - 59/12x + 6 = 0
(x - 8/3)(x - 9/4) = 0
x - 8/3 = 0  or  x - 9/4 = 0
x = 8/3
x = 9/4


Input: Solve 1x + 8/3 = 0

Output:
1x + 8/3 = 0
1x = -8/3
x = -8/3 / 1
x = -8/3


Input: Determine x in x^3 - 141/14x^2 + 51/14x + 578/7 = 0

Output:
x^3 - 141/14x^2 + 51/14x + 578/7 = 0
(x - -17/7)(x - 4)(x - 17/2) = 0
x - -17/7 = 0
x - 4 = 0
x - 17/2 = 0
x = -17/7
x = 4
x = 17/2


Input: Determine x in x^3 - 91/18x^2 - 37/18x + 35/3 = 0

Output:
x^3 - 91/18x^2 - 37/18x + 35/3 = 0
(x - 14/9)(x - 5)(x - -3/2) = 0
x - 14/9 = 0
x - 5 = 0
x - -3/2 = 0
x = 14/9
x = 5
x = -3/2


Input: Find x for x^2 - 173/36x + 91/18 = 0

Output:
x^2 - 173/36x + 91/18 = 0
(x - 13/4)(x - 14/9) = 0
x - 13/4 = 0  or  x - 14/9 = 0
x = 13/4
x = 14/9


Input:
Solve the equations:
8x + 1y = 23/2
9x + 1y = 107/8

Output:
8x + 1y = 23/2
9x + 1y = 107/8

Using elimination
9*(8x + 1y = 23/2)
8*(9x + 1y = 107/8)
72x + 9y = 207/2
72x + 8y = 107
Subtract equations
1y = -7/2
y = -7/2/1
y = -7/2

Substitute y
8x + 1(-7/2) = 23/2
8x = 15
x = 15/8
x = 15/8


Input: Find x for x^3 + 179/42x^2 - 5/147x - 1700/147 = 0

Output:
x^3 + 179/42x^2 - 5/147x - 1700/147 = 0
(x - -17/6)(x - -20/7)(x - 10/7) = 0
x - -17/6 = 0
x - -20/7 = 0
x - 10/7 = 0
x = -17/6
x = -20/7
x = 10/7


Input: Find the solution to 8x + 72/7 = 0

Output:
8x + 72/7 = 0
8x = -72/7
x = -72/7 / 8
x = -9/7


Input: Find x in 4x - 56/9 = 0

Output:
4x - 56/9 = 0
4x = 56/9
x = 56/9 / 4
x = 14/9


Input: Find x in x^2 - 99/5x + 238/5 = 0

Output:
x^2 - 99/5x + 238/5 = 0
(x - 17)(x - 14/5) = 0
x - 17 = 0  or  x - 14/5 = 0
x = 17
x = 14/5


Input: Find x for x^3 + 1x^2 - 173/100x - 819/500 = 0

Output:
x^3 + 1x^2 - 173/100x - 819/500 = 0
(x - -9/10)(x - 13/10)(x - -7/5) = 0
x - -9/10 = 0
x - 13/10 = 0
x - -7/5 = 0
x = -9/10
x = 13/10
x = -7/5


Input: Determine x in x^3 + 79/120x^2 - 63/20x - 3 = 0

Output:
x^3 + 79/120x^2 - 63/20x - 3 = 0
(x - -6/5)(x - 15/8)(x - -4/3) = 0
x - -6/5 = 0
x - 15/8 = 0
x - -4/3 = 0
x = -6/5
x = 15/8
x = -4/3


Input: Compute the solution of x^2 + 32/15x - 4 = 0

Output:
x^2 + 32/15x - 4 = 0
(x - -10/3)(x - 6/5) = 0
x - -10/3 = 0  or  x - 6/5 = 0
x = -10/3
x = 6/5


Input: Solve 9x + 18 = 0

Output:
9x + 18 = 0
9x = -18
x = -18 / 9
x = -2


Input:
Solve the system:
9x + 7y = -7/2
7x + 7y = -7/2

Output:
9x + 7y = -7/2
7x + 7y = -7/2

Using elimination
7*(9x + 7y = -7/2)
9*(7x + 7y = -7/2)
63x + 49y = -49/2
63x + 63y = -63/2
Subtract equations
-14y = 7
y = 7/-14
y = -1/2

Substitute y
9x + 7(-1/2) = -7/2
9x = 0
x = 0/9
x = 0


Input: Find the solution to x^3 - 73/40x^2 - 323/40x + 273/20 = 0

Output:
x^3 - 73/40x^2 - 323/40x + 273/20 = 0
(x - 13/8)(x - 3)(x - -14/5) = 0
x - 13/8 = 0
x - 3 = 0
x - -14/5 = 0
x = 13/8
x = 3
x = -14/5


Input: Solve the equation x^2 + 23/4x - 39/8 = 0

Output:
x^2 + 23/4x - 39/8 = 0
(x - 3/4)(x - -13/2) = 0
x - 3/4 = 0  or  x - -13/2 = 0
x = 3/4
x = -13/2


Input: Compute the solution of x^2 + 37/10x + 33/10 = 0

Output:
x^2 + 37/10x + 33/10 = 0
(x - -11/5)(x - -3/2) = 0
x - -11/5 = 0  or  x - -3/2 = 0
x = -11/5
x = -3/2


Input: Solve quickly: 3x + 30/7 = 0

Output:
3x + 30/7 = 0
3x = -30/7
x = -30/7 / 3
x = -10/7


Input: Find x for 3x + 24/5 = 0

Output:
3x + 24/5 = 0
3x = -24/5
x = -24/5 / 3
x = -8/5


Input: Find the solution to x^3 - 35/24x^2 - 47/144x + 13/144 = 0

Output:
x^3 - 35/24x^2 - 47/144x + 13/144 = 0
(x - 13/8)(x - -1/3)(x - 1/6) = 0
x - 13/8 = 0
x - -1/3 = 0
x - 1/6 = 0
x = 13/8
x = -1/3
x = 1/6


Input: Find x in x^2 + 43/18x - 5/18 = 0

Output:
x^2 + 43/18x - 5/18 = 0
(x - -5/2)(x - 1/9) = 0
x - -5/2 = 0  or  x - 1/9 = 0
x = -5/2
x = 1/9


Input: Solve the equation x^3 - 3/5x^2 - 22/25x + 24/125 = 0

Output:
x^3 - 3/5x^2 - 22/25x + 24/125 = 0
(x - 6/5)(x - 1/5)(x - -4/5) = 0
x - 6/5 = 0
x - 1/5 = 0
x - -4/5 = 0
x = 6/5
x = 1/5
x = -4/5


Input: Determine x in 5x + 35/6 = 0

Output:
5x + 35/6 = 0
5x = -35/6
x = -35/6 / 5
x = -7/6


Input: Determine x in x^3 + 4x^2 + 13/4x + 3/4 = 0

Output:
x^3 + 4x^2 + 13/4x + 3/4 = 0
(x - -1/2)(x - -1/2)(x - -3) = 0
x - -1/2 = 0
x - -1/2 = 0
x - -3 = 0
x = -1/2
x = -1/2
x = -3


Input: Find the solution to x^3 - 35/6x^2 - 1127/6x - 561 = 0

Output:
x^3 - 35/6x^2 - 1127/6x - 561 = 0
(x - -11/3)(x - 18)(x - -17/2) = 0
x - -11/3 = 0
x - 18 = 0
x - -17/2 = 0
x = -11/3
x = 18
x = -17/2


Input: Determine x in x^2 + 8x - 20 = 0

Output:
x^2 + 8x - 20 = 0
(x - -10)(x - 2) = 0
x - -10 = 0  or  x - 2 = 0
x = -10
x = 2


Input: Solve the equation x^3 + 9/2x^2 - 61/16x - 819/32 = 0

Output:
x^3 + 9/2x^2 - 61/16x - 819/32 = 0
(x - -13/4)(x - -7/2)(x - 9/4) = 0
x - -13/4 = 0
x - -7/2 = 0
x - 9/4 = 0
x = -13/4
x = -7/2
x = 9/4


Input: What value of x satisfies x^2 + 9x  = 0

Output:
x^2 + 9x  = 0
(x - -9)(x - 0) = 0
x - -9 = 0  or  x - 0 = 0
x = -9
x = 0


Input: Solve x^3 - 32/5x^2 + 52/25x + 48/25 = 0

Output:
x^3 - 32/5x^2 + 52/25x + 48/25 = 0
(x - 4/5)(x - 6)(x - -2/5) = 0
x - 4/5 = 0
x - 6 = 0
x - -2/5 = 0
x = 4/5
x = 6
x = -2/5


Input:
Find x and y such that
1x + 7y = -139/8
6x + 2y = -317/4

Output:
1x + 7y = -139/8
6x + 2y = -317/4

Using elimination
6*(1x + 7y = -139/8)
1*(6x + 2y = -317/4)
6x + 42y = -417/4
6x + 2y = -317/4
Subtract equations
40y = -25
y = -25/40
y = -5/8

Substitute y
1x + 7(-5/8) = -139/8
1x = -13
x = -13/1
x = -13


Input: Solve the equation x^3 - 23/10x^2 - 116/45x + 136/45 = 0

Output:
x^3 - 23/10x^2 - 116/45x + 136/45 = 0
(x - 4/5)(x - -4/3)(x - 17/6) = 0
x - 4/5 = 0
x - -4/3 = 0
x - 17/6 = 0
x = 4/5
x = -4/3
x = 17/6


