Input:
Solve the system:
7x + 4y = -163/5
10x + 7y = -256/5

Output:
7x + 4y = -163/5
10x + 7y = -256/5

Using elimination
10*(7x + 4y = -163/5)
7*(10x + 7y = -256/5)
70x + 40y = -326
70x + 49y = -1792/5
Subtract equations
-9y = 162/5
y = 162/5/-9
y = -18/5

Substitute y
7x + 4(-18/5) = -163/5
7x = -91/5
x = -91/5/7
x = -13/5


Input: Solve quickly: 5x - 10/9 = 0

Output:
5x - 10/9 = 0
5x = 10/9
x = 10/9 / 5
x = 2/9


Input: Find x in x^2 + 13/2x + 15/2 = 0

Output:
x^2 + 13/2x + 15/2 = 0
(x - -5)(x - -3/2) = 0
x - -5 = 0  or  x - -3/2 = 0
x = -5
x = -3/2


Input: Determine x in 5x - 95/3 = 0

Output:
5x - 95/3 = 0
5x = 95/3
x = 95/3 / 5
x = 19/3


Input: Solve quickly: 5x + 15 = 0

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


Input: Find the solution to x^2 - 2x - 8 = 0

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


Input: Solve quickly: x^2 - 50/3x - 17/3 = 0

Output:
x^2 - 50/3x - 17/3 = 0
(x - 17)(x - -1/3) = 0
x - 17 = 0  or  x - -1/3 = 0
x = 17
x = -1/3


Input:
Find x and y such that
10x + 8y = -247/12
10x + 9y = -87/4

Output:
10x + 8y = -247/12
10x + 9y = -87/4

Using elimination
10*(10x + 8y = -247/12)
10*(10x + 9y = -87/4)
100x + 80y = -1235/6
100x + 90y = -435/2
Subtract equations
-10y = 35/3
y = 35/3/-10
y = -7/6

Substitute y
10x + 8(-7/6) = -247/12
10x = -45/4
x = -45/4/10
x = -9/8


Input:
Solve the system:
9x + 1y = -149/4
5x + 6y = -67/6

Output:
9x + 1y = -149/4
5x + 6y = -67/6

Using elimination
5*(9x + 1y = -149/4)
9*(5x + 6y = -67/6)
45x + 5y = -745/4
45x + 54y = -201/2
Subtract equations
-49y = -343/4
y = -343/4/-49
y = 7/4

Substitute y
9x + 1(7/4) = -149/4
9x = -39
x = -39/9
x = -13/3


Input:
Find x and y such that
4x + 4y = 388/15
6x + 8y = 722/15

Output:
4x + 4y = 388/15
6x + 8y = 722/15

Using elimination
6*(4x + 4y = 388/15)
4*(6x + 8y = 722/15)
24x + 24y = 776/5
24x + 32y = 2888/15
Subtract equations
-8y = -112/3
y = -112/3/-8
y = 14/3

Substitute y
4x + 4(14/3) = 388/15
4x = 36/5
x = 36/5/4
x = 9/5


Input: Compute the solution of x^3 + 37/15x^2 - 236/15x + 68/5 = 0

Output:
x^3 + 37/15x^2 - 236/15x + 68/5 = 0
(x - 2)(x - -17/3)(x - 6/5) = 0
x - 2 = 0
x - -17/3 = 0
x - 6/5 = 0
x = 2
x = -17/3
x = 6/5


Input: Solve 4x + 26/3 = 0

Output:
4x + 26/3 = 0
4x = -26/3
x = -26/3 / 4
x = -13/6


Input:
Solve the system:
8x + 8y = 32/5
8x + 2y = -22/5

Output:
8x + 8y = 32/5
8x + 2y = -22/5

Using elimination
8*(8x + 8y = 32/5)
8*(8x + 2y = -22/5)
64x + 64y = 256/5
64x + 16y = -176/5
Subtract equations
48y = 432/5
y = 432/5/48
y = 9/5

Substitute y
8x + 8(9/5) = 32/5
8x = -8
x = -8/8
x = -1


Input: Find the solution to x^2 + 89/5x - 18/5 = 0

Output:
x^2 + 89/5x - 18/5 = 0
(x - -18)(x - 1/5) = 0
x - -18 = 0  or  x - 1/5 = 0
x = -18
x = 1/5


Input:
Solve simultaneously:
1x + 4y = -56/9
9x + 1y = 91/9

Output:
1x + 4y = -56/9
9x + 1y = 91/9

Using elimination
9*(1x + 4y = -56/9)
1*(9x + 1y = 91/9)
9x + 36y = -56
9x + 1y = 91/9
Subtract equations
35y = -595/9
y = -595/9/35
y = -17/9

Substitute y
1x + 4(-17/9) = -56/9
1x = 4/3
x = 4/3/1
x = 4/3


Input: Find the solution to x^2 - 44/3x + 140/3 = 0

Output:
x^2 - 44/3x + 140/3 = 0
(x - 14/3)(x - 10) = 0
x - 14/3 = 0  or  x - 10 = 0
x = 14/3
x = 10


Input: Solve the equation 6x + 6 = 0

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


Input: What value of x satisfies x^2 - 81/14x + 8 = 0

Output:
x^2 - 81/14x + 8 = 0
(x - 7/2)(x - 16/7) = 0
x - 7/2 = 0  or  x - 16/7 = 0
x = 7/2
x = 16/7


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

Output:
x^2 + 13/3x - 3/4 = 0
(x - 1/6)(x - -9/2) = 0
x - 1/6 = 0  or  x - -9/2 = 0
x = 1/6
x = -9/2


Input:
Solve the system:
6x + 3y = -166/5
8x + 8y = -688/15

Output:
6x + 3y = -166/5
8x + 8y = -688/15

Using elimination
8*(6x + 3y = -166/5)
6*(8x + 8y = -688/15)
48x + 24y = -1328/5
48x + 48y = -1376/5
Subtract equations
-24y = 48/5
y = 48/5/-24
y = -2/5

Substitute y
6x + 3(-2/5) = -166/5
6x = -32
x = -32/6
x = -16/3


Input: Compute the solution of 2x - 15/2 = 0

Output:
2x - 15/2 = 0
2x = 15/2
x = 15/2 / 2
x = 15/4


Input: What value of x satisfies 3x + 27/2 = 0

Output:
3x + 27/2 = 0
3x = -27/2
x = -27/2 / 3
x = -9/2


Input: Compute the solution of x^2 + 14/15x - 16/15 = 0

Output:
x^2 + 14/15x - 16/15 = 0
(x - -8/5)(x - 2/3) = 0
x - -8/5 = 0  or  x - 2/3 = 0
x = -8/5
x = 2/3


Input: Find x for x^3 + 37/2x^2 + 1643/64x + 187/64 = 0

Output:
x^3 + 37/2x^2 + 1643/64x + 187/64 = 0
(x - -11/8)(x - -1/8)(x - -17) = 0
x - -11/8 = 0
x - -1/8 = 0
x - -17 = 0
x = -11/8
x = -1/8
x = -17


Input: Find x in x^3 - 187/72x^2 + 265/144x - 7/24 = 0

Output:
x^3 - 187/72x^2 + 265/144x - 7/24 = 0
(x - 3/2)(x - 7/8)(x - 2/9) = 0
x - 3/2 = 0
x - 7/8 = 0
x - 2/9 = 0
x = 3/2
x = 7/8
x = 2/9


Input: Find x in x^3 + 47/15x^2 - 157/60x - 13/2 = 0

Output:
x^3 + 47/15x^2 - 157/60x - 13/2 = 0
(x - 3/2)(x - -13/10)(x - -10/3) = 0
x - 3/2 = 0
x - -13/10 = 0
x - -10/3 = 0
x = 3/2
x = -13/10
x = -10/3


Input: Compute the solution of x^2 - 46/9x - 16/3 = 0

Output:
x^2 - 46/9x - 16/3 = 0
(x - 6)(x - -8/9) = 0
x - 6 = 0  or  x - -8/9 = 0
x = 6
x = -8/9


Input: Solve x^3 - 71/15x^2 + 446/75x - 112/75 = 0

Output:
x^3 - 71/15x^2 + 446/75x - 112/75 = 0
(x - 1/3)(x - 14/5)(x - 8/5) = 0
x - 1/3 = 0
x - 14/5 = 0
x - 8/5 = 0
x = 1/3
x = 14/5
x = 8/5


Input: Compute the solution of x^2 - 31/45x - 34/15 = 0

Output:
x^2 - 31/45x - 34/15 = 0
(x - -6/5)(x - 17/9) = 0
x - -6/5 = 0  or  x - 17/9 = 0
x = -6/5
x = 17/9


Input: What value of x satisfies 1x + 2 = 0

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


Input:
Solve the system:
10x + 3y = 191/7
10x + 7y = 219/7

Output:
10x + 3y = 191/7
10x + 7y = 219/7

Using elimination
10*(10x + 3y = 191/7)
10*(10x + 7y = 219/7)
100x + 30y = 1910/7
100x + 70y = 2190/7
Subtract equations
-40y = -40
y = -40/-40
y = 1

Substitute y
10x + 3(1) = 191/7
10x = 170/7
x = 170/7/10
x = 17/7


Input: Find the solution to 2x - 2/3 = 0

Output:
2x - 2/3 = 0
2x = 2/3
x = 2/3 / 2
x = 1/3


Input: Find x for 3x - 54/7 = 0

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


Input:
Solve simultaneously:
7x + 10y = 654/35
10x + 10y = 114/7

Output:
7x + 10y = 654/35
10x + 10y = 114/7

Using elimination
10*(7x + 10y = 654/35)
7*(10x + 10y = 114/7)
70x + 100y = 1308/7
70x + 70y = 114
Subtract equations
30y = 510/7
y = 510/7/30
y = 17/7

Substitute y
7x + 10(17/7) = 654/35
7x = -28/5
x = -28/5/7
x = -4/5


Input:
Solve the equations:
3x + 6y = 30
1x + 6y = 34

Output:
3x + 6y = 30
1x + 6y = 34

Using elimination
1*(3x + 6y = 30)
3*(1x + 6y = 34)
3x + 6y = 30
3x + 18y = 102
Subtract equations
-12y = -72
y = -72/-12
y = 6

Substitute y
3x + 6(6) = 30
3x = -6
x = -6/3
x = -2


Input: Determine x in x^3 - 93/5x^2 - 551/20x - 9 = 0

Output:
x^3 - 93/5x^2 - 551/20x - 9 = 0
(x - 20)(x - -9/10)(x - -1/2) = 0
x - 20 = 0
x - -9/10 = 0
x - -1/2 = 0
x = 20
x = -9/10
x = -1/2