Input: Find x for 2x - 32/5 = 0

Output:
2x - 32/5 = 0
2x = 32/5
x = 32/5 / 2
x = 16/5


Input: Find x in x^2 + 38/5x - 16/5 = 0

Output:
x^2 + 38/5x - 16/5 = 0
(x - 2/5)(x - -8) = 0
x - 2/5 = 0  or  x - -8 = 0
x = 2/5
x = -8


Input: Solve the equation x^2 - 16/3x - 19/3 = 0

Output:
x^2 - 16/3x - 19/3 = 0
(x - -1)(x - 19/3) = 0
x - -1 = 0  or  x - 19/3 = 0
x = -1
x = 19/3


Input: Determine x in 8x - 56 = 0

Output:
8x - 56 = 0
8x = 56
x = 56 / 8
x = 7


Input: Determine x in x^2 + 5/3x - 22/3 = 0

Output:
x^2 + 5/3x - 22/3 = 0
(x - -11/3)(x - 2) = 0
x - -11/3 = 0  or  x - 2 = 0
x = -11/3
x = 2


Input:
Solve the system:
8x + 10y = -428/21
8x + 7y = -38/3

Output:
8x + 10y = -428/21
8x + 7y = -38/3

Using elimination
8*(8x + 10y = -428/21)
8*(8x + 7y = -38/3)
64x + 80y = -3424/21
64x + 56y = -304/3
Subtract equations
24y = -432/7
y = -432/7/24
y = -18/7

Substitute y
8x + 10(-18/7) = -428/21
8x = 16/3
x = 16/3/8
x = 2/3


Input: Solve x^2 + 19/10x + 3/5 = 0

Output:
x^2 + 19/10x + 3/5 = 0
(x - -2/5)(x - -3/2) = 0
x - -2/5 = 0  or  x - -3/2 = 0
x = -2/5
x = -3/2


Input: Find x for 9x + 39/2 = 0

Output:
9x + 39/2 = 0
9x = -39/2
x = -39/2 / 9
x = -13/6


Input: Solve x^3 - 257/63x^2 + 26/7x - 40/63 = 0

Output:
x^3 - 257/63x^2 + 26/7x - 40/63 = 0
(x - 2/9)(x - 20/7)(x - 1) = 0
x - 2/9 = 0
x - 20/7 = 0
x - 1 = 0
x = 2/9
x = 20/7
x = 1


Input: Determine x in 3x - 6/5 = 0

Output:
3x - 6/5 = 0
3x = 6/5
x = 6/5 / 3
x = 2/5


Input: Solve the equation x^3 + 41/30x^2 - 889/30x + 38 = 0

Output:
x^3 + 41/30x^2 - 889/30x + 38 = 0
(x - 3/2)(x - 19/5)(x - -20/3) = 0
x - 3/2 = 0
x - 19/5 = 0
x - -20/3 = 0
x = 3/2
x = 19/5
x = -20/3


Input: Find x for x^2 - 104/21x + 128/21 = 0

Output:
x^2 - 104/21x + 128/21 = 0
(x - 8/3)(x - 16/7) = 0
x - 8/3 = 0  or  x - 16/7 = 0
x = 8/3
x = 16/7


Input: Solve quickly: x^2 + 10x + 25 = 0

Output:
x^2 + 10x + 25 = 0
(x - -5)(x - -5) = 0
x - -5 = 0  or  x - -5 = 0
x = -5
x = -5


Input: What value of x satisfies 3x + 48/5 = 0

Output:
3x + 48/5 = 0
3x = -48/5
x = -48/5 / 3
x = -16/5


Input: What value of x satisfies x^3 - 103/15x^2 + 12x - 32/15 = 0

Output:
x^3 - 103/15x^2 + 12x - 32/15 = 0
(x - 8/3)(x - 1/5)(x - 4) = 0
x - 8/3 = 0
x - 1/5 = 0
x - 4 = 0
x = 8/3
x = 1/5
x = 4


Input: Determine x in x^3 - 25/18x^2 + 41/150x + 11/225 = 0

Output:
x^3 - 25/18x^2 + 41/150x + 11/225 = 0
(x - 2/5)(x - 11/10)(x - -1/9) = 0
x - 2/5 = 0
x - 11/10 = 0
x - -1/9 = 0
x = 2/5
x = 11/10
x = -1/9


Input: What value of x satisfies 4x - 18 = 0

Output:
4x - 18 = 0
4x = 18
x = 18 / 4
x = 9/2


Input: Compute the solution of x^2 - 37/9x + 38/9 = 0

Output:
x^2 - 37/9x + 38/9 = 0
(x - 19/9)(x - 2) = 0
x - 19/9 = 0  or  x - 2 = 0
x = 19/9
x = 2


Input: Solve quickly: x^3 + 5/6x^2 - 263/192x - 15/16 = 0

Output:
x^3 + 5/6x^2 - 263/192x - 15/16 = 0
(x - -5/8)(x - -4/3)(x - 9/8) = 0
x - -5/8 = 0
x - -4/3 = 0
x - 9/8 = 0
x = -5/8
x = -4/3
x = 9/8


Input: Find x for 5x - 8 = 0

Output:
5x - 8 = 0
5x = 8
x = 8 / 5
x = 8/5


Input: Compute the solution of 8x - 8 = 0

Output:
8x - 8 = 0
8x = 8
x = 8 / 8
x = 1


Input: Compute the solution of 9x + 90 = 0

Output:
9x + 90 = 0
9x = -90
x = -90 / 9
x = -10


Input: Determine x in 6x + 6 = 0

Output:
6x + 6 = 0
6x = -6
x = -6 / 6
x = -1


Input:
Solve the system:
6x + 6y = -720/7
10x + 3y = -1242/7

Output:
6x + 6y = -720/7
10x + 3y = -1242/7

Using elimination
10*(6x + 6y = -720/7)
6*(10x + 3y = -1242/7)
60x + 60y = -7200/7
60x + 18y = -7452/7
Subtract equations
42y = 36
y = 36/42
y = 6/7

Substitute y
6x + 6(6/7) = -720/7
6x = -108
x = -108/6
x = -18


Input: Find x in x^2 - 10x + 19/4 = 0

Output:
x^2 - 10x + 19/4 = 0
(x - 19/2)(x - 1/2) = 0
x - 19/2 = 0  or  x - 1/2 = 0
x = 19/2
x = 1/2


Input: Find x in 1x + 15 = 0

Output:
1x + 15 = 0
1x = -15
x = -15 / 1
x = -15


Input: Solve quickly: 4x - 32/3 = 0

Output:
4x - 32/3 = 0
4x = 32/3
x = 32/3 / 4
x = 8/3


Input: Solve the equation x^2 + 114/7x - 361/7 = 0

Output:
x^2 + 114/7x - 361/7 = 0
(x - -19)(x - 19/7) = 0
x - -19 = 0  or  x - 19/7 = 0
x = -19
x = 19/7


Input: Solve the equation 5x + 30/7 = 0

Output:
5x + 30/7 = 0
5x = -30/7
x = -30/7 / 5
x = -6/7


Input:
Solve simultaneously:
3x + 8y = 110/3
9x + 7y = 58/3

Output:
3x + 8y = 110/3
9x + 7y = 58/3

Using elimination
9*(3x + 8y = 110/3)
3*(9x + 7y = 58/3)
27x + 72y = 330
27x + 21y = 58
Subtract equations
51y = 272
y = 272/51
y = 16/3

Substitute y
3x + 8(16/3) = 110/3
3x = -6
x = -6/3
x = -2


Input:
Solve the equations:
5x + 4y = -1
7x + 5y = -3/2

Output:
5x + 4y = -1
7x + 5y = -3/2

Using elimination
7*(5x + 4y = -1)
5*(7x + 5y = -3/2)
35x + 28y = -7
35x + 25y = -15/2
Subtract equations
3y = 1/2
y = 1/2/3
y = 1/6

Substitute y
5x + 4(1/6) = -1
5x = -5/3
x = -5/3/5
x = -1/3


Input: Solve quickly: 4x - 28 = 0

Output:
4x - 28 = 0
4x = 28
x = 28 / 4
x = 7


Input: Determine x in x^3 - 3/35x^2 - 108/35x  = 0

Output:
x^3 - 3/35x^2 - 108/35x  = 0
(x - 9/5)(x - -12/7)(x - 0) = 0
x - 9/5 = 0
x - -12/7 = 0
x - 0 = 0
x = 9/5
x = -12/7
x = 0


Input: Find x in 5x + 5/2 = 0

Output:
5x + 5/2 = 0
5x = -5/2
x = -5/2 / 5
x = -1/2


Input: Solve quickly: x^2 + 11/6x - 17/6 = 0

Output:
x^2 + 11/6x - 17/6 = 0
(x - 1)(x - -17/6) = 0
x - 1 = 0  or  x - -17/6 = 0
x = 1
x = -17/6


Input: Compute the solution of 3x + 11/3 = 0

Output:
3x + 11/3 = 0
3x = -11/3
x = -11/3 / 3
x = -11/9


Input: Compute the solution of 8x + 16 = 0

Output:
8x + 16 = 0
8x = -16
x = -16 / 8
x = -2


Input:
Solve the equations:
7x + 10y = 155/6
7x + 9y = 265/12

Output:
7x + 10y = 155/6
7x + 9y = 265/12

Using elimination
7*(7x + 10y = 155/6)
7*(7x + 9y = 265/12)
49x + 70y = 1085/6
49x + 63y = 1855/12
Subtract equations
7y = 105/4
y = 105/4/7
y = 15/4