Input: Find the solution to 9x + 12 = 0

Output:
9x + 12 = 0
9x = -12
x = -12 / 9
x = -4/3


Input: Compute the solution of x^2 + 21x + 80 = 0

Output:
x^2 + 21x + 80 = 0
(x - -16)(x - -5) = 0
x - -16 = 0  or  x - -5 = 0
x = -16
x = -5


Input: Find x in 6x + 10/3 = 0

Output:
6x + 10/3 = 0
6x = -10/3
x = -10/3 / 6
x = -5/9


Input: Solve 9x + 18 = 0

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


Input:
Solve the system:
4x + 2y = 44/15
9x + 1y = -187/30

Output:
4x + 2y = 44/15
9x + 1y = -187/30

Using elimination
9*(4x + 2y = 44/15)
4*(9x + 1y = -187/30)
36x + 18y = 132/5
36x + 4y = -374/15
Subtract equations
14y = 154/3
y = 154/3/14
y = 11/3

Substitute y
4x + 2(11/3) = 44/15
4x = -22/5
x = -22/5/4
x = -11/10


Input: Find x in x^2 - 49/12x + 49/12 = 0

Output:
x^2 - 49/12x + 49/12 = 0
(x - 7/3)(x - 7/4) = 0
x - 7/3 = 0  or  x - 7/4 = 0
x = 7/3
x = 7/4


Input: Solve quickly: x^3 - 11/21x^2 - 10x + 200/21 = 0

Output:
x^3 - 11/21x^2 - 10x + 200/21 = 0
(x - 20/7)(x - -10/3)(x - 1) = 0
x - 20/7 = 0
x - -10/3 = 0
x - 1 = 0
x = 20/7
x = -10/3
x = 1


Input:
Find x and y such that
3x + 1y = 29/3
2x + 5y = 67/3

Output:
3x + 1y = 29/3
2x + 5y = 67/3

Using elimination
2*(3x + 1y = 29/3)
3*(2x + 5y = 67/3)
6x + 2y = 58/3
6x + 15y = 67
Subtract equations
-13y = -143/3
y = -143/3/-13
y = 11/3

Substitute y
3x + 1(11/3) = 29/3
3x = 6
x = 6/3
x = 2


Input: Compute the solution of 8x - 18 = 0

Output:
8x - 18 = 0
8x = 18
x = 18 / 8
x = 9/4


Input:
Solve simultaneously:
5x + 1y = 31/21
8x + 6y = -122/21

Output:
5x + 1y = 31/21
8x + 6y = -122/21

Using elimination
8*(5x + 1y = 31/21)
5*(8x + 6y = -122/21)
40x + 8y = 248/21
40x + 30y = -610/21
Subtract equations
-22y = 286/7
y = 286/7/-22
y = -13/7

Substitute y
5x + 1(-13/7) = 31/21
5x = 10/3
x = 10/3/5
x = 2/3


Input: Determine x in x^3 + 13/18x^2 - 53/18x - 8/3 = 0

Output:
x^3 + 13/18x^2 - 53/18x - 8/3 = 0
(x - 16/9)(x - -1)(x - -3/2) = 0
x - 16/9 = 0
x - -1 = 0
x - -3/2 = 0
x = 16/9
x = -1
x = -3/2


Input:
Solve the system:
3x + 2y = -31
6x + 7y = -263/4

Output:
3x + 2y = -31
6x + 7y = -263/4

Using elimination
6*(3x + 2y = -31)
3*(6x + 7y = -263/4)
18x + 12y = -186
18x + 21y = -789/4
Subtract equations
-9y = 45/4
y = 45/4/-9
y = -5/4

Substitute y
3x + 2(-5/4) = -31
3x = -57/2
x = -57/2/3
x = -19/2


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

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


Input: Compute the solution of 9x + 45/8 = 0

Output:
9x + 45/8 = 0
9x = -45/8
x = -45/8 / 9
x = -5/8


Input: Determine x in x^3 + 233/28x^2 + 1283/56x + 585/28 = 0

Output:
x^3 + 233/28x^2 + 1283/56x + 585/28 = 0
(x - -18/7)(x - -5/2)(x - -13/4) = 0
x - -18/7 = 0
x - -5/2 = 0
x - -13/4 = 0
x = -18/7
x = -5/2
x = -13/4


Input: Solve quickly: 6x + 60 = 0

Output:
6x + 60 = 0
6x = -60
x = -60 / 6
x = -10


Input:
Solve simultaneously:
8x + 7y = -10
5x + 1y = -23/8

Output:
8x + 7y = -10
5x + 1y = -23/8

Using elimination
5*(8x + 7y = -10)
8*(5x + 1y = -23/8)
40x + 35y = -50
40x + 8y = -23
Subtract equations
27y = -27
y = -27/27
y = -1

Substitute y
8x + 7(-1) = -10
8x = -3
x = -3/8
x = -3/8


Input: Solve quickly: x^2 + 157/36x + 19/4 = 0

Output:
x^2 + 157/36x + 19/4 = 0
(x - -9/4)(x - -19/9) = 0
x - -9/4 = 0  or  x - -19/9 = 0
x = -9/4
x = -19/9


Input:
Solve the system:
5x + 8y = 293/8
9x + 7y = 335/8

Output:
5x + 8y = 293/8
9x + 7y = 335/8

Using elimination
9*(5x + 8y = 293/8)
5*(9x + 7y = 335/8)
45x + 72y = 2637/8
45x + 35y = 1675/8
Subtract equations
37y = 481/4
y = 481/4/37
y = 13/4

Substitute y
5x + 8(13/4) = 293/8
5x = 85/8
x = 85/8/5
x = 17/8


Input: Solve quickly: 1x - 3/2 = 0

Output:
1x - 3/2 = 0
1x = 3/2
x = 3/2 / 1
x = 3/2


Input: Find the solution to x^3 - 29/6x^2 - 55/2x + 325/3 = 0

Output:
x^3 - 29/6x^2 - 55/2x + 325/3 = 0
(x - -5)(x - 10/3)(x - 13/2) = 0
x - -5 = 0
x - 10/3 = 0
x - 13/2 = 0
x = -5
x = 10/3
x = 13/2


Input: Solve the equation 3x + 48/7 = 0

Output:
3x + 48/7 = 0
3x = -48/7
x = -48/7 / 3
x = -16/7


Input: Solve x^3 + 269/105x^2 + 142/105x - 8/21 = 0

Output:
x^3 + 269/105x^2 + 142/105x - 8/21 = 0
(x - 1/5)(x - -4/3)(x - -10/7) = 0
x - 1/5 = 0
x - -4/3 = 0
x - -10/7 = 0
x = 1/5
x = -4/3
x = -10/7


Input: Solve the equation x^3 + 16/5x^2 - 28/5x - 48/5 = 0

Output:
x^3 + 16/5x^2 - 28/5x - 48/5 = 0
(x - -6/5)(x - 2)(x - -4) = 0
x - -6/5 = 0
x - 2 = 0
x - -4 = 0
x = -6/5
x = 2
x = -4


Input: Solve x^2 + 21/5x - 54/5 = 0

Output:
x^2 + 21/5x - 54/5 = 0
(x - 9/5)(x - -6) = 0
x - 9/5 = 0  or  x - -6 = 0
x = 9/5
x = -6


Input:
Solve the equations:
4x + 5y = -655/8
6x + 4y = -243/2

Output:
4x + 5y = -655/8
6x + 4y = -243/2

Using elimination
6*(4x + 5y = -655/8)
4*(6x + 4y = -243/2)
24x + 30y = -1965/4
24x + 16y = -486
Subtract equations
14y = -21/4
y = -21/4/14
y = -3/8

Substitute y
4x + 5(-3/8) = -655/8
4x = -80
x = -80/4
x = -20


Input: Find x for x^3 + 221/10x^2 + 95x - 208/5 = 0

Output:
x^3 + 221/10x^2 + 95x - 208/5 = 0
(x - -16)(x - 2/5)(x - -13/2) = 0
x - -16 = 0
x - 2/5 = 0
x - -13/2 = 0
x = -16
x = 2/5
x = -13/2


Input:
Solve the system:
2x + 8y = -292/15
8x + 1y = -424/15

Output:
2x + 8y = -292/15
8x + 1y = -424/15

Using elimination
8*(2x + 8y = -292/15)
2*(8x + 1y = -424/15)
16x + 64y = -2336/15
16x + 2y = -848/15
Subtract equations
62y = -496/5
y = -496/5/62
y = -8/5

Substitute y
2x + 8(-8/5) = -292/15
2x = -20/3
x = -20/3/2
x = -10/3


Input: What value of x satisfies 8x - 104/3 = 0

Output:
8x - 104/3 = 0
8x = 104/3
x = 104/3 / 8
x = 13/3


Input: What value of x satisfies 1x + 11 = 0

Output:
1x + 11 = 0
1x = -11
x = -11 / 1
x = -11


Input: Find x for x^2 - 34/5x + 24/5 = 0

Output:
x^2 - 34/5x + 24/5 = 0
(x - 6)(x - 4/5) = 0
x - 6 = 0  or  x - 4/5 = 0
x = 6
x = 4/5


Input: Determine x in x^3 + 293/24x^2 + 691/16x + 2261/48 = 0

Output:
x^3 + 293/24x^2 + 691/16x + 2261/48 = 0
(x - -19/8)(x - -17/6)(x - -7) = 0
x - -19/8 = 0
x - -17/6 = 0
x - -7 = 0
x = -19/8
x = -17/6
x = -7


Input: Determine x in 10x - 6 = 0

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


Input:
Find x and y such that
3x + 9y = 177/14
2x + 4y = 38/7

Output:
3x + 9y = 177/14
2x + 4y = 38/7

Using elimination
2*(3x + 9y = 177/14)
3*(2x + 4y = 38/7)
6x + 18y = 177/7
6x + 12y = 114/7
Subtract equations
6y = 9
y = 9/6
y = 3/2

Substitute y
3x + 9(3/2) = 177/14
3x = -6/7
x = -6/7/3
x = -2/7


Input:
Find x and y such that
10x + 1y = -26
6x + 1y = -16

Output:
10x + 1y = -26
6x + 1y = -16

Using elimination
6*(10x + 1y = -26)
10*(6x + 1y = -16)
60x + 6y = -156
60x + 10y = -160
Subtract equations
-4y = 4
y = 4/-4
y = -1