Substitute y
7x + 10(15/4) = 155/6
7x = -35/3
x = -35/3/7
x = -5/3


Input: Solve 10x - 25/4 = 0

Output:
10x - 25/4 = 0
10x = 25/4
x = 25/4 / 10
x = 5/8


Input: Compute the solution of x^2 - 21x + 54 = 0

Output:
x^2 - 21x + 54 = 0
(x - 18)(x - 3) = 0
x - 18 = 0  or  x - 3 = 0
x = 18
x = 3


Input:
Solve simultaneously:
6x + 8y = -86/15
4x + 7y = -232/45

Output:
6x + 8y = -86/15
4x + 7y = -232/45

Using elimination
4*(6x + 8y = -86/15)
6*(4x + 7y = -232/45)
24x + 32y = -344/15
24x + 42y = -464/15
Subtract equations
-10y = 8
y = 8/-10
y = -4/5

Substitute y
6x + 8(-4/5) = -86/15
6x = 2/3
x = 2/3/6
x = 1/9


Input:
Find x and y such that
2x + 1y = 1/5
7x + 2y = 19/10

Output:
2x + 1y = 1/5
7x + 2y = 19/10

Using elimination
7*(2x + 1y = 1/5)
2*(7x + 2y = 19/10)
14x + 7y = 7/5
14x + 4y = 19/5
Subtract equations
3y = -12/5
y = -12/5/3
y = -4/5

Substitute y
2x + 1(-4/5) = 1/5
2x = 1
x = 1/2
x = 1/2


Input: Find x in x^3 + 94/9x^2 + 835/36x + 25/3 = 0

Output:
x^3 + 94/9x^2 + 835/36x + 25/3 = 0
(x - -5/2)(x - -15/2)(x - -4/9) = 0
x - -5/2 = 0
x - -15/2 = 0
x - -4/9 = 0
x = -5/2
x = -15/2
x = -4/9


Input: Solve the equation 7x + 7/2 = 0

Output:
7x + 7/2 = 0
7x = -7/2
x = -7/2 / 7
x = -1/2


Input: Determine x in x^2 + 5/2x + 9/16 = 0

Output:
x^2 + 5/2x + 9/16 = 0
(x - -9/4)(x - -1/4) = 0
x - -9/4 = 0  or  x - -1/4 = 0
x = -9/4
x = -1/4


Input: Solve quickly: x^3 + 34/7x^2 + 33/28x - 27/14 = 0

Output:
x^3 + 34/7x^2 + 33/28x - 27/14 = 0
(x - 1/2)(x - -9/2)(x - -6/7) = 0
x - 1/2 = 0
x - -9/2 = 0
x - -6/7 = 0
x = 1/2
x = -9/2
x = -6/7


Input: Find x in x^3 + 27x^2 + 194x + 408 = 0

Output:
x^3 + 27x^2 + 194x + 408 = 0
(x - -4)(x - -6)(x - -17) = 0
x - -4 = 0
x - -6 = 0
x - -17 = 0
x = -4
x = -6
x = -17


Input:
Solve the system:
4x + 8y = -80/7
8x + 10y = -55/7

Output:
4x + 8y = -80/7
8x + 10y = -55/7

Using elimination
8*(4x + 8y = -80/7)
4*(8x + 10y = -55/7)
32x + 64y = -640/7
32x + 40y = -220/7
Subtract equations
24y = -60
y = -60/24
y = -5/2

Substitute y
4x + 8(-5/2) = -80/7
4x = 60/7
x = 60/7/4
x = 15/7


Input: Find x for x^2 - 95/63x - 16/9 = 0

Output:
x^2 - 95/63x - 16/9 = 0
(x - -7/9)(x - 16/7) = 0
x - -7/9 = 0  or  x - 16/7 = 0
x = -7/9
x = 16/7


Input: Solve quickly: x^3 - 7x^2 - 69/4x - 27/4 = 0

Output:
x^3 - 7x^2 - 69/4x - 27/4 = 0
(x - -3/2)(x - -1/2)(x - 9) = 0
x - -3/2 = 0
x - -1/2 = 0
x - 9 = 0
x = -3/2
x = -1/2
x = 9


Input:
Solve the equations:
5x + 8y = 20
10x + 1y = -65/4

Output:
5x + 8y = 20
10x + 1y = -65/4

Using elimination
10*(5x + 8y = 20)
5*(10x + 1y = -65/4)
50x + 80y = 200
50x + 5y = -325/4
Subtract equations
75y = 1125/4
y = 1125/4/75
y = 15/4

Substitute y
5x + 8(15/4) = 20
5x = -10
x = -10/5
x = -2


Input: Find the solution to x^3 + 14x^2 + 105/4x - 297/4 = 0

Output:
x^3 + 14x^2 + 105/4x - 297/4 = 0
(x - -9/2)(x - -11)(x - 3/2) = 0
x - -9/2 = 0
x - -11 = 0
x - 3/2 = 0
x = -9/2
x = -11
x = 3/2


Input: Find x for x^2 - 26x + 168 = 0

Output:
x^2 - 26x + 168 = 0
(x - 12)(x - 14) = 0
x - 12 = 0  or  x - 14 = 0
x = 12
x = 14


Input: What value of x satisfies x^3 + 14/15x^2 - 8/15x  = 0

Output:
x^3 + 14/15x^2 - 8/15x  = 0
(x - -4/3)(x - 2/5)(x - 0) = 0
x - -4/3 = 0
x - 2/5 = 0
x - 0 = 0
x = -4/3
x = 2/5
x = 0


Input: Find x for 5x + 35/9 = 0

Output:
5x + 35/9 = 0
5x = -35/9
x = -35/9 / 5
x = -7/9


Input: Compute the solution of 7x - 77/8 = 0

Output:
7x - 77/8 = 0
7x = 77/8
x = 77/8 / 7
x = 11/8


Input:
Find x and y such that
4x + 3y = 19
9x + 4y = 469/12

Output:
4x + 3y = 19
9x + 4y = 469/12

Using elimination
9*(4x + 3y = 19)
4*(9x + 4y = 469/12)
36x + 27y = 171
36x + 16y = 469/3
Subtract equations
11y = 44/3
y = 44/3/11
y = 4/3

Substitute y
4x + 3(4/3) = 19
4x = 15
x = 15/4
x = 15/4


Input: Find x in x^3 - 73/10x^2 - 793/10x + 338/5 = 0

Output:
x^3 - 73/10x^2 - 793/10x + 338/5 = 0
(x - 4/5)(x - 13)(x - -13/2) = 0
x - 4/5 = 0
x - 13 = 0
x - -13/2 = 0
x = 4/5
x = 13
x = -13/2


Input: Solve 5x - 2 = 0

Output:
5x - 2 = 0
5x = 2
x = 2 / 5
x = 2/5


Input: Solve x^3 + 73/4x^2 + 107/8x - 1071/8 = 0

Output:
x^3 + 73/4x^2 + 107/8x - 1071/8 = 0
(x - -7/2)(x - -17)(x - 9/4) = 0
x - -7/2 = 0
x - -17 = 0
x - 9/4 = 0
x = -7/2
x = -17
x = 9/4


Input: Compute the solution of x^3 + 35/6x^2 + 1681/150x + 532/75 = 0

Output:
x^3 + 35/6x^2 + 1681/150x + 532/75 = 0
(x - -19/10)(x - -7/3)(x - -8/5) = 0
x - -19/10 = 0
x - -7/3 = 0
x - -8/5 = 0
x = -19/10
x = -7/3
x = -8/5


Input: Solve quickly: x^2 - 91/6x + 38 = 0

Output:
x^2 - 91/6x + 38 = 0
(x - 12)(x - 19/6) = 0
x - 12 = 0  or  x - 19/6 = 0
x = 12
x = 19/6


Input: Solve quickly: x^2 - 29/4x - 63/4 = 0

Output:
x^2 - 29/4x - 63/4 = 0
(x - -7/4)(x - 9) = 0
x - -7/4 = 0  or  x - 9 = 0
x = -7/4
x = 9


Input:
Solve simultaneously:
8x + 10y = 81/7
10x + 9y = 841/70

Output:
8x + 10y = 81/7
10x + 9y = 841/70

Using elimination
10*(8x + 10y = 81/7)
8*(10x + 9y = 841/70)
80x + 100y = 810/7
80x + 72y = 3364/35
Subtract equations
28y = 98/5
y = 98/5/28
y = 7/10

Substitute y
8x + 10(7/10) = 81/7
8x = 32/7
x = 32/7/8
x = 4/7


Input:
Find x and y such that
1x + 8y = 317/9
4x + 8y = 350/9

Output:
1x + 8y = 317/9
4x + 8y = 350/9

Using elimination
4*(1x + 8y = 317/9)
1*(4x + 8y = 350/9)
4x + 32y = 1268/9
4x + 8y = 350/9
Subtract equations
24y = 102
y = 102/24
y = 17/4

Substitute y
1x + 8(17/4) = 317/9
1x = 11/9
x = 11/9/1
x = 11/9


Input: Solve the equation 5x + 95/6 = 0

Output:
5x + 95/6 = 0
5x = -95/6
x = -95/6 / 5
x = -19/6


Input: Find the solution to 7x - 49 = 0

Output:
7x - 49 = 0
7x = 49
x = 49 / 7
x = 7


Input: What value of x satisfies x^3 - 71/21x^2 + 320/147x - 12/49 = 0

Output:
x^3 - 71/21x^2 + 320/147x - 12/49 = 0
(x - 2/3)(x - 1/7)(x - 18/7) = 0
x - 2/3 = 0
x - 1/7 = 0
x - 18/7 = 0
x = 2/3
x = 1/7
x = 18/7