Substitute y
10x + 1(-1) = -26
10x = -25
x = -25/10
x = -5/2


Input:
Solve the equations:
8x + 2y = 892/9
6x + 5y = 718/9

Output:
8x + 2y = 892/9
6x + 5y = 718/9

Using elimination
6*(8x + 2y = 892/9)
8*(6x + 5y = 718/9)
48x + 12y = 1784/3
48x + 40y = 5744/9
Subtract equations
-28y = -392/9
y = -392/9/-28
y = 14/9

Substitute y
8x + 2(14/9) = 892/9
8x = 96
x = 96/8
x = 12


Input: Solve x^3 - 233/72x^2 + 1379/648x + 5/18 = 0

Output:
x^3 - 233/72x^2 + 1379/648x + 5/18 = 0
(x - 9/8)(x - 20/9)(x - -1/9) = 0
x - 9/8 = 0
x - 20/9 = 0
x - -1/9 = 0
x = 9/8
x = 20/9
x = -1/9


Input: Solve x^3 - 775/36x^2 + 1777/36x - 76/3 = 0

Output:
x^3 - 775/36x^2 + 1777/36x - 76/3 = 0
(x - 19)(x - 3/4)(x - 16/9) = 0
x - 19 = 0
x - 3/4 = 0
x - 16/9 = 0
x = 19
x = 3/4
x = 16/9


Input: Solve the equation x^3 + 18/5x^2 - 1x - 18/5 = 0

Output:
x^3 + 18/5x^2 - 1x - 18/5 = 0
(x - -1)(x - 1)(x - -18/5) = 0
x - -1 = 0
x - 1 = 0
x - -18/5 = 0
x = -1
x = 1
x = -18/5


Input: Find x for 7x - 63/4 = 0

Output:
7x - 63/4 = 0
7x = 63/4
x = 63/4 / 7
x = 9/4


Input:
Solve the equations:
9x + 3y = -21
1x + 1y = -7

Output:
9x + 3y = -21
1x + 1y = -7

Using elimination
1*(9x + 3y = -21)
9*(1x + 1y = -7)
9x + 3y = -21
9x + 9y = -63
Subtract equations
-6y = 42
y = 42/-6
y = -7

Substitute y
9x + 3(-7) = -21
9x = 0
x = 0/9
x = 0


Input:
Solve the system:
5x + 2y = 53/63
8x + 1y = -23/63

Output:
5x + 2y = 53/63
8x + 1y = -23/63

Using elimination
8*(5x + 2y = 53/63)
5*(8x + 1y = -23/63)
40x + 16y = 424/63
40x + 5y = -115/63
Subtract equations
11y = 77/9
y = 77/9/11
y = 7/9

Substitute y
5x + 2(7/9) = 53/63
5x = -5/7
x = -5/7/5
x = -1/7


Input:
Solve the equations:
10x + 5y = 130/3
10x + 6y = 137/3

Output:
10x + 5y = 130/3
10x + 6y = 137/3

Using elimination
10*(10x + 5y = 130/3)
10*(10x + 6y = 137/3)
100x + 50y = 1300/3
100x + 60y = 1370/3
Subtract equations
-10y = -70/3
y = -70/3/-10
y = 7/3

Substitute y
10x + 5(7/3) = 130/3
10x = 95/3
x = 95/3/10
x = 19/6


Input: Solve 1x  = 0

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


Input: Find x for 6x - 6 = 0

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


Input: Compute the solution of x^2 + 35/6x + 13/2 = 0

Output:
x^2 + 35/6x + 13/2 = 0
(x - -13/3)(x - -3/2) = 0
x - -13/3 = 0  or  x - -3/2 = 0
x = -13/3
x = -3/2


Input: Solve the equation 1x + 1 = 0

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


Input: Find x for x^2 - 17/8x - 21/8 = 0

Output:
x^2 - 17/8x - 21/8 = 0
(x - 3)(x - -7/8) = 0
x - 3 = 0  or  x - -7/8 = 0
x = 3
x = -7/8


Input: Find x for x^2 + 21/2x + 19/2 = 0

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


Input: Find x for 9x - 9/10 = 0

Output:
9x - 9/10 = 0
9x = 9/10
x = 9/10 / 9
x = 1/10


Input: Determine x in x^3 + 221/28x^2 - 16/7x - 80/7 = 0

Output:
x^3 + 221/28x^2 - 16/7x - 80/7 = 0
(x - 5/4)(x - -8)(x - -8/7) = 0
x - 5/4 = 0
x - -8 = 0
x - -8/7 = 0
x = 5/4
x = -8
x = -8/7


Input: What value of x satisfies x^2 - 9x + 45/4 = 0

Output:
x^2 - 9x + 45/4 = 0
(x - 3/2)(x - 15/2) = 0
x - 3/2 = 0  or  x - 15/2 = 0
x = 3/2
x = 15/2


Input: Determine x in 5x + 90/7 = 0

Output:
5x + 90/7 = 0
5x = -90/7
x = -90/7 / 5
x = -18/7


Input: Solve 1x  = 0

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


Input: What value of x satisfies x^2 + 53/30x - 133/30 = 0

Output:
x^2 + 53/30x - 133/30 = 0
(x - 7/5)(x - -19/6) = 0
x - 7/5 = 0  or  x - -19/6 = 0
x = 7/5
x = -19/6


Input: Find the solution to x^3 + 136/15x^2 - 5x - 252/5 = 0

Output:
x^3 + 136/15x^2 - 5x - 252/5 = 0
(x - -12/5)(x - -9)(x - 7/3) = 0
x - -12/5 = 0
x - -9 = 0
x - 7/3 = 0
x = -12/5
x = -9
x = 7/3


Input:
Solve simultaneously:
8x + 5y = -83/4
4x + 4y = -7

Output:
8x + 5y = -83/4
4x + 4y = -7

Using elimination
4*(8x + 5y = -83/4)
8*(4x + 4y = -7)
32x + 20y = -83
32x + 32y = -56
Subtract equations
-12y = -27
y = -27/-12
y = 9/4

Substitute y
8x + 5(9/4) = -83/4
8x = -32
x = -32/8
x = -4


Input:
Solve the system:
3x + 10y = 188/3
1x + 7y = 125/3

Output:
3x + 10y = 188/3
1x + 7y = 125/3

Using elimination
1*(3x + 10y = 188/3)
3*(1x + 7y = 125/3)
3x + 10y = 188/3
3x + 21y = 125
Subtract equations
-11y = -187/3
y = -187/3/-11
y = 17/3

Substitute y
3x + 10(17/3) = 188/3
3x = 6
x = 6/3
x = 2


Input:
Find x and y such that
3x + 2y = -16/3
2x + 2y = -44/9

Output:
3x + 2y = -16/3
2x + 2y = -44/9

Using elimination
2*(3x + 2y = -16/3)
3*(2x + 2y = -44/9)
6x + 4y = -32/3
6x + 6y = -44/3
Subtract equations
-2y = 4
y = 4/-2
y = -2

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


Input: Find x for x^3 + 35/3x^2 - 316/3x + 156 = 0

Output:
x^3 + 35/3x^2 - 316/3x + 156 = 0
(x - 13/3)(x - -18)(x - 2) = 0
x - 13/3 = 0
x - -18 = 0
x - 2 = 0
x = 13/3
x = -18
x = 2


Input: Find x in x^2 - 20/9x - 32/27 = 0

Output:
x^2 - 20/9x - 32/27 = 0
(x - 8/3)(x - -4/9) = 0
x - 8/3 = 0  or  x - -4/9 = 0
x = 8/3
x = -4/9


Input: What value of x satisfies x^2 - 13/4x  = 0

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


Input: Find x for x^3 - 6x^2 + 11/4x  = 0

Output:
x^3 - 6x^2 + 11/4x  = 0
(x - 11/2)(x - 1/2)(x - 0) = 0
x - 11/2 = 0
x - 1/2 = 0
x - 0 = 0
x = 11/2
x = 1/2
x = 0


Input: Solve the equation x^2 - 61/36x + 5/9 = 0

Output:
x^2 - 61/36x + 5/9 = 0
(x - 5/4)(x - 4/9) = 0
x - 5/4 = 0  or  x - 4/9 = 0
x = 5/4
x = 4/9


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

Output:
x^2  - 9/16 = 0
(x - -3/4)(x - 3/4) = 0
x - -3/4 = 0  or  x - 3/4 = 0
x = -3/4
x = 3/4


Input: Solve quickly: 6x - 33/5 = 0

Output:
6x - 33/5 = 0
6x = 33/5
x = 33/5 / 6
x = 11/10


Input:
Solve the equations:
6x + 3y = -347/15
3x + 7y = -1043/45

Output:
6x + 3y = -347/15
3x + 7y = -1043/45

Using elimination
3*(6x + 3y = -347/15)
6*(3x + 7y = -1043/45)
18x + 9y = -347/5
18x + 42y = -2086/15
Subtract equations
-33y = 209/3
y = 209/3/-33
y = -19/9

Substitute y
6x + 3(-19/9) = -347/15
6x = -84/5
x = -84/5/6
x = -14/5


Input: Determine x in x^3 - 77/12x^2 - 229/2x - 855/4 = 0

Output:
x^3 - 77/12x^2 - 229/2x - 855/4 = 0
(x - 15)(x - -19/3)(x - -9/4) = 0
x - 15 = 0
x - -19/3 = 0
x - -9/4 = 0
x = 15
x = -19/3
x = -9/4


Input: Find the solution to x^3 + 31/3x^2 + 101/3x + 35 = 0

Output:
x^3 + 31/3x^2 + 101/3x + 35 = 0
(x - -3)(x - -7/3)(x - -5) = 0
x - -3 = 0
x - -7/3 = 0
x - -5 = 0
x = -3
x = -7/3
x = -5


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

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


Input: Solve the equation x^3 + 11/9x^2 - 292/81x - 2240/729 = 0

Output:
x^3 + 11/9x^2 - 292/81x - 2240/729 = 0
(x - -7/9)(x - -20/9)(x - 16/9) = 0
x - -7/9 = 0
x - -20/9 = 0
x - 16/9 = 0
x = -7/9
x = -20/9
x = 16/9


Input: What value of x satisfies x^3 + 11/6x^2 - 1/2x - 1/3 = 0

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


Input: Find x in 3x - 21/4 = 0

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


Input: Find the solution to 10x + 4 = 0

Output:
10x + 4 = 0
10x = -4
x = -4 / 10
x = -2/5


Input:
Solve the system:
4x + 2y = -59/3
1x + 2y = -65/12

Output:
4x + 2y = -59/3
1x + 2y = -65/12

Using elimination
1*(4x + 2y = -59/3)
4*(1x + 2y = -65/12)
4x + 2y = -59/3
4x + 8y = -65/3
Subtract equations
-6y = 2
y = 2/-6
y = -1/3

Substitute y
4x + 2(-1/3) = -59/3
4x = -19
x = -19/4
x = -19/4


Input:
Find x and y such that
9x + 1y = 39/4
1x + 1y = 15/4

Output:
9x + 1y = 39/4
1x + 1y = 15/4

Using elimination
1*(9x + 1y = 39/4)
9*(1x + 1y = 15/4)
9x + 1y = 39/4
9x + 9y = 135/4
Subtract equations
-8y = -24
y = -24/-8
y = 3

Substitute y
9x + 1(3) = 39/4
9x = 27/4
x = 27/4/9
x = 3/4


Input: What value of x satisfies 1x + 3 = 0

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


Input: Determine x in x^2 - 61/5x + 144/5 = 0

Output:
x^2 - 61/5x + 144/5 = 0
(x - 9)(x - 16/5) = 0
x - 9 = 0  or  x - 16/5 = 0
x = 9
x = 16/5


Input: Solve the equation x^3 + 28/15x^2 - 113/5x - 176/3 = 0

Output:
x^3 + 28/15x^2 - 113/5x - 176/3 = 0
(x - 5)(x - -16/5)(x - -11/3) = 0
x - 5 = 0
x - -16/5 = 0
x - -11/3 = 0
x = 5
x = -16/5
x = -11/3


Input: Solve the equation 9x - 9/2 = 0

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


Input:
Solve the system:
7x + 1y = 365/21
4x + 6y = 62/21

Output:
7x + 1y = 365/21
4x + 6y = 62/21

Using elimination
4*(7x + 1y = 365/21)
7*(4x + 6y = 62/21)
28x + 4y = 1460/21
28x + 42y = 62/3
Subtract equations
-38y = 342/7
y = 342/7/-38
y = -9/7

Substitute y
7x + 1(-9/7) = 365/21
7x = 56/3
x = 56/3/7
x = 8/3


Input: Solve the equation x^2 + 19x  = 0

Output:
x^2 + 19x  = 0
(x - 0)(x - -19) = 0
x - 0 = 0  or  x - -19 = 0
x = 0
x = -19


Input: Solve 5x + 10 = 0

Output:
5x + 10 = 0
5x = -10
x = -10 / 5
x = -2


Input:
Solve the system:
5x + 3y = -563/9
2x + 8y = -1388/9

Output:
5x + 3y = -563/9
2x + 8y = -1388/9

Using elimination
2*(5x + 3y = -563/9)
5*(2x + 8y = -1388/9)
10x + 6y = -1126/9
10x + 40y = -6940/9
Subtract equations
-34y = 646
y = 646/-34
y = -19

Substitute y
5x + 3(-19) = -563/9
5x = -50/9
x = -50/9/5
x = -10/9


Input: Find x in x^3 - 3/2x^2 - 49x - 24 = 0

Output:
x^3 - 3/2x^2 - 49x - 24 = 0
(x - 8)(x - -1/2)(x - -6) = 0
x - 8 = 0
x - -1/2 = 0
x - -6 = 0
x = 8
x = -1/2
x = -6


Input:
Solve simultaneously:
1x + 8y = 277/20
2x + 3y = -9/10

Output:
1x + 8y = 277/20
2x + 3y = -9/10

Using elimination
2*(1x + 8y = 277/20)
1*(2x + 3y = -9/10)
2x + 16y = 277/10
2x + 3y = -9/10
Subtract equations
13y = 143/5
y = 143/5/13
y = 11/5

Substitute y
1x + 8(11/5) = 277/20
1x = -15/4
x = -15/4/1
x = -15/4


Input: Find the solution to x^3 - 9/2x^2 - 89/18x + 110/9 = 0

Output:
x^3 - 9/2x^2 - 89/18x + 110/9 = 0
(x - 5)(x - -11/6)(x - 4/3) = 0
x - 5 = 0
x - -11/6 = 0
x - 4/3 = 0
x = 5
x = -11/6
x = 4/3


Input:
Find x and y such that
2x + 2y = -11/6
10x + 9y = -113/12

Output:
2x + 2y = -11/6
10x + 9y = -113/12

Using elimination
10*(2x + 2y = -11/6)
2*(10x + 9y = -113/12)
20x + 20y = -55/3
20x + 18y = -113/6
Subtract equations
2y = 1/2
y = 1/2/2
y = 1/4

Substitute y
2x + 2(1/4) = -11/6
2x = -7/3
x = -7/3/2
x = -7/6


Input: Determine x in 3x + 39/10 = 0

Output:
3x + 39/10 = 0
3x = -39/10
x = -39/10 / 3
x = -13/10


Input:
Solve simultaneously:
5x + 5y = -35/6
10x + 5y = -35/3

Output:
5x + 5y = -35/6
10x + 5y = -35/3

Using elimination
10*(5x + 5y = -35/6)
5*(10x + 5y = -35/3)
50x + 50y = -175/3
50x + 25y = -175/3
Subtract equations
25y = 0
y = 0/25
y = 0

Substitute y
5x + 5(0) = -35/6
5x = -35/6
x = -35/6/5
x = -7/6


Input: Find x for x^2 + 47/9x + 104/27 = 0

Output:
x^2 + 47/9x + 104/27 = 0
(x - -8/9)(x - -13/3) = 0
x - -8/9 = 0  or  x - -13/3 = 0
x = -8/9
x = -13/3


Input: Determine x in x^2 - 63/20x - 187/40 = 0

Output:
x^2 - 63/20x - 187/40 = 0
(x - 17/4)(x - -11/10) = 0
x - 17/4 = 0  or  x - -11/10 = 0
x = 17/4
x = -11/10


Input: Find the solution to x^3 + 11/14x^2 - 51/14x - 27/7 = 0

Output:
x^3 + 11/14x^2 - 51/14x - 27/7 = 0
(x - 2)(x - -3/2)(x - -9/7) = 0
x - 2 = 0
x - -3/2 = 0
x - -9/7 = 0
x = 2
x = -3/2
x = -9/7


Input: Compute the solution of x^2 + 10/3x + 1 = 0

Output:
x^2 + 10/3x + 1 = 0
(x - -3)(x - -1/3) = 0
x - -3 = 0  or  x - -1/3 = 0
x = -3
x = -1/3


Input:
Find x and y such that
4x + 9y = -325/21
4x + 5y = -193/21

Output:
4x + 9y = -325/21
4x + 5y = -193/21

Using elimination
4*(4x + 9y = -325/21)
4*(4x + 5y = -193/21)
16x + 36y = -1300/21
16x + 20y = -772/21
Subtract equations
16y = -176/7
y = -176/7/16
y = -11/7

Substitute y
4x + 9(-11/7) = -325/21
4x = -4/3
x = -4/3/4
x = -1/3


Input: Solve x^3 + 947/56x^2 - 13/8x - 51/28 = 0

Output:
x^3 + 947/56x^2 - 13/8x - 51/28 = 0
(x - -2/7)(x - -17)(x - 3/8) = 0
x - -2/7 = 0
x - -17 = 0
x - 3/8 = 0
x = -2/7
x = -17
x = 3/8


Input: Find x for 7x + 14 = 0

Output:
7x + 14 = 0
7x = -14
x = -14 / 7
x = -2


Input:
Solve simultaneously:
9x + 8y = 1101/35
2x + 3y = 296/35

Output:
9x + 8y = 1101/35
2x + 3y = 296/35

Using elimination
2*(9x + 8y = 1101/35)
9*(2x + 3y = 296/35)
18x + 16y = 2202/35
18x + 27y = 2664/35
Subtract equations
-11y = -66/5
y = -66/5/-11
y = 6/5

Substitute y
9x + 8(6/5) = 1101/35
9x = 153/7
x = 153/7/9
x = 17/7


Input:
Solve simultaneously:
9x + 5y = 61/7
8x + 4y = 484/63

Output:
9x + 5y = 61/7
8x + 4y = 484/63

Using elimination
8*(9x + 5y = 61/7)
9*(8x + 4y = 484/63)
72x + 40y = 488/7
72x + 36y = 484/7
Subtract equations
4y = 4/7
y = 4/7/4
y = 1/7

Substitute y
9x + 5(1/7) = 61/7
9x = 8
x = 8/9
x = 8/9


Input: Find x for 7x + 56/5 = 0

Output:
7x + 56/5 = 0
7x = -56/5
x = -56/5 / 7
x = -8/5


Input:
Solve the equations:
9x + 8y = 43/14
5x + 2y = 13/42

Output:
9x + 8y = 43/14
5x + 2y = 13/42

Using elimination
5*(9x + 8y = 43/14)
9*(5x + 2y = 13/42)
45x + 40y = 215/14
45x + 18y = 39/14
Subtract equations
22y = 88/7
y = 88/7/22
y = 4/7

Substitute y
9x + 8(4/7) = 43/14
9x = -3/2
x = -3/2/9
x = -1/6


Input: Find x in 3x + 9/8 = 0

Output:
3x + 9/8 = 0
3x = -9/8
x = -9/8 / 3
x = -3/8


Input: Solve the equation 9x - 45/2 = 0

Output:
9x - 45/2 = 0
9x = 45/2
x = 45/2 / 9
x = 5/2


Input: What value of x satisfies 9x - 12 = 0

Output:
9x - 12 = 0
9x = 12
x = 12 / 9
x = 4/3


Input: Find x for x^3 + 10/9x^2 - 23/81x - 44/243 = 0

Output:
x^3 + 10/9x^2 - 23/81x - 44/243 = 0
(x - -1/3)(x - 4/9)(x - -11/9) = 0
x - -1/3 = 0
x - 4/9 = 0
x - -11/9 = 0
x = -1/3
x = 4/9
x = -11/9


Input: Find x for 7x + 56/5 = 0

Output:
7x + 56/5 = 0
7x = -56/5
x = -56/5 / 7
x = -8/5


Input: Find x for x^3 + 11/6x^2 + 1/2x  = 0

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


Input: What value of x satisfies x^2 - 137/14x + 19/7 = 0

Output:
x^2 - 137/14x + 19/7 = 0
(x - 2/7)(x - 19/2) = 0
x - 2/7 = 0  or  x - 19/2 = 0
x = 2/7
x = 19/2


Input:
Solve the system:
7x + 10y = -44
7x + 6y = -46

Output:
7x + 10y = -44
7x + 6y = -46

Using elimination
7*(7x + 10y = -44)
7*(7x + 6y = -46)
49x + 70y = -308
49x + 42y = -322
Subtract equations
28y = 14
y = 14/28
y = 1/2