Input: Find the solution to x^2 + 31/36x - 14/9 = 0

Output:
x^2 + 31/36x - 14/9 = 0
(x - -7/4)(x - 8/9) = 0
x - -7/4 = 0  or  x - 8/9 = 0
x = -7/4
x = 8/9


Input:
Solve simultaneously:
4x + 7y = 221/5
5x + 7y = 43

Output:
4x + 7y = 221/5
5x + 7y = 43

Using elimination
5*(4x + 7y = 221/5)
4*(5x + 7y = 43)
20x + 35y = 221
20x + 28y = 172
Subtract equations
7y = 49
y = 49/7
y = 7

Substitute y
4x + 7(7) = 221/5
4x = -24/5
x = -24/5/4
x = -6/5


Input:
Solve the equations:
1x + 4y = 43/7
2x + 10y = 235/14

Output:
1x + 4y = 43/7
2x + 10y = 235/14

Using elimination
2*(1x + 4y = 43/7)
1*(2x + 10y = 235/14)
2x + 8y = 86/7
2x + 10y = 235/14
Subtract equations
-2y = -9/2
y = -9/2/-2
y = 9/4

Substitute y
1x + 4(9/4) = 43/7
1x = -20/7
x = -20/7/1
x = -20/7


Input: Solve x^2 + 62/5x + 77/5 = 0

Output:
x^2 + 62/5x + 77/5 = 0
(x - -7/5)(x - -11) = 0
x - -7/5 = 0  or  x - -11 = 0
x = -7/5
x = -11


Input:
Solve simultaneously:
7x + 1y = -11/24
10x + 10y = 185/12

Output:
7x + 1y = -11/24
10x + 10y = 185/12

Using elimination
10*(7x + 1y = -11/24)
7*(10x + 10y = 185/12)
70x + 10y = -55/12
70x + 70y = 1295/12
Subtract equations
-60y = -225/2
y = -225/2/-60
y = 15/8

Substitute y
7x + 1(15/8) = -11/24
7x = -7/3
x = -7/3/7
x = -1/3


Input: Solve the equation 3x - 14 = 0

Output:
3x - 14 = 0
3x = 14
x = 14 / 3
x = 14/3


Input: Find the solution to x^3 - 669/40x^2 + 639/16x - 1001/40 = 0

Output:
x^3 - 669/40x^2 + 639/16x - 1001/40 = 0
(x - 14)(x - 13/8)(x - 11/10) = 0
x - 14 = 0
x - 13/8 = 0
x - 11/10 = 0
x = 14
x = 13/8
x = 11/10


Input: Solve the equation 7x + 56 = 0

Output:
7x + 56 = 0
7x = -56
x = -56 / 7
x = -8


Input: Solve quickly: 6x - 30 = 0

Output:
6x - 30 = 0
6x = 30
x = 30 / 6
x = 5


Input:
Solve the equations:
2x + 3y = -26
4x + 1y = -72

Output:
2x + 3y = -26
4x + 1y = -72

Using elimination
4*(2x + 3y = -26)
2*(4x + 1y = -72)
8x + 12y = -104
8x + 2y = -144
Subtract equations
10y = 40
y = 40/10
y = 4

Substitute y
2x + 3(4) = -26
2x = -38
x = -38/2
x = -19


Input:
Solve the system:
3x + 3y = -1/2
3x + 6y = -5

Output:
3x + 3y = -1/2
3x + 6y = -5

Using elimination
3*(3x + 3y = -1/2)
3*(3x + 6y = -5)
9x + 9y = -3/2
9x + 18y = -15
Subtract equations
-9y = 27/2
y = 27/2/-9
y = -3/2

Substitute y
3x + 3(-3/2) = -1/2
3x = 4
x = 4/3
x = 4/3


Input: Solve x^2 + 5/4x  = 0

Output:
x^2 + 5/4x  = 0
(x - 0)(x - -5/4) = 0
x - 0 = 0  or  x - -5/4 = 0
x = 0
x = -5/4


Input:
Solve simultaneously:
9x + 6y = 3/5
1x + 3y = -81/10

Output:
9x + 6y = 3/5
1x + 3y = -81/10

Using elimination
1*(9x + 6y = 3/5)
9*(1x + 3y = -81/10)
9x + 6y = 3/5
9x + 27y = -729/10
Subtract equations
-21y = 147/2
y = 147/2/-21
y = -7/2

Substitute y
9x + 6(-7/2) = 3/5
9x = 108/5
x = 108/5/9
x = 12/5


Input: Find x in x^2 + 7/3x + 10/9 = 0

Output:
x^2 + 7/3x + 10/9 = 0
(x - -5/3)(x - -2/3) = 0
x - -5/3 = 0  or  x - -2/3 = 0
x = -5/3
x = -2/3


Input: Find x in 3x - 1 = 0

Output:
3x - 1 = 0
3x = 1
x = 1 / 3
x = 1/3


Input: Find x in 1x + 19/9 = 0

Output:
1x + 19/9 = 0
1x = -19/9
x = -19/9 / 1
x = -19/9


Input: Compute the solution of 4x - 16 = 0

Output:
4x - 16 = 0
4x = 16
x = 16 / 4
x = 4


Input: What value of x satisfies 2x - 1/2 = 0

Output:
2x - 1/2 = 0
2x = 1/2
x = 1/2 / 2
x = 1/4


Input:
Solve the system:
3x + 6y = 15/4
9x + 7y = -9/8

Output:
3x + 6y = 15/4
9x + 7y = -9/8

Using elimination
9*(3x + 6y = 15/4)
3*(9x + 7y = -9/8)
27x + 54y = 135/4
27x + 21y = -27/8
Subtract equations
33y = 297/8
y = 297/8/33
y = 9/8

Substitute y
3x + 6(9/8) = 15/4
3x = -3
x = -3/3
x = -1


Input: Solve x^3 + 113/9x^2 + 20/3x  = 0

Output:
x^3 + 113/9x^2 + 20/3x  = 0
(x - 0)(x - -12)(x - -5/9) = 0
x - 0 = 0
x - -12 = 0
x - -5/9 = 0
x = 0
x = -12
x = -5/9


Input: What value of x satisfies 9x - 45/4 = 0

Output:
9x - 45/4 = 0
9x = 45/4
x = 45/4 / 9
x = 5/4


Input: Solve the equation x^2 - 104/5x + 171/5 = 0

Output:
x^2 - 104/5x + 171/5 = 0
(x - 9/5)(x - 19) = 0
x - 9/5 = 0  or  x - 19 = 0
x = 9/5
x = 19


Input: Find x in 9x - 14 = 0

Output:
9x - 14 = 0
9x = 14
x = 14 / 9
x = 14/9


Input: What value of x satisfies x^2 + 97/12x + 44/3 = 0

Output:
x^2 + 97/12x + 44/3 = 0
(x - -11/4)(x - -16/3) = 0
x - -11/4 = 0  or  x - -16/3 = 0
x = -11/4
x = -16/3


Input: Find x in x^2 + 49/18x + 5/9 = 0

Output:
x^2 + 49/18x + 5/9 = 0
(x - -5/2)(x - -2/9) = 0
x - -5/2 = 0  or  x - -2/9 = 0
x = -5/2
x = -2/9


Input: Determine x in x^2 - 23/24x - 119/48 = 0

Output:
x^2 - 23/24x - 119/48 = 0
(x - 17/8)(x - -7/6) = 0
x - 17/8 = 0  or  x - -7/6 = 0
x = 17/8
x = -7/6


Input:
Find x and y such that
8x + 3y = 154/5
3x + 2y = 147/10

Output:
8x + 3y = 154/5
3x + 2y = 147/10

Using elimination
3*(8x + 3y = 154/5)
8*(3x + 2y = 147/10)
24x + 9y = 462/5
24x + 16y = 588/5
Subtract equations
-7y = -126/5
y = -126/5/-7
y = 18/5

Substitute y
8x + 3(18/5) = 154/5
8x = 20
x = 20/8
x = 5/2


Input: Compute the solution of x^3 + 159/10x^2 + 27/2x  = 0

Output:
x^3 + 159/10x^2 + 27/2x  = 0
(x - 0)(x - -9/10)(x - -15) = 0
x - 0 = 0
x - -9/10 = 0
x - -15 = 0
x = 0
x = -9/10
x = -15


Input: Solve quickly: x^3 - 2/7x^2 - 19/7x - 10/7 = 0

Output:
x^3 - 2/7x^2 - 19/7x - 10/7 = 0
(x - -1)(x - 2)(x - -5/7) = 0
x - -1 = 0
x - 2 = 0
x - -5/7 = 0
x = -1
x = 2
x = -5/7


Input:
Solve simultaneously:
1x + 6y = -79/7
9x + 6y = -39/7

Output:
1x + 6y = -79/7
9x + 6y = -39/7

Using elimination
9*(1x + 6y = -79/7)
1*(9x + 6y = -39/7)
9x + 54y = -711/7
9x + 6y = -39/7
Subtract equations
48y = -96
y = -96/48
y = -2

Substitute y
1x + 6(-2) = -79/7
1x = 5/7
x = 5/7/1
x = 5/7


Input:
Solve the equations:
1x + 8y = -43/2
10x + 4y = -44

Output:
1x + 8y = -43/2
10x + 4y = -44

Using elimination
10*(1x + 8y = -43/2)
1*(10x + 4y = -44)
10x + 80y = -215
10x + 4y = -44
Subtract equations
76y = -171
y = -171/76
y = -9/4

Substitute y
1x + 8(-9/4) = -43/2
1x = -7/2
x = -7/2/1
x = -7/2


Input: Find x in x^2 + 25/6x + 19/6 = 0

Output:
x^2 + 25/6x + 19/6 = 0
(x - -1)(x - -19/6) = 0
x - -1 = 0  or  x - -19/6 = 0
x = -1
x = -19/6