Substitute y
7x + 10(1/2) = -44
7x = -49
x = -49/7
x = -7


Input: Solve x^3 - 2x^2 - 20x - 24 = 0

Output:
x^3 - 2x^2 - 20x - 24 = 0
(x - -2)(x - -2)(x - 6) = 0
x - -2 = 0
x - -2 = 0
x - 6 = 0
x = -2
x = -2
x = 6


Input: Determine x in x^2 - 4x + 32/9 = 0

Output:
x^2 - 4x + 32/9 = 0
(x - 8/3)(x - 4/3) = 0
x - 8/3 = 0  or  x - 4/3 = 0
x = 8/3
x = 4/3


Input: Find the solution to 5x - 9/2 = 0

Output:
5x - 9/2 = 0
5x = 9/2
x = 9/2 / 5
x = 9/10


Input: Compute the solution of 1x + 10 = 0

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


Input: Find x for 6x + 30 = 0

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


Input: Find x for x^2 - 67/63x - 80/63 = 0

Output:
x^2 - 67/63x - 80/63 = 0
(x - 16/9)(x - -5/7) = 0
x - 16/9 = 0  or  x - -5/7 = 0
x = 16/9
x = -5/7


Input:
Solve the equations:
9x + 1y = -142
3x + 3y = -18

Output:
9x + 1y = -142
3x + 3y = -18

Using elimination
3*(9x + 1y = -142)
9*(3x + 3y = -18)
27x + 3y = -426
27x + 27y = -162
Subtract equations
-24y = -264
y = -264/-24
y = 11

Substitute y
9x + 1(11) = -142
9x = -153
x = -153/9
x = -17


Input:
Solve the equations:
9x + 10y = 119/5
9x + 8y = 203/10

Output:
9x + 10y = 119/5
9x + 8y = 203/10

Using elimination
9*(9x + 10y = 119/5)
9*(9x + 8y = 203/10)
81x + 90y = 1071/5
81x + 72y = 1827/10
Subtract equations
18y = 63/2
y = 63/2/18
y = 7/4

Substitute y
9x + 10(7/4) = 119/5
9x = 63/10
x = 63/10/9
x = 7/10


Input: What value of x satisfies x^2 + 6x - 160 = 0

Output:
x^2 + 6x - 160 = 0
(x - 10)(x - -16) = 0
x - 10 = 0  or  x - -16 = 0
x = 10
x = -16


Input: Solve the equation 2x - 14 = 0

Output:
2x - 14 = 0
2x = 14
x = 14 / 2
x = 7


Input:
Solve the system:
9x + 1y = 35/4
10x + 8y = -77/2

Output:
9x + 1y = 35/4
10x + 8y = -77/2

Using elimination
10*(9x + 1y = 35/4)
9*(10x + 8y = -77/2)
90x + 10y = 175/2
90x + 72y = -693/2
Subtract equations
-62y = 434
y = 434/-62
y = -7

Substitute y
9x + 1(-7) = 35/4
9x = 63/4
x = 63/4/9
x = 7/4


Input: Find the solution to x^3 - 37/7x^2 - 50/49x + 600/49 = 0

Output:
x^3 - 37/7x^2 - 50/49x + 600/49 = 0
(x - 12/7)(x - 5)(x - -10/7) = 0
x - 12/7 = 0
x - 5 = 0
x - -10/7 = 0
x = 12/7
x = 5
x = -10/7


Input:
Solve the system:
9x + 9y = -195/4
2x + 8y = -118/3

Output:
9x + 9y = -195/4
2x + 8y = -118/3

Using elimination
2*(9x + 9y = -195/4)
9*(2x + 8y = -118/3)
18x + 18y = -195/2
18x + 72y = -354
Subtract equations
-54y = 513/2
y = 513/2/-54
y = -19/4

Substitute y
9x + 9(-19/4) = -195/4
9x = -6
x = -6/9
x = -2/3


Input: Solve the equation x^2 - 38/15x - 32/15 = 0

Output:
x^2 - 38/15x - 32/15 = 0
(x - 16/5)(x - -2/3) = 0
x - 16/5 = 0  or  x - -2/3 = 0
x = 16/5
x = -2/3


Input: Solve x^3 - 33/8x^2 - 159/16x + 209/16 = 0

Output:
x^3 - 33/8x^2 - 159/16x + 209/16 = 0
(x - -19/8)(x - 11/2)(x - 1) = 0
x - -19/8 = 0
x - 11/2 = 0
x - 1 = 0
x = -19/8
x = 11/2
x = 1


Input: What value of x satisfies x^2 - 15x - 16 = 0

Output:
x^2 - 15x - 16 = 0
(x - 16)(x - -1) = 0
x - 16 = 0  or  x - -1 = 0
x = 16
x = -1


Input: Solve quickly: 1x + 4/3 = 0

Output:
1x + 4/3 = 0
1x = -4/3
x = -4/3 / 1
x = -4/3


Input:
Find x and y such that
6x + 1y = 97/10
8x + 6y = 53/5

Output:
6x + 1y = 97/10
8x + 6y = 53/5

Using elimination
8*(6x + 1y = 97/10)
6*(8x + 6y = 53/5)
48x + 8y = 388/5
48x + 36y = 318/5
Subtract equations
-28y = 14
y = 14/-28
y = -1/2

Substitute y
6x + 1(-1/2) = 97/10
6x = 51/5
x = 51/5/6
x = 17/10


Input:
Find x and y such that
4x + 9y = 194/9
7x + 8y = 200/9

Output:
4x + 9y = 194/9
7x + 8y = 200/9

Using elimination
7*(4x + 9y = 194/9)
4*(7x + 8y = 200/9)
28x + 63y = 1358/9
28x + 32y = 800/9
Subtract equations
31y = 62
y = 62/31
y = 2

Substitute y
4x + 9(2) = 194/9
4x = 32/9
x = 32/9/4
x = 8/9


Input: Solve quickly: x^2 + 9/10x + 1/5 = 0

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


Input: Solve quickly: 10x - 5/3 = 0

Output:
10x - 5/3 = 0
10x = 5/3
x = 5/3 / 10
x = 1/6


Input: Find the solution to x^3 + 16/9x^2 - 220/9x + 16/3 = 0

Output:
x^3 + 16/9x^2 - 220/9x + 16/3 = 0
(x - -6)(x - 2/9)(x - 4) = 0
x - -6 = 0
x - 2/9 = 0
x - 4 = 0
x = -6
x = 2/9
x = 4


Input:
Solve simultaneously:
1x + 7y = 148/5
7x + 3y = 116/5

Output:
1x + 7y = 148/5
7x + 3y = 116/5

Using elimination
7*(1x + 7y = 148/5)
1*(7x + 3y = 116/5)
7x + 49y = 1036/5
7x + 3y = 116/5
Subtract equations
46y = 184
y = 184/46
y = 4

Substitute y
1x + 7(4) = 148/5
1x = 8/5
x = 8/5/1
x = 8/5


Input:
Find x and y such that
8x + 3y = 35/3
7x + 8y = 79/3

Output:
8x + 3y = 35/3
7x + 8y = 79/3

Using elimination
7*(8x + 3y = 35/3)
8*(7x + 8y = 79/3)
56x + 21y = 245/3
56x + 64y = 632/3
Subtract equations
-43y = -129
y = -129/-43
y = 3

Substitute y
8x + 3(3) = 35/3
8x = 8/3
x = 8/3/8
x = 1/3


Input:
Solve simultaneously:
6x + 10y = -45
1x + 5y = -45/2

Output:
6x + 10y = -45
1x + 5y = -45/2

Using elimination
1*(6x + 10y = -45)
6*(1x + 5y = -45/2)
6x + 10y = -45
6x + 30y = -135
Subtract equations
-20y = 90
y = 90/-20
y = -9/2

Substitute y
6x + 10(-9/2) = -45
6x = 0
x = 0/6
x = 0


Input:
Solve the equations:
8x + 4y = 178/15
4x + 7y = 353/30

Output:
8x + 4y = 178/15
4x + 7y = 353/30

Using elimination
4*(8x + 4y = 178/15)
8*(4x + 7y = 353/30)
32x + 16y = 712/15
32x + 56y = 1412/15
Subtract equations
-40y = -140/3
y = -140/3/-40
y = 7/6

Substitute y
8x + 4(7/6) = 178/15
8x = 36/5
x = 36/5/8
x = 9/10


Input: Solve x^2 + 17/15x - 14/5 = 0

Output:
x^2 + 17/15x - 14/5 = 0
(x - -7/3)(x - 6/5) = 0
x - -7/3 = 0  or  x - 6/5 = 0
x = -7/3
x = 6/5


Input: Find the solution to x^3 + 49/9x^2 + 133/27x + 13/27 = 0

Output:
x^3 + 49/9x^2 + 133/27x + 13/27 = 0
(x - -1)(x - -13/3)(x - -1/9) = 0
x - -1 = 0
x - -13/3 = 0
x - -1/9 = 0
x = -1
x = -13/3
x = -1/9


Input: Find the solution to x^3 + 123/56x^2 + 47/112x - 99/112 = 0

Output:
x^3 + 123/56x^2 + 47/112x - 99/112 = 0
(x - -11/7)(x - 1/2)(x - -9/8) = 0
x - -11/7 = 0
x - 1/2 = 0
x - -9/8 = 0
x = -11/7
x = 1/2
x = -9/8


Input: Solve the equation x^3 + 7/24x^2 - 55/24x  = 0

Output:
x^3 + 7/24x^2 - 55/24x  = 0
(x - -5/3)(x - 0)(x - 11/8) = 0
x - -5/3 = 0
x - 0 = 0
x - 11/8 = 0
x = -5/3
x = 0
x = 11/8


Input: What value of x satisfies x^2 + 139/10x + 114/5 = 0

Output:
x^2 + 139/10x + 114/5 = 0
(x - -19/10)(x - -12) = 0
x - -19/10 = 0  or  x - -12 = 0
x = -19/10
x = -12


Input:
Find x and y such that
8x + 3y = 285/7
10x + 4y = 352/7

Output:
8x + 3y = 285/7
10x + 4y = 352/7

Using elimination
10*(8x + 3y = 285/7)
8*(10x + 4y = 352/7)
80x + 30y = 2850/7
80x + 32y = 2816/7
Subtract equations
-2y = 34/7
y = 34/7/-2
y = -17/7

Substitute y
8x + 3(-17/7) = 285/7
8x = 48
x = 48/8
x = 6


Input: Compute the solution of x^3 - 29/9x^2 + 56/27x  = 0

Output:
x^3 - 29/9x^2 + 56/27x  = 0
(x - 8/9)(x - 7/3)(x - 0) = 0
x - 8/9 = 0
x - 7/3 = 0
x - 0 = 0
x = 8/9
x = 7/3
x = 0