Input:
Solve the system:
8x + 4y = -384/35
5x + 7y = -3

Output:
8x + 4y = -384/35
5x + 7y = -3

Using elimination
5*(8x + 4y = -384/35)
8*(5x + 7y = -3)
40x + 20y = -384/7
40x + 56y = -24
Subtract equations
-36y = -216/7
y = -216/7/-36
y = 6/7

Substitute y
8x + 4(6/7) = -384/35
8x = -72/5
x = -72/5/8
x = -9/5


Input: What value of x satisfies 7x - 98/9 = 0

Output:
7x - 98/9 = 0
7x = 98/9
x = 98/9 / 7
x = 14/9


Input:
Find x and y such that
5x + 3y = 11/2
9x + 9y = 33/2

Output:
5x + 3y = 11/2
9x + 9y = 33/2

Using elimination
9*(5x + 3y = 11/2)
5*(9x + 9y = 33/2)
45x + 27y = 99/2
45x + 45y = 165/2
Subtract equations
-18y = -33
y = -33/-18
y = 11/6

Substitute y
5x + 3(11/6) = 11/2
5x = 0
x = 0/5
x = 0


Input: What value of x satisfies x^3 + 115/12x^2 + 27x + 221/12 = 0

Output:
x^3 + 115/12x^2 + 27x + 221/12 = 0
(x - -13/3)(x - -1)(x - -17/4) = 0
x - -13/3 = 0
x - -1 = 0
x - -17/4 = 0
x = -13/3
x = -1
x = -17/4


Input: Solve 3x + 9 = 0

Output:
3x + 9 = 0
3x = -9
x = -9 / 3
x = -3


Input: Find the solution to x^2 + 11/24x + 1/24 = 0

Output:
x^2 + 11/24x + 1/24 = 0
(x - -1/3)(x - -1/8) = 0
x - -1/3 = 0  or  x - -1/8 = 0
x = -1/3
x = -1/8


Input: Solve the equation x^3 - 107/20x^2 + 281/40x - 13/20 = 0

Output:
x^3 - 107/20x^2 + 281/40x - 13/20 = 0
(x - 2)(x - 1/10)(x - 13/4) = 0
x - 2 = 0
x - 1/10 = 0
x - 13/4 = 0
x = 2
x = 1/10
x = 13/4


Input: Find x for x^3 + 13/5x^2 - 96/25x - 108/125 = 0

Output:
x^3 + 13/5x^2 - 96/25x - 108/125 = 0
(x - -18/5)(x - -1/5)(x - 6/5) = 0
x - -18/5 = 0
x - -1/5 = 0
x - 6/5 = 0
x = -18/5
x = -1/5
x = 6/5


Input: Solve 6x  = 0

Output:
6x  = 0
6x = 0
x = 0 / 6
x = 0


Input:
Solve the system:
10x + 4y = -54
4x + 6y = -26

Output:
10x + 4y = -54
4x + 6y = -26

Using elimination
4*(10x + 4y = -54)
10*(4x + 6y = -26)
40x + 16y = -216
40x + 60y = -260
Subtract equations
-44y = 44
y = 44/-44
y = -1

Substitute y
10x + 4(-1) = -54
10x = -50
x = -50/10
x = -5


Input: Determine x in x^2 + 1/6x - 13/3 = 0

Output:
x^2 + 1/6x - 13/3 = 0
(x - 2)(x - -13/6) = 0
x - 2 = 0  or  x - -13/6 = 0
x = 2
x = -13/6


Input:
Solve simultaneously:
6x + 10y = 364/15
8x + 3y = 24/5

Output:
6x + 10y = 364/15
8x + 3y = 24/5

Using elimination
8*(6x + 10y = 364/15)
6*(8x + 3y = 24/5)
48x + 80y = 2912/15
48x + 18y = 144/5
Subtract equations
62y = 496/3
y = 496/3/62
y = 8/3

Substitute y
6x + 10(8/3) = 364/15
6x = -12/5
x = -12/5/6
x = -2/5


Input:
Find x and y such that
7x + 6y = 42
10x + 7y = 158/3

Output:
7x + 6y = 42
10x + 7y = 158/3

Using elimination
10*(7x + 6y = 42)
7*(10x + 7y = 158/3)
70x + 60y = 420
70x + 49y = 1106/3
Subtract equations
11y = 154/3
y = 154/3/11
y = 14/3

Substitute y
7x + 6(14/3) = 42
7x = 14
x = 14/7
x = 2


Input:
Solve the equations:
9x + 3y = -41
7x + 2y = -266/9

Output:
9x + 3y = -41
7x + 2y = -266/9

Using elimination
7*(9x + 3y = -41)
9*(7x + 2y = -266/9)
63x + 21y = -287
63x + 18y = -266
Subtract equations
3y = -21
y = -21/3
y = -7

Substitute y
9x + 3(-7) = -41
9x = -20
x = -20/9
x = -20/9


Input: Compute the solution of x^2 - 39/20x + 9/10 = 0

Output:
x^2 - 39/20x + 9/10 = 0
(x - 6/5)(x - 3/4) = 0
x - 6/5 = 0  or  x - 3/4 = 0
x = 6/5
x = 3/4


Input: Solve the equation 2x - 4/5 = 0

Output:
2x - 4/5 = 0
2x = 4/5
x = 4/5 / 2
x = 2/5


Input:
Solve the equations:
7x + 6y = -121/2
1x + 5y = -47/4

Output:
7x + 6y = -121/2
1x + 5y = -47/4

Using elimination
1*(7x + 6y = -121/2)
7*(1x + 5y = -47/4)
7x + 6y = -121/2
7x + 35y = -329/4
Subtract equations
-29y = 87/4
y = 87/4/-29
y = -3/4

Substitute y
7x + 6(-3/4) = -121/2
7x = -56
x = -56/7
x = -8


Input: Solve x^2 - 45/14x + 25/14 = 0

Output:
x^2 - 45/14x + 25/14 = 0
(x - 5/2)(x - 5/7) = 0
x - 5/2 = 0  or  x - 5/7 = 0
x = 5/2
x = 5/7


Input: Solve the equation 6x - 15 = 0

Output:
6x - 15 = 0
6x = 15
x = 15 / 6
x = 5/2


Input:
Solve simultaneously:
8x + 10y = 64/5
8x + 6y = 64/5

Output:
8x + 10y = 64/5
8x + 6y = 64/5

Using elimination
8*(8x + 10y = 64/5)
8*(8x + 6y = 64/5)
64x + 80y = 512/5
64x + 48y = 512/5
Subtract equations
32y = 0
y = 0/32
y = 0

Substitute y
8x + 10(0) = 64/5
8x = 64/5
x = 64/5/8
x = 8/5


Input:
Solve the system:
1x + 3y = 236/45
1x + 6y = 452/45

Output:
1x + 3y = 236/45
1x + 6y = 452/45

Using elimination
1*(1x + 3y = 236/45)
1*(1x + 6y = 452/45)
1x + 3y = 236/45
1x + 6y = 452/45
Subtract equations
-3y = -24/5
y = -24/5/-3
y = 8/5

Substitute y
1x + 3(8/5) = 236/45
1x = 4/9
x = 4/9/1
x = 4/9


Input: Determine x in 7x - 35/3 = 0

Output:
7x - 35/3 = 0
7x = 35/3
x = 35/3 / 7
x = 5/3


Input: Solve x^2 - 101/45x + 4/5 = 0

Output:
x^2 - 101/45x + 4/5 = 0
(x - 4/9)(x - 9/5) = 0
x - 4/9 = 0  or  x - 9/5 = 0
x = 4/9
x = 9/5


Input: What value of x satisfies x^2 - 37/10x - 6/5 = 0

Output:
x^2 - 37/10x - 6/5 = 0
(x - -3/10)(x - 4) = 0
x - -3/10 = 0  or  x - 4 = 0
x = -3/10
x = 4


Input: What value of x satisfies x^2 - 125/72x + 13/72 = 0

Output:
x^2 - 125/72x + 13/72 = 0
(x - 13/8)(x - 1/9) = 0
x - 13/8 = 0  or  x - 1/9 = 0
x = 13/8
x = 1/9


Input: What value of x satisfies 5x + 20 = 0

Output:
5x + 20 = 0
5x = -20
x = -20 / 5
x = -4


Input: Determine x in x^3 - 13/2x^2 - 77/2x + 95 = 0

Output:
x^3 - 13/2x^2 - 77/2x + 95 = 0
(x - 2)(x - 19/2)(x - -5) = 0
x - 2 = 0
x - 19/2 = 0
x - -5 = 0
x = 2
x = 19/2
x = -5


Input:
Find x and y such that
7x + 9y = 75/4
10x + 3y = 117/4

Output:
7x + 9y = 75/4
10x + 3y = 117/4

Using elimination
10*(7x + 9y = 75/4)
7*(10x + 3y = 117/4)
70x + 90y = 375/2
70x + 21y = 819/4
Subtract equations
69y = -69/4
y = -69/4/69
y = -1/4

Substitute y
7x + 9(-1/4) = 75/4
7x = 21
x = 21/7
x = 3


Input: Solve quickly: x^2 + 137/10x - 21/5 = 0

Output:
x^2 + 137/10x - 21/5 = 0
(x - 3/10)(x - -14) = 0
x - 3/10 = 0  or  x - -14 = 0
x = 3/10
x = -14