Input: What value of x satisfies x^3 + 55/14x^2 - 214/7x + 16 = 0

Output:
x^3 + 55/14x^2 - 214/7x + 16 = 0
(x - -8)(x - 4/7)(x - 7/2) = 0
x - -8 = 0
x - 4/7 = 0
x - 7/2 = 0
x = -8
x = 4/7
x = 7/2


Input:
Solve simultaneously:
9x + 1y = 253/8
9x + 10y = 1477/8

Output:
9x + 1y = 253/8
9x + 10y = 1477/8

Using elimination
9*(9x + 1y = 253/8)
9*(9x + 10y = 1477/8)
81x + 9y = 2277/8
81x + 90y = 13293/8
Subtract equations
-81y = -1377
y = -1377/-81
y = 17

Substitute y
9x + 1(17) = 253/8
9x = 117/8
x = 117/8/9
x = 13/8


Input:
Solve simultaneously:
3x + 7y = -3/2
6x + 7y = -69/2

Output:
3x + 7y = -3/2
6x + 7y = -69/2

Using elimination
6*(3x + 7y = -3/2)
3*(6x + 7y = -69/2)
18x + 42y = -9
18x + 21y = -207/2
Subtract equations
21y = 189/2
y = 189/2/21
y = 9/2

Substitute y
3x + 7(9/2) = -3/2
3x = -33
x = -33/3
x = -11


Input: Solve x^3 + 85/18x^2 + 6x + 10/9 = 0

Output:
x^3 + 85/18x^2 + 6x + 10/9 = 0
(x - -2)(x - -2/9)(x - -5/2) = 0
x - -2 = 0
x - -2/9 = 0
x - -5/2 = 0
x = -2
x = -2/9
x = -5/2


Input: Solve 8x + 96/5 = 0

Output:
8x + 96/5 = 0
8x = -96/5
x = -96/5 / 8
x = -12/5


Input: Determine x in 4x - 24 = 0

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


Input: What value of x satisfies x^3 - 607/60x^2 + 391/15x - 289/60 = 0

Output:
x^3 - 607/60x^2 + 391/15x - 289/60 = 0
(x - 17/4)(x - 1/5)(x - 17/3) = 0
x - 17/4 = 0
x - 1/5 = 0
x - 17/3 = 0
x = 17/4
x = 1/5
x = 17/3


Input: Compute the solution of x^2 - 18/5x  = 0

Output:
x^2 - 18/5x  = 0
(x - 0)(x - 18/5) = 0
x - 0 = 0  or  x - 18/5 = 0
x = 0
x = 18/5


Input:
Find x and y such that
5x + 4y = -641/35
7x + 5y = -49/2

Output:
5x + 4y = -641/35
7x + 5y = -49/2

Using elimination
7*(5x + 4y = -641/35)
5*(7x + 5y = -49/2)
35x + 28y = -641/5
35x + 25y = -245/2
Subtract equations
3y = -57/10
y = -57/10/3
y = -19/10

Substitute y
5x + 4(-19/10) = -641/35
5x = -75/7
x = -75/7/5
x = -15/7


Input: Solve 5x + 50/9 = 0

Output:
5x + 50/9 = 0
5x = -50/9
x = -50/9 / 5
x = -10/9


Input: Solve quickly: 7x - 28 = 0

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


Input: Find x in x^3 + 597/40x^2 + 903/40x - 637/20 = 0

Output:
x^3 + 597/40x^2 + 903/40x - 637/20 = 0
(x - 7/8)(x - -14/5)(x - -13) = 0
x - 7/8 = 0
x - -14/5 = 0
x - -13 = 0
x = 7/8
x = -14/5
x = -13


Input: Determine x in 6x + 22/3 = 0

Output:
6x + 22/3 = 0
6x = -22/3
x = -22/3 / 6
x = -11/9


Input: Solve the equation x^2  - 36/49 = 0

Output:
x^2  - 36/49 = 0
(x - 6/7)(x - -6/7) = 0
x - 6/7 = 0  or  x - -6/7 = 0
x = 6/7
x = -6/7


Input: Solve quickly: x^3 - 113/20x^2 + 209/20x - 63/10 = 0

Output:
x^3 - 113/20x^2 + 209/20x - 63/10 = 0
(x - 7/5)(x - 2)(x - 9/4) = 0
x - 7/5 = 0
x - 2 = 0
x - 9/4 = 0
x = 7/5
x = 2
x = 9/4


Input: Compute the solution of 7x + 35 = 0

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


Input: Find the solution to x^3 - 13/15x^2 - 62/5x + 304/15 = 0

Output:
x^3 - 13/15x^2 - 62/5x + 304/15 = 0
(x - 2)(x - -19/5)(x - 8/3) = 0
x - 2 = 0
x - -19/5 = 0
x - 8/3 = 0
x = 2
x = -19/5
x = 8/3


Input: Solve the equation x^2 + 2/3x - 1/3 = 0

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


Input: Determine x in x^2 + 7/4x  = 0

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


Input: Solve the equation 3x + 30 = 0

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


Input: Find the solution to x^3 - 1x^2 - 4x + 4 = 0

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


Input:
Solve the system:
8x + 10y = -200/3
4x + 7y = -68/3

Output:
8x + 10y = -200/3
4x + 7y = -68/3

Using elimination
4*(8x + 10y = -200/3)
8*(4x + 7y = -68/3)
32x + 40y = -800/3
32x + 56y = -544/3
Subtract equations
-16y = -256/3
y = -256/3/-16
y = 16/3

Substitute y
8x + 10(16/3) = -200/3
8x = -120
x = -120/8
x = -15


Input: Solve the equation x^3 + 35/12x^2 - 23/12x - 5 = 0

Output:
x^3 + 35/12x^2 - 23/12x - 5 = 0
(x - 4/3)(x - -3)(x - -5/4) = 0
x - 4/3 = 0
x - -3 = 0
x - -5/4 = 0
x = 4/3
x = -3
x = -5/4


Input: Find x in x^3 + 23/180x^2 - 65/72x + 11/60 = 0

Output:
x^3 + 23/180x^2 - 65/72x + 11/60 = 0
(x - 3/4)(x - 2/9)(x - -11/10) = 0
x - 3/4 = 0
x - 2/9 = 0
x - -11/10 = 0
x = 3/4
x = 2/9
x = -11/10


Input: Solve the equation x^3 - 229/42x^2 + 1157/126x - 40/9 = 0

Output:
x^3 - 229/42x^2 + 1157/126x - 40/9 = 0
(x - 16/7)(x - 5/6)(x - 7/3) = 0
x - 16/7 = 0
x - 5/6 = 0
x - 7/3 = 0
x = 16/7
x = 5/6
x = 7/3


Input: Compute the solution of x^2 + 10x + 75/4 = 0

Output:
x^2 + 10x + 75/4 = 0
(x - -15/2)(x - -5/2) = 0
x - -15/2 = 0  or  x - -5/2 = 0
x = -15/2
x = -5/2


Input: Solve 1x - 2 = 0

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


Input:
Solve the equations:
7x + 8y = 415/21
8x + 10y = 482/21

Output:
7x + 8y = 415/21
8x + 10y = 482/21

Using elimination
8*(7x + 8y = 415/21)
7*(8x + 10y = 482/21)
56x + 64y = 3320/21
56x + 70y = 482/3
Subtract equations
-6y = -18/7
y = -18/7/-6
y = 3/7

Substitute y
7x + 8(3/7) = 415/21
7x = 49/3
x = 49/3/7
x = 7/3


Input:
Find x and y such that
10x + 9y = -709/15
4x + 9y = -559/15

Output:
10x + 9y = -709/15
4x + 9y = -559/15

Using elimination
4*(10x + 9y = -709/15)
10*(4x + 9y = -559/15)
40x + 36y = -2836/15
40x + 90y = -1118/3
Subtract equations
-54y = 918/5
y = 918/5/-54
y = -17/5

Substitute y
10x + 9(-17/5) = -709/15
10x = -50/3
x = -50/3/10
x = -5/3


Input: Find the solution to x^3 + 35/6x^2 + 25/3x  = 0

Output:
x^3 + 35/6x^2 + 25/3x  = 0
(x - -10/3)(x - -5/2)(x - 0) = 0
x - -10/3 = 0
x - -5/2 = 0
x - 0 = 0
x = -10/3
x = -5/2
x = 0


Input: Find x in x^2 + 27/10x - 81/10 = 0

Output:
x^2 + 27/10x - 81/10 = 0
(x - 9/5)(x - -9/2) = 0
x - 9/5 = 0  or  x - -9/2 = 0
x = 9/5
x = -9/2


Input: Find the solution to x^2 + 17/3x  = 0

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


Input:
Find x and y such that
8x + 1y = -121/7
7x + 8y = -170/7

Output:
8x + 1y = -121/7
7x + 8y = -170/7

Using elimination
7*(8x + 1y = -121/7)
8*(7x + 8y = -170/7)
56x + 7y = -121
56x + 64y = -1360/7
Subtract equations
-57y = 513/7
y = 513/7/-57
y = -9/7

Substitute y
8x + 1(-9/7) = -121/7
8x = -16
x = -16/8
x = -2


Input: Find x for x^3 - 313/180x^2 - 341/60x + 51/5 = 0

Output:
x^3 - 313/180x^2 - 341/60x + 51/5 = 0
(x - 17/9)(x - 9/4)(x - -12/5) = 0
x - 17/9 = 0
x - 9/4 = 0
x - -12/5 = 0
x = 17/9
x = 9/4
x = -12/5


Input: Solve the equation 1x + 3/8 = 0

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


Input: What value of x satisfies x^2 + 7/3x - 16 = 0

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


Input: Solve x^3 + 92/35x^2 + 47/35x + 6/35 = 0

Output:
x^3 + 92/35x^2 + 47/35x + 6/35 = 0
(x - -3/7)(x - -2)(x - -1/5) = 0
x - -3/7 = 0
x - -2 = 0
x - -1/5 = 0
x = -3/7
x = -2
x = -1/5


Input: Solve quickly: x^2 - 2/5x  = 0

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


Input:
Solve the system:
9x + 1y = 1555/9
2x + 8y = 470/9

Output:
9x + 1y = 1555/9
2x + 8y = 470/9

Using elimination
2*(9x + 1y = 1555/9)
9*(2x + 8y = 470/9)
18x + 2y = 3110/9
18x + 72y = 470
Subtract equations
-70y = -1120/9
y = -1120/9/-70
y = 16/9

Substitute y
9x + 1(16/9) = 1555/9
9x = 171
x = 171/9
x = 19


Input: What value of x satisfies x^2 + 35/36x - 25/9 = 0

Output:
x^2 + 35/36x - 25/9 = 0
(x - 5/4)(x - -20/9) = 0
x - 5/4 = 0  or  x - -20/9 = 0
x = 5/4
x = -20/9


Input: What value of x satisfies x^3 - 116/9x^2 - 827/27x - 140/9 = 0

Output:
x^3 - 116/9x^2 - 827/27x - 140/9 = 0
(x - -4/3)(x - 15)(x - -7/9) = 0
x - -4/3 = 0
x - 15 = 0
x - -7/9 = 0
x = -4/3
x = 15
x = -7/9


Input: What value of x satisfies x^2 + 13x + 40 = 0

Output:
x^2 + 13x + 40 = 0
(x - -8)(x - -5) = 0
x - -8 = 0  or  x - -5 = 0
x = -8
x = -5


Input:
Solve the system:
2x + 9y = 10/3
4x + 8y = 40/9

Output:
2x + 9y = 10/3
4x + 8y = 40/9

Using elimination
4*(2x + 9y = 10/3)
2*(4x + 8y = 40/9)
8x + 36y = 40/3
8x + 16y = 80/9
Subtract equations
20y = 40/9
y = 40/9/20
y = 2/9

Substitute y
2x + 9(2/9) = 10/3
2x = 4/3
x = 4/3/2
x = 2/3


Input: Find the solution to x^3 - 37/6x^2 + 23/3x + 11/2 = 0

Output:
x^3 - 37/6x^2 + 23/3x + 11/2 = 0
(x - 3)(x - 11/3)(x - -1/2) = 0
x - 3 = 0
x - 11/3 = 0
x - -1/2 = 0
x = 3
x = 11/3
x = -1/2


Input: What value of x satisfies x^3 + 35/4x^2 + 63/8x - 45/4 = 0

Output:
x^3 + 35/4x^2 + 63/8x - 45/4 = 0
(x - 3/4)(x - -15/2)(x - -2) = 0
x - 3/4 = 0
x - -15/2 = 0
x - -2 = 0
x = 3/4
x = -15/2
x = -2


Input: Find the solution to 10x + 55/4 = 0

Output:
10x + 55/4 = 0
10x = -55/4
x = -55/4 / 10
x = -11/8


Input:
Find x and y such that
3x + 10y = 70
5x + 9y = 195/2

Output:
3x + 10y = 70
5x + 9y = 195/2

Using elimination
5*(3x + 10y = 70)
3*(5x + 9y = 195/2)
15x + 50y = 350
15x + 27y = 585/2
Subtract equations
23y = 115/2
y = 115/2/23
y = 5/2

Substitute y
3x + 10(5/2) = 70
3x = 45
x = 45/3
x = 15


Input: Solve the equation 3x - 10/3 = 0

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


Input: Compute the solution of x^2 + 28/3x + 65/3 = 0

Output:
x^2 + 28/3x + 65/3 = 0
(x - -13/3)(x - -5) = 0
x - -13/3 = 0  or  x - -5 = 0
x = -13/3
x = -5


Input: Solve x^2 + 1/3x - 2/9 = 0

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


Input: What value of x satisfies 1x + 5/6 = 0

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


Input: Determine x in x^2 - 15x - 54 = 0

Output:
x^2 - 15x - 54 = 0
(x - 18)(x - -3) = 0
x - 18 = 0  or  x - -3 = 0
x = 18
x = -3


Input: Find x for 9x + 45 = 0

Output:
9x + 45 = 0
9x = -45
x = -45 / 9
x = -5


Input: Solve 5x - 15/2 = 0

Output:
5x - 15/2 = 0
5x = 15/2
x = 15/2 / 5
x = 3/2


Input: Compute the solution of x^3 + 5/3x^2 - 157/300x - 13/10 = 0

Output:
x^3 + 5/3x^2 - 157/300x - 13/10 = 0
(x - -6/5)(x - -13/10)(x - 5/6) = 0
x - -6/5 = 0
x - -13/10 = 0
x - 5/6 = 0
x = -6/5
x = -13/10
x = 5/6


Input: Find the solution to x^3 - 197/21x^2 - 710/21x + 200/7 = 0

Output:
x^3 - 197/21x^2 - 710/21x + 200/7 = 0
(x - -10/3)(x - 12)(x - 5/7) = 0
x - -10/3 = 0
x - 12 = 0
x - 5/7 = 0
x = -10/3
x = 12
x = 5/7


Input: Find the solution to x^3 + 223/42x^2 + 277/42x + 44/21 = 0

Output:
x^3 + 223/42x^2 + 277/42x + 44/21 = 0
(x - -11/3)(x - -1/2)(x - -8/7) = 0
x - -11/3 = 0
x - -1/2 = 0
x - -8/7 = 0
x = -11/3
x = -1/2
x = -8/7


Input: Compute the solution of x^3 + 113/7x^2 + 428/7x + 352/7 = 0

Output:
x^3 + 113/7x^2 + 428/7x + 352/7 = 0
(x - -4)(x - -11)(x - -8/7) = 0
x - -4 = 0
x - -11 = 0
x - -8/7 = 0
x = -4
x = -11
x = -8/7


Input: Solve the equation 7x + 21 = 0

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


Input:
Solve the system:
3x + 7y = 6
10x + 3y = -1/3

Output:
3x + 7y = 6
10x + 3y = -1/3

Using elimination
10*(3x + 7y = 6)
3*(10x + 3y = -1/3)
30x + 70y = 60
30x + 9y = -1
Subtract equations
61y = 61
y = 61/61
y = 1

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


Input: Find x for x^3 - 23/70x^2 - 203/50x - 442/175 = 0

Output:
x^3 - 23/70x^2 - 203/50x - 442/175 = 0
(x - -4/5)(x - 17/7)(x - -13/10) = 0
x - -4/5 = 0
x - 17/7 = 0
x - -13/10 = 0
x = -4/5
x = 17/7
x = -13/10


Input: Compute the solution of x^2 - 15/2x + 25/2 = 0

Output:
x^2 - 15/2x + 25/2 = 0
(x - 5)(x - 5/2) = 0
x - 5 = 0  or  x - 5/2 = 0
x = 5
x = 5/2


Input: Solve quickly: 3x - 21/5 = 0

Output:
3x - 21/5 = 0
3x = 21/5
x = 21/5 / 3
x = 7/5


Input: Find x for x^2 + 33/2x + 135/2 = 0

Output:
x^2 + 33/2x + 135/2 = 0
(x - -15/2)(x - -9) = 0
x - -15/2 = 0  or  x - -9 = 0
x = -15/2
x = -9


Input: Compute the solution of x^3 + 11/5x^2 - 46/5x - 96/5 = 0

Output:
x^3 + 11/5x^2 - 46/5x - 96/5 = 0
(x - -16/5)(x - -2)(x - 3) = 0
x - -16/5 = 0
x - -2 = 0
x - 3 = 0
x = -16/5
x = -2
x = 3


Input: Solve the equation 3x - 57/7 = 0

Output:
3x - 57/7 = 0
3x = 57/7
x = 57/7 / 3
x = 19/7


Input:
Find x and y such that
3x + 5y = 389/10
6x + 3y = 144/5

Output:
3x + 5y = 389/10
6x + 3y = 144/5

Using elimination
6*(3x + 5y = 389/10)
3*(6x + 3y = 144/5)
18x + 30y = 1167/5
18x + 9y = 432/5
Subtract equations
21y = 147
y = 147/21
y = 7

Substitute y
3x + 5(7) = 389/10
3x = 39/10
x = 39/10/3
x = 13/10


Input: Determine x in x^3 - 11/30x^2 - 607/60x - 119/40 = 0

Output:
x^3 - 11/30x^2 - 607/60x - 119/40 = 0
(x - -3/10)(x - -17/6)(x - 7/2) = 0
x - -3/10 = 0
x - -17/6 = 0
x - 7/2 = 0
x = -3/10
x = -17/6
x = 7/2


Input: Find x in x^2 - 55/6x + 119/6 = 0

Output:
x^2 - 55/6x + 119/6 = 0
(x - 7/2)(x - 17/3) = 0
x - 7/2 = 0  or  x - 17/3 = 0
x = 7/2
x = 17/3


Input: Solve the equation x^2 - 71/12x + 35/6 = 0

Output:
x^2 - 71/12x + 35/6 = 0
(x - 14/3)(x - 5/4) = 0
x - 14/3 = 0  or  x - 5/4 = 0
x = 14/3
x = 5/4


Input: Solve the equation 2x + 9/4 = 0

Output:
2x + 9/4 = 0
2x = -9/4
x = -9/4 / 2
x = -9/8


Input: Solve 7x + 21/2 = 0

Output:
7x + 21/2 = 0
7x = -21/2
x = -21/2 / 7
x = -3/2


Input: Solve quickly: 4x + 3 = 0

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


Input:
Solve simultaneously:
9x + 9y = 63/10
6x + 2y = 51/5

Output:
9x + 9y = 63/10
6x + 2y = 51/5

Using elimination
6*(9x + 9y = 63/10)
9*(6x + 2y = 51/5)
54x + 54y = 189/5
54x + 18y = 459/5
Subtract equations
36y = -54
y = -54/36
y = -3/2

Substitute y
9x + 9(-3/2) = 63/10
9x = 99/5
x = 99/5/9
x = 11/5


Input:
Find x and y such that
3x + 3y = 19/12
10x + 4y = 119/18

Output:
3x + 3y = 19/12
10x + 4y = 119/18

Using elimination
10*(3x + 3y = 19/12)
3*(10x + 4y = 119/18)
30x + 30y = 95/6
30x + 12y = 119/6
Subtract equations
18y = -4
y = -4/18
y = -2/9

Substitute y
3x + 3(-2/9) = 19/12
3x = 9/4
x = 9/4/3
x = 3/4


Input: What value of x satisfies x^3 - 27/10x^2 - 47/5x + 84/5 = 0

Output:
x^3 - 27/10x^2 - 47/5x + 84/5 = 0
(x - 4)(x - -14/5)(x - 3/2) = 0
x - 4 = 0
x - -14/5 = 0
x - 3/2 = 0
x = 4
x = -14/5
x = 3/2


Input: Solve quickly: 8x - 136 = 0

Output:
8x - 136 = 0
8x = 136
x = 136 / 8
x = 17


Input: Find x in 4x + 72/7 = 0

Output:
4x + 72/7 = 0
4x = -72/7
x = -72/7 / 4
x = -18/7


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

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


Input: Solve the equation x^3 - 57/8x^2 - 627/16x - 605/16 = 0

Output:
x^3 - 57/8x^2 - 627/16x - 605/16 = 0
(x - -11/8)(x - 11)(x - -5/2) = 0
x - -11/8 = 0
x - 11 = 0
x - -5/2 = 0
x = -11/8
x = 11
x = -5/2