Input: Solve quickly: x^2 + 31/10x + 3/10 = 0

Output:
x^2 + 31/10x + 3/10 = 0
(x - -3)(x - -1/10) = 0
x - -3 = 0  or  x - -1/10 = 0
x = -3
x = -1/10


Input:
Solve simultaneously:
3x + 10y = -117/7
1x + 9y = -141/7

Output:
3x + 10y = -117/7
1x + 9y = -141/7

Using elimination
1*(3x + 10y = -117/7)
3*(1x + 9y = -141/7)
3x + 10y = -117/7
3x + 27y = -423/7
Subtract equations
-17y = 306/7
y = 306/7/-17
y = -18/7

Substitute y
3x + 10(-18/7) = -117/7
3x = 9
x = 9/3
x = 3


Input: Compute the solution of x^2 + 15/2x - 54 = 0

Output:
x^2 + 15/2x - 54 = 0
(x - 9/2)(x - -12) = 0
x - 9/2 = 0  or  x - -12 = 0
x = 9/2
x = -12


Input: Find x in x^3 - 215/9x^2 + 883/9x + 323 = 0

Output:
x^3 - 215/9x^2 + 883/9x + 323 = 0
(x - 17)(x - -19/9)(x - 9) = 0
x - 17 = 0
x - -19/9 = 0
x - 9 = 0
x = 17
x = -19/9
x = 9


Input: Compute the solution of 6x + 30/7 = 0

Output:
6x + 30/7 = 0
6x = -30/7
x = -30/7 / 6
x = -5/7


Input:
Find x and y such that
1x + 5y = 45/4
6x + 10y = 65/2

Output:
1x + 5y = 45/4
6x + 10y = 65/2

Using elimination
6*(1x + 5y = 45/4)
1*(6x + 10y = 65/2)
6x + 30y = 135/2
6x + 10y = 65/2
Subtract equations
20y = 35
y = 35/20
y = 7/4

Substitute y
1x + 5(7/4) = 45/4
1x = 5/2
x = 5/2/1
x = 5/2


Input:
Solve the equations:
9x + 7y = 55/2
1x + 4y = 19/2

Output:
9x + 7y = 55/2
1x + 4y = 19/2

Using elimination
1*(9x + 7y = 55/2)
9*(1x + 4y = 19/2)
9x + 7y = 55/2
9x + 36y = 171/2
Subtract equations
-29y = -58
y = -58/-29
y = 2

Substitute y
9x + 7(2) = 55/2
9x = 27/2
x = 27/2/9
x = 3/2


Input:
Solve simultaneously:
9x + 7y = -84
7x + 4y = -445/9

Output:
9x + 7y = -84
7x + 4y = -445/9

Using elimination
7*(9x + 7y = -84)
9*(7x + 4y = -445/9)
63x + 49y = -588
63x + 36y = -445
Subtract equations
13y = -143
y = -143/13
y = -11

Substitute y
9x + 7(-11) = -84
9x = -7
x = -7/9
x = -7/9


Input:
Solve simultaneously:
8x + 5y = 545/8
10x + 9y = 629/8

Output:
8x + 5y = 545/8
10x + 9y = 629/8

Using elimination
10*(8x + 5y = 545/8)
8*(10x + 9y = 629/8)
80x + 50y = 2725/4
80x + 72y = 629
Subtract equations
-22y = 209/4
y = 209/4/-22
y = -19/8

Substitute y
8x + 5(-19/8) = 545/8
8x = 80
x = 80/8
x = 10


Input: Solve the equation 6x + 54/5 = 0

Output:
6x + 54/5 = 0
6x = -54/5
x = -54/5 / 6
x = -9/5


Input: What value of x satisfies x^3 + 17/2x^2 - 10x - 112 = 0

Output:
x^3 + 17/2x^2 - 10x - 112 = 0
(x - 7/2)(x - -8)(x - -4) = 0
x - 7/2 = 0
x - -8 = 0
x - -4 = 0
x = 7/2
x = -8
x = -4


Input: Find the solution to x^3 - 59/14x^2 + 1023/175x - 468/175 = 0

Output:
x^3 - 59/14x^2 + 1023/175x - 468/175 = 0
(x - 12/7)(x - 6/5)(x - 13/10) = 0
x - 12/7 = 0
x - 6/5 = 0
x - 13/10 = 0
x = 12/7
x = 6/5
x = 13/10


Input:
Solve the system:
5x + 3y = 119/6
10x + 10y = 215/3

Output:
5x + 3y = 119/6
10x + 10y = 215/3

Using elimination
10*(5x + 3y = 119/6)
5*(10x + 10y = 215/3)
50x + 30y = 595/3
50x + 50y = 1075/3
Subtract equations
-20y = -160
y = -160/-20
y = 8

Substitute y
5x + 3(8) = 119/6
5x = -25/6
x = -25/6/5
x = -5/6


Input: Find x in x^2 - 3/2x - 1 = 0

Output:
x^2 - 3/2x - 1 = 0
(x - -1/2)(x - 2) = 0
x - -1/2 = 0  or  x - 2 = 0
x = -1/2
x = 2


Input: Compute the solution of x^3 + 13/5x^2 - 57/20x - 99/20 = 0

Output:
x^3 + 13/5x^2 - 57/20x - 99/20 = 0
(x - -3)(x - -11/10)(x - 3/2) = 0
x - -3 = 0
x - -11/10 = 0
x - 3/2 = 0
x = -3
x = -11/10
x = 3/2


Input: Find x for x^2 + 79/20x + 3/4 = 0

Output:
x^2 + 79/20x + 3/4 = 0
(x - -1/5)(x - -15/4) = 0
x - -1/5 = 0  or  x - -15/4 = 0
x = -1/5
x = -15/4


Input: Find x in x^2 - 35/2x + 153/2 = 0

Output:
x^2 - 35/2x + 153/2 = 0
(x - 17/2)(x - 9) = 0
x - 17/2 = 0  or  x - 9 = 0
x = 17/2
x = 9


Input: Determine x in x^2 + 21/4x + 19/8 = 0

Output:
x^2 + 21/4x + 19/8 = 0
(x - -19/4)(x - -1/2) = 0
x - -19/4 = 0  or  x - -1/2 = 0
x = -19/4
x = -1/2


Input: Compute the solution of 6x - 12 = 0

Output:
6x - 12 = 0
6x = 12
x = 12 / 6
x = 2


Input: Compute the solution of 8x + 14 = 0

Output:
8x + 14 = 0
8x = -14
x = -14 / 8
x = -7/4


Input: Solve quickly: 7x + 105/4 = 0

Output:
7x + 105/4 = 0
7x = -105/4
x = -105/4 / 7
x = -15/4


Input: Solve x^2 - 144/7x + 80/7 = 0

Output:
x^2 - 144/7x + 80/7 = 0
(x - 4/7)(x - 20) = 0
x - 4/7 = 0  or  x - 20 = 0
x = 4/7
x = 20


Input:
Solve simultaneously:
10x + 6y = 74/3
4x + 2y = 20/3

Output:
10x + 6y = 74/3
4x + 2y = 20/3

Using elimination
4*(10x + 6y = 74/3)
10*(4x + 2y = 20/3)
40x + 24y = 296/3
40x + 20y = 200/3
Subtract equations
4y = 32
y = 32/4
y = 8

Substitute y
10x + 6(8) = 74/3
10x = -70/3
x = -70/3/10
x = -7/3


Input: Find the solution to 5x - 2 = 0

Output:
5x - 2 = 0
5x = 2
x = 2 / 5
x = 2/5


Input: Compute the solution of x^3 + 11/2x^2 - 15x - 63/2 = 0

Output:
x^3 + 11/2x^2 - 15x - 63/2 = 0
(x - 3)(x - -3/2)(x - -7) = 0
x - 3 = 0
x - -3/2 = 0
x - -7 = 0
x = 3
x = -3/2
x = -7


Input: Solve the equation 9x - 18 = 0

Output:
9x - 18 = 0
9x = 18
x = 18 / 9
x = 2


Input: What value of x satisfies x^2 + 9/10x - 18/5 = 0

Output:
x^2 + 9/10x - 18/5 = 0
(x - 3/2)(x - -12/5) = 0
x - 3/2 = 0  or  x - -12/5 = 0
x = 3/2
x = -12/5


Input: Find the solution to x^2 + 10/3x - 19 = 0

Output:
x^2 + 10/3x - 19 = 0
(x - 3)(x - -19/3) = 0
x - 3 = 0  or  x - -19/3 = 0
x = 3
x = -19/3


Input: Find x in x^2 + 64/15x - 119/15 = 0

Output:
x^2 + 64/15x - 119/15 = 0
(x - -17/3)(x - 7/5) = 0
x - -17/3 = 0  or  x - 7/5 = 0
x = -17/3
x = 7/5


Input: Find x in x^3 - 191/12x^2 + 407/6x - 260/3 = 0

Output:
x^3 - 191/12x^2 + 407/6x - 260/3 = 0
(x - 13/4)(x - 8/3)(x - 10) = 0
x - 13/4 = 0
x - 8/3 = 0
x - 10 = 0
x = 13/4
x = 8/3
x = 10


Input: Solve 3x  = 0

Output:
3x  = 0
3x = 0
x = 0 / 3
x = 0


Input:
Solve the equations:
6x + 7y = 79
4x + 8y = 332/7

Output:
6x + 7y = 79
4x + 8y = 332/7

Using elimination
4*(6x + 7y = 79)
6*(4x + 8y = 332/7)
24x + 28y = 316
24x + 48y = 1992/7
Subtract equations
-20y = 220/7
y = 220/7/-20
y = -11/7

Substitute y
6x + 7(-11/7) = 79
6x = 90
x = 90/6
x = 15


Input:
Solve simultaneously:
2x + 3y = -33/2
9x + 1y = -47/4

Output:
2x + 3y = -33/2
9x + 1y = -47/4

Using elimination
9*(2x + 3y = -33/2)
2*(9x + 1y = -47/4)
18x + 27y = -297/2
18x + 2y = -47/2
Subtract equations
25y = -125
y = -125/25
y = -5

Substitute y
2x + 3(-5) = -33/2
2x = -3/2
x = -3/2/2
x = -3/4


Input: Find x in x^2 + 67/15x + 24/5 = 0

Output:
x^2 + 67/15x + 24/5 = 0
(x - -8/3)(x - -9/5) = 0
x - -8/3 = 0  or  x - -9/5 = 0
x = -8/3
x = -9/5


Input: Compute the solution of 8x - 40/7 = 0

Output:
8x - 40/7 = 0
8x = 40/7
x = 40/7 / 8
x = 5/7


Input: Find x in 6x - 12 = 0

Output:
6x - 12 = 0
6x = 12
x = 12 / 6
x = 2


Input:
Solve the system:
6x + 10y = -70
2x + 4y = -22

Output:
6x + 10y = -70
2x + 4y = -22

Using elimination
2*(6x + 10y = -70)
6*(2x + 4y = -22)
12x + 20y = -140
12x + 24y = -132
Subtract equations
-4y = -8
y = -8/-4
y = 2

Substitute y
6x + 10(2) = -70
6x = -90
x = -90/6
x = -15


Input: Find x in x^2 + 41/40x - 9/80 = 0

Output:
x^2 + 41/40x - 9/80 = 0
(x - 1/10)(x - -9/8) = 0
x - 1/10 = 0  or  x - -9/8 = 0
x = 1/10
x = -9/8


Input: Solve quickly: 8x - 3 = 0

Output:
8x - 3 = 0
8x = 3
x = 3 / 8
x = 3/8


Input: What value of x satisfies 1x + 19/4 = 0

Output:
1x + 19/4 = 0
1x = -19/4
x = -19/4 / 1
x = -19/4


Input: Find x in 3x + 51/7 = 0

Output:
3x + 51/7 = 0
3x = -51/7
x = -51/7 / 3
x = -17/7


Input: Determine x in 1x + 5/2 = 0

Output:
1x + 5/2 = 0
1x = -5/2
x = -5/2 / 1
x = -5/2


Input: Solve quickly: 6x + 3 = 0

Output:
6x + 3 = 0
6x = -3
x = -3 / 6
x = -1/2


Input: Find x for x^3 + 237/40x^2 + 4619/400x + 741/100 = 0

Output:
x^3 + 237/40x^2 + 4619/400x + 741/100 = 0
(x - -13/8)(x - -12/5)(x - -19/10) = 0
x - -13/8 = 0
x - -12/5 = 0
x - -19/10 = 0
x = -13/8
x = -12/5
x = -19/10


Input:
Solve the system:
7x + 8y = -59/9
3x + 8y = -71/9

Output:
7x + 8y = -59/9
3x + 8y = -71/9

Using elimination
3*(7x + 8y = -59/9)
7*(3x + 8y = -71/9)
21x + 24y = -59/3
21x + 56y = -497/9
Subtract equations
-32y = 320/9
y = 320/9/-32
y = -10/9

Substitute y
7x + 8(-10/9) = -59/9
7x = 7/3
x = 7/3/7
x = 1/3


Input: Solve the equation x^2 + 99/14x - 45/14 = 0

Output:
x^2 + 99/14x - 45/14 = 0
(x - 3/7)(x - -15/2) = 0
x - 3/7 = 0  or  x - -15/2 = 0
x = 3/7
x = -15/2


Input: Compute the solution of x^3 + 361/42x^2 + 479/42x + 5/3 = 0

Output:
x^3 + 361/42x^2 + 479/42x + 5/3 = 0
(x - -7)(x - -1/6)(x - -10/7) = 0
x - -7 = 0
x - -1/6 = 0
x - -10/7 = 0
x = -7
x = -1/6
x = -10/7


Input: Solve the equation x^3 + 73/72x^2 - 15/8x + 7/36 = 0

Output:
x^3 + 73/72x^2 - 15/8x + 7/36 = 0
(x - -2)(x - 7/8)(x - 1/9) = 0
x - -2 = 0
x - 7/8 = 0
x - 1/9 = 0
x = -2
x = 7/8
x = 1/9


Input: Find x for 2x + 1 = 0

Output:
2x + 1 = 0
2x = -1
x = -1 / 2
x = -1/2


Input:
Solve the equations:
3x + 5y = -19
5x + 1y = -217/5

Output:
3x + 5y = -19
5x + 1y = -217/5

Using elimination
5*(3x + 5y = -19)
3*(5x + 1y = -217/5)
15x + 25y = -95
15x + 3y = -651/5
Subtract equations
22y = 176/5
y = 176/5/22
y = 8/5

Substitute y
3x + 5(8/5) = -19
3x = -27
x = -27/3
x = -9


Input: Solve x^2 - 7/2x + 5/2 = 0

Output:
x^2 - 7/2x + 5/2 = 0
(x - 1)(x - 5/2) = 0
x - 1 = 0  or  x - 5/2 = 0
x = 1
x = 5/2


Input: Solve quickly: x^3 + 8/3x^2 - 25/12x - 25/4 = 0

Output:
x^3 + 8/3x^2 - 25/12x - 25/4 = 0
(x - -5/3)(x - 3/2)(x - -5/2) = 0
x - -5/3 = 0
x - 3/2 = 0
x - -5/2 = 0
x = -5/3
x = 3/2
x = -5/2


Input:
Find x and y such that
10x + 3y = -107/21
6x + 7y = 499/63

Output:
10x + 3y = -107/21
6x + 7y = 499/63

Using elimination
6*(10x + 3y = -107/21)
10*(6x + 7y = 499/63)
60x + 18y = -214/7
60x + 70y = 4990/63
Subtract equations
-52y = -988/9
y = -988/9/-52
y = 19/9

Substitute y
10x + 3(19/9) = -107/21
10x = -80/7
x = -80/7/10
x = -8/7


Input:
Solve the system:
1x + 6y = -4/7
8x + 6y = 94/7

Output:
1x + 6y = -4/7
8x + 6y = 94/7

Using elimination
8*(1x + 6y = -4/7)
1*(8x + 6y = 94/7)
8x + 48y = -32/7
8x + 6y = 94/7
Subtract equations
42y = -18
y = -18/42
y = -3/7

Substitute y
1x + 6(-3/7) = -4/7
1x = 2
x = 2/1
x = 2


Input: Solve quickly: x^3 - 67/6x^2 + 27x - 40/3 = 0

Output:
x^3 - 67/6x^2 + 27x - 40/3 = 0
(x - 2/3)(x - 8)(x - 5/2) = 0
x - 2/3 = 0
x - 8 = 0
x - 5/2 = 0
x = 2/3
x = 8
x = 5/2


Input: Solve quickly: x^3 + 3/40x^2 - 109/160x - 21/160 = 0

Output:
x^3 + 3/40x^2 - 109/160x - 21/160 = 0
(x - -1/5)(x - 7/8)(x - -3/4) = 0
x - -1/5 = 0
x - 7/8 = 0
x - -3/4 = 0
x = -1/5
x = 7/8
x = -3/4


Input:
Solve simultaneously:
1x + 2y = 7/2
5x + 1y = -101/4

Output:
1x + 2y = 7/2
5x + 1y = -101/4

Using elimination
5*(1x + 2y = 7/2)
1*(5x + 1y = -101/4)
5x + 10y = 35/2
5x + 1y = -101/4
Subtract equations
9y = 171/4
y = 171/4/9
y = 19/4

Substitute y
1x + 2(19/4) = 7/2
1x = -6
x = -6/1
x = -6


Input: Solve quickly: x^3 + 81/35x^2 - 264/7x + 2176/35 = 0

Output:
x^3 + 81/35x^2 - 264/7x + 2176/35 = 0
(x - 16/7)(x - -8)(x - 17/5) = 0
x - 16/7 = 0
x - -8 = 0
x - 17/5 = 0
x = 16/7
x = -8
x = 17/5


Input: Find the solution to 8x - 52/3 = 0

Output:
8x - 52/3 = 0
8x = 52/3
x = 52/3 / 8
x = 13/6


Input:
Solve the equations:
7x + 8y = 19/2
10x + 1y = -123/4

Output:
7x + 8y = 19/2
10x + 1y = -123/4

Using elimination
10*(7x + 8y = 19/2)
7*(10x + 1y = -123/4)
70x + 80y = 95
70x + 7y = -861/4
Subtract equations
73y = 1241/4
y = 1241/4/73
y = 17/4

Substitute y
7x + 8(17/4) = 19/2
7x = -49/2
x = -49/2/7
x = -7/2


Input: Solve the equation x^2 + 93/10x - 19/10 = 0

Output:
x^2 + 93/10x - 19/10 = 0
(x - 1/5)(x - -19/2) = 0
x - 1/5 = 0  or  x - -19/2 = 0
x = 1/5
x = -19/2


Input:
Solve simultaneously:
3x + 4y = 30/7
9x + 8y = 27/7

Output:
3x + 4y = 30/7
9x + 8y = 27/7

Using elimination
9*(3x + 4y = 30/7)
3*(9x + 8y = 27/7)
27x + 36y = 270/7
27x + 24y = 81/7
Subtract equations
12y = 27
y = 27/12
y = 9/4