Input:
Solve simultaneously:
10x + 3y = -50/3
3x + 3y = -5

Output:
10x + 3y = -50/3
3x + 3y = -5

Using elimination
3*(10x + 3y = -50/3)
10*(3x + 3y = -5)
30x + 9y = -50
30x + 30y = -50
Subtract equations
-21y = 0
y = 0/-21
y = 0

Substitute y
10x + 3(0) = -50/3
10x = -50/3
x = -50/3/10
x = -5/3


Input: Find the solution to x^3 - 9/4x^2 - 4x + 39/16 = 0

Output:
x^3 - 9/4x^2 - 4x + 39/16 = 0
(x - 1/2)(x - -3/2)(x - 13/4) = 0
x - 1/2 = 0
x - -3/2 = 0
x - 13/4 = 0
x = 1/2
x = -3/2
x = 13/4


Input:
Solve simultaneously:
7x + 6y = 74
9x + 9y = 96

Output:
7x + 6y = 74
9x + 9y = 96

Using elimination
9*(7x + 6y = 74)
7*(9x + 9y = 96)
63x + 54y = 666
63x + 63y = 672
Subtract equations
-9y = -6
y = -6/-9
y = 2/3

Substitute y
7x + 6(2/3) = 74
7x = 70
x = 70/7
x = 10


Input: Find x in 10x + 70/3 = 0

Output:
10x + 70/3 = 0
10x = -70/3
x = -70/3 / 10
x = -7/3


Input: Find the solution to 5x + 9 = 0

Output:
5x + 9 = 0
5x = -9
x = -9 / 5
x = -9/5


Input:
Find x and y such that
2x + 2y = -94/7
2x + 9y = -178/7

Output:
2x + 2y = -94/7
2x + 9y = -178/7

Using elimination
2*(2x + 2y = -94/7)
2*(2x + 9y = -178/7)
4x + 4y = -188/7
4x + 18y = -356/7
Subtract equations
-14y = 24
y = 24/-14
y = -12/7

Substitute y
2x + 2(-12/7) = -94/7
2x = -10
x = -10/2
x = -5


Input:
Solve the system:
4x + 7y = -92/9
2x + 2y = -25/9

Output:
4x + 7y = -92/9
2x + 2y = -25/9

Using elimination
2*(4x + 7y = -92/9)
4*(2x + 2y = -25/9)
8x + 14y = -184/9
8x + 8y = -100/9
Subtract equations
6y = -28/3
y = -28/3/6
y = -14/9

Substitute y
4x + 7(-14/9) = -92/9
4x = 2/3
x = 2/3/4
x = 1/6


Input:
Solve simultaneously:
9x + 6y = -63/10
3x + 8y = 69/10

Output:
9x + 6y = -63/10
3x + 8y = 69/10

Using elimination
3*(9x + 6y = -63/10)
9*(3x + 8y = 69/10)
27x + 18y = -189/10
27x + 72y = 621/10
Subtract equations
-54y = -81
y = -81/-54
y = 3/2

Substitute y
9x + 6(3/2) = -63/10
9x = -153/10
x = -153/10/9
x = -17/10


Input:
Solve simultaneously:
6x + 3y = -147/10
4x + 10y = -269/5

Output:
6x + 3y = -147/10
4x + 10y = -269/5

Using elimination
4*(6x + 3y = -147/10)
6*(4x + 10y = -269/5)
24x + 12y = -294/5
24x + 60y = -1614/5
Subtract equations
-48y = 264
y = 264/-48
y = -11/2

Substitute y
6x + 3(-11/2) = -147/10
6x = 9/5
x = 9/5/6
x = 3/10


Input: Solve the equation x^2 - 27/35x - 22/7 = 0

Output:
x^2 - 27/35x - 22/7 = 0
(x - -10/7)(x - 11/5) = 0
x - -10/7 = 0  or  x - 11/5 = 0
x = -10/7
x = 11/5


Input: Solve x^3 - 233/30x^2 - 109/5x + 152/3 = 0

Output:
x^3 - 233/30x^2 - 109/5x + 152/3 = 0
(x - 19/2)(x - 8/5)(x - -10/3) = 0
x - 19/2 = 0
x - 8/5 = 0
x - -10/3 = 0
x = 19/2
x = 8/5
x = -10/3


Input:
Solve the system:
4x + 3y = -257/10
9x + 4y = -186/5

Output:
4x + 3y = -257/10
9x + 4y = -186/5

Using elimination
9*(4x + 3y = -257/10)
4*(9x + 4y = -186/5)
36x + 27y = -2313/10
36x + 16y = -744/5
Subtract equations
11y = -165/2
y = -165/2/11
y = -15/2

Substitute y
4x + 3(-15/2) = -257/10
4x = -16/5
x = -16/5/4
x = -4/5


Input: Find x in 10x - 150 = 0

Output:
10x - 150 = 0
10x = 150
x = 150 / 10
x = 15


Input: Find x in 5x - 50/7 = 0

Output:
5x - 50/7 = 0
5x = 50/7
x = 50/7 / 5
x = 10/7


Input: Compute the solution of 8x - 16 = 0

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


Input:
Solve the system:
10x + 3y = -89/6
2x + 9y = 461/6

Output:
10x + 3y = -89/6
2x + 9y = 461/6

Using elimination
2*(10x + 3y = -89/6)
10*(2x + 9y = 461/6)
20x + 6y = -89/3
20x + 90y = 2305/3
Subtract equations
-84y = -798
y = -798/-84
y = 19/2

Substitute y
10x + 3(19/2) = -89/6
10x = -130/3
x = -130/3/10
x = -13/3


Input: Compute the solution of 1x + 16/5 = 0

Output:
1x + 16/5 = 0
1x = -16/5
x = -16/5 / 1
x = -16/5


Input: Compute the solution of 5x - 5/3 = 0

Output:
5x - 5/3 = 0
5x = 5/3
x = 5/3 / 5
x = 1/3


Input:
Solve the equations:
5x + 6y = 77/4
6x + 8y = 161/6

Output:
5x + 6y = 77/4
6x + 8y = 161/6

Using elimination
6*(5x + 6y = 77/4)
5*(6x + 8y = 161/6)
30x + 36y = 231/2
30x + 40y = 805/6
Subtract equations
-4y = -56/3
y = -56/3/-4
y = 14/3

Substitute y
5x + 6(14/3) = 77/4
5x = -35/4
x = -35/4/5
x = -7/4


Input: Solve quickly: 2x + 32/7 = 0

Output:
2x + 32/7 = 0
2x = -32/7
x = -32/7 / 2
x = -16/7


Input: Solve quickly: x^2 - 22/5x + 117/25 = 0

Output:
x^2 - 22/5x + 117/25 = 0
(x - 13/5)(x - 9/5) = 0
x - 13/5 = 0  or  x - 9/5 = 0
x = 13/5
x = 9/5


Input: What value of x satisfies x^3 + 214/45x^2 + 151/180x - 7/5 = 0

Output:
x^3 + 214/45x^2 + 151/180x - 7/5 = 0
(x - -7/10)(x - 4/9)(x - -9/2) = 0
x - -7/10 = 0
x - 4/9 = 0
x - -9/2 = 0
x = -7/10
x = 4/9
x = -9/2


Input:
Solve simultaneously:
8x + 2y = -66/7
8x + 3y = -85/7

Output:
8x + 2y = -66/7
8x + 3y = -85/7

Using elimination
8*(8x + 2y = -66/7)
8*(8x + 3y = -85/7)
64x + 16y = -528/7
64x + 24y = -680/7
Subtract equations
-8y = 152/7
y = 152/7/-8
y = -19/7

Substitute y
8x + 2(-19/7) = -66/7
8x = -4
x = -4/8
x = -1/2


Input: Compute the solution of x^3 + 19x^2 - 251/4x - 2907/2 = 0

Output:
x^3 + 19x^2 - 251/4x - 2907/2 = 0
(x - 17/2)(x - -18)(x - -19/2) = 0
x - 17/2 = 0
x - -18 = 0
x - -19/2 = 0
x = 17/2
x = -18
x = -19/2


Input: Compute the solution of x^2 + 17/2x + 4 = 0

Output:
x^2 + 17/2x + 4 = 0
(x - -8)(x - -1/2) = 0
x - -8 = 0  or  x - -1/2 = 0
x = -8
x = -1/2


Input:
Solve the system:
8x + 7y = 72
10x + 2y = 36

Output:
8x + 7y = 72
10x + 2y = 36

Using elimination
10*(8x + 7y = 72)
8*(10x + 2y = 36)
80x + 70y = 720
80x + 16y = 288
Subtract equations
54y = 432
y = 432/54
y = 8

Substitute y
8x + 7(8) = 72
8x = 16
x = 16/8
x = 2


Input: Solve the equation x^3 - 123/10x^2 - 591/25x - 56/25 = 0

Output:
x^3 - 123/10x^2 - 591/25x - 56/25 = 0
(x - 14)(x - -8/5)(x - -1/10) = 0
x - 14 = 0
x - -8/5 = 0
x - -1/10 = 0
x = 14
x = -8/5
x = -1/10


Input: Compute the solution of x^3 + 49/20x^2 + 3/2x  = 0

Output:
x^3 + 49/20x^2 + 3/2x  = 0
(x - -6/5)(x - 0)(x - -5/4) = 0
x - -6/5 = 0
x - 0 = 0
x - -5/4 = 0
x = -6/5
x = 0
x = -5/4


Input: Solve the equation x^2 + 27/5x - 18/5 = 0

Output:
x^2 + 27/5x - 18/5 = 0
(x - -6)(x - 3/5) = 0
x - -6 = 0  or  x - 3/5 = 0
x = -6
x = 3/5


Input: Find x in 2x + 4 = 0

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


Input: Solve 3x + 13/3 = 0

Output:
3x + 13/3 = 0
3x = -13/3
x = -13/3 / 3
x = -13/9


Input:
Find x and y such that
10x + 5y = 63/2
7x + 4y = 479/20

Output:
10x + 5y = 63/2
7x + 4y = 479/20

Using elimination
7*(10x + 5y = 63/2)
10*(7x + 4y = 479/20)
70x + 35y = 441/2
70x + 40y = 479/2
Subtract equations
-5y = -19
y = -19/-5
y = 19/5

Substitute y
10x + 5(19/5) = 63/2
10x = 25/2
x = 