Substitute y
3x + 4(9/4) = 30/7
3x = -33/7
x = -33/7/3
x = -11/7


Input: Find x in x^2 + 21/8x - 9/8 = 0

Output:
x^2 + 21/8x - 9/8 = 0
(x - -3)(x - 3/8) = 0
x - -3 = 0  or  x - 3/8 = 0
x = -3
x = 3/8


Input: Solve x^3 - 35/72x^2 - 247/72x  = 0

Output:
x^3 - 35/72x^2 - 247/72x  = 0
(x - 19/9)(x - -13/8)(x - 0) = 0
x - 19/9 = 0
x - -13/8 = 0
x - 0 = 0
x = 19/9
x = -13/8
x = 0


Input: Solve quickly: 6x - 12 = 0

Output:
6x - 12 = 0
6x = 12
x = 12 / 6
x = 2


Input: Determine x in x^2 + 1/5x - 22/5 = 0

Output:
x^2 + 1/5x - 22/5 = 0
(x - -11/5)(x - 2) = 0
x - -11/5 = 0  or  x - 2 = 0
x = -11/5
x = 2


Input: Find x in x^2 - 8/15x - 4/5 = 0

Output:
x^2 - 8/15x - 4/5 = 0
(x - -2/3)(x - 6/5) = 0
x - -2/3 = 0  or  x - 6/5 = 0
x = -2/3
x = 6/5


Input:
Solve the equations:
10x + 2y = 47/3
5x + 2y = 59/6

Output:
10x + 2y = 47/3
5x + 2y = 59/6

Using elimination
5*(10x + 2y = 47/3)
10*(5x + 2y = 59/6)
50x + 10y = 235/3
50x + 20y = 295/3
Subtract equations
-10y = -20
y = -20/-10
y = 2

Substitute y
10x + 2(2) = 47/3
10x = 35/3
x = 35/3/10
x = 7/6


Input: Solve quickly: x^3 + 2x^2 - 39/4x - 2261/108 = 0

Output:
x^3 + 2x^2 - 39/4x - 2261/108 = 0
(x - 19/6)(x - -7/3)(x - -17/6) = 0
x - 19/6 = 0
x - -7/3 = 0
x - -17/6 = 0
x = 19/6
x = -7/3
x = -17/6


Input: Find the solution to x^2 - 5/9x - 28/27 = 0

Output:
x^2 - 5/9x - 28/27 = 0
(x - 4/3)(x - -7/9) = 0
x - 4/3 = 0  or  x - -7/9 = 0
x = 4/3
x = -7/9


Input: Find the solution to 9x - 27/2 = 0

Output:
9x - 27/2 = 0
9x = 27/2
x = 27/2 / 9
x = 3/2


Input: Determine x in x^2 - 23/5x + 18/5 = 0

Output:
x^2 - 23/5x + 18/5 = 0
(x - 18/5)(x - 1) = 0
x - 18/5 = 0  or  x - 1 = 0
x = 18/5
x = 1


Input: Find the solution to x^2 + 13/4x + 5/2 = 0

Output:
x^2 + 13/4x + 5/2 = 0
(x - -2)(x - -5/4) = 0
x - -2 = 0  or  x - -5/4 = 0
x = -2
x = -5/4


Input: Solve the equation x^2 + 89/7x + 60/7 = 0

Output:
x^2 + 89/7x + 60/7 = 0
(x - -5/7)(x - -12) = 0
x - -5/7 = 0  or  x - -12 = 0
x = -5/7
x = -12


Input: What value of x satisfies 7x  = 0

Output:
7x  = 0
7x = 0
x = 0 / 7
x = 0


Input: What value of x satisfies x^3 + 127/70x^2 - 717/490x - 216/245 = 0

Output:
x^3 + 127/70x^2 - 717/490x - 216/245 = 0
(x - 9/10)(x - -3/7)(x - -16/7) = 0
x - 9/10 = 0
x - -3/7 = 0
x - -16/7 = 0
x = 9/10
x = -3/7
x = -16/7


Input: Solve the equation x^2 - 23/18x - 55/54 = 0

Output:
x^2 - 23/18x - 55/54 = 0
(x - -5/9)(x - 11/6) = 0
x - -5/9 = 0  or  x - 11/6 = 0
x = -5/9
x = 11/6


Input: Find the solution to 5x + 50/9 = 0

Output:
5x + 50/9 = 0
5x = -50/9
x = -50/9 / 5
x = -10/9


Input:
Solve simultaneously:
3x + 9y = 4
3x + 4y = 7/3

Output:
3x + 9y = 4
3x + 4y = 7/3

Using elimination
3*(3x + 9y = 4)
3*(3x + 4y = 7/3)
9x + 27y = 12
9x + 12y = 7
Subtract equations
15y = 5
y = 5/15
y = 1/3

Substitute y
3x + 9(1/3) = 4
3x = 1
x = 1/3
x = 1/3


Input: Solve quickly: x^2 + 41/9x + 14/3 = 0

Output:
x^2 + 41/9x + 14/3 = 0
(x - -14/9)(x - -3) = 0
x - -14/9 = 0  or  x - -3 = 0
x = -14/9
x = -3


Input: Find x in x^3 + 3/2x^2 - 3/2x - 1 = 0

Output:
x^3 + 3/2x^2 - 3/2x - 1 = 0
(x - -1/2)(x - -2)(x - 1) = 0
x - -1/2 = 0
x - -2 = 0
x - 1 = 0
x = -1/2
x = -2
x = 1


Input:
Find x and y such that
8x + 10y = 548/3
5x + 8y = 895/6

Output:
8x + 10y = 548/3
5x + 8y = 895/6

Using elimination
5*(8x + 10y = 548/3)
8*(5x + 8y = 895/6)
40x + 50y = 2740/3
40x + 64y = 3580/3
Subtract equations
-14y = -280
y = -280/-14
y = 20

Substitute y
8x + 10(20) = 548/3
8x = -52/3
x = -52/3/8
x = -13/6


Input: Compute the solution of x^2 - 3/2x  = 0

Output:
x^2 - 3/2x  = 0
(x - 0)(x - 3/2) = 0
x - 0 = 0  or  x - 3/2 = 0
x = 0
x = 3/2


Input: Find the solution to x^3 + 343/30x^2 + 115/6x + 38/5 = 0

Output:
x^3 + 343/30x^2 + 115/6x + 38/5 = 0
(x - -19/2)(x - -3/5)(x - -4/3) = 0
x - -19/2 = 0
x - -3/5 = 0
x - -4/3 = 0
x = -19/2
x = -3/5
x = -4/3


Input: Solve quickly: 7x + 14 = 0

Output:
7x + 14 = 0
7x = -14
x = -14 / 7
x = -2


Input: Solve x^3 + 22/9x^2 + 4/27x - 40/27 = 0

Output:
x^3 + 22/9x^2 + 4/27x - 40/27 = 0
(x - -10/9)(x - 2/3)(x - -2) = 0
x - -10/9 = 0
x - 2/3 = 0
x - -2 = 0
x = -10/9
x = 2/3
x = -2


Input:
Solve the equations:
9x + 9y = 315/4
7x + 5y = 185/4

Output:
9x + 9y = 315/4
7x + 5y = 185/4

Using elimination
7*(9x + 9y = 315/4)
9*(7x + 5y = 185/4)
63x + 63y = 2205/4
63x + 45y = 1665/4
Subtract equations
18y = 135
y = 135/18
y = 15/2

Substitute y
9x + 9(15/2) = 315/4
9x = 45/4
x = 45/4/9
x = 5/4


Input: What value of x satisfies x^3 - 299/126x^2 - 75/7x + 36/7 = 0

Output:
x^3 - 299/126x^2 - 75/7x + 36/7 = 0
(x - 4/9)(x - 9/2)(x - -18/7) = 0
x - 4/9 = 0
x - 9/2 = 0
x - -18/7 = 0
x = 4/9
x = 9/2
x = -18/7


Input: Determine x in x^3 + 9/10x^2 - 4x  = 0

Output:
x^3 + 9/10x^2 - 4x  = 0
(x - 8/5)(x - 0)(x - -5/2) = 0
x - 8/5 = 0
x - 0 = 0
x - -5/2 = 0
x = 8/5
x = 0
x = -5/2


Input:
Solve simultaneously:
4x + 3y = 16/3
4x + 1y = 56/3

Output:
4x + 3y = 16/3
4x + 1y = 56/3

Using elimination
4*(4x + 3y = 16/3)
4*(4x + 1y = 56/3)
16x + 12y = 64/3
16x + 4y = 224/3
Subtract equations
8y = -160/3
y = -160/3/8
y = -20/3

Substitute y
4x + 3(-20/3) = 16/3
4x = 76/3
x = 76/3/4
x = 19/3


Input: Solve the equation x^3 + 31/18x^2 - 143/18x + 14/3 = 0

Output:
x^3 + 31/18x^2 - 143/18x + 14/3 = 0
(x - 3/2)(x - -4)(x - 7/9) = 0
x - 3/2 = 0
x - -4 = 0
x - 7/9 = 0
x = 3/2
x = -4
x = 7/9


Input: Solve the equation x^2 - 7x + 12 = 0

Output:
x^2 - 7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 = 0  or  x - 3 = 0
x = 4
x = 3


Input: What value of x satisfies x^3 + 83/8x^2 + 423/16x + 315/16 = 0

Output:
x^3 + 83/8x^2 + 423/16x + 315/16 = 0
(x - -15/8)(x - -7)(x - -3/2) = 0
x - -15/8 = 0
x - -7 = 0
x - -3/2 = 0
x = -15/8
x = -7
x = -3/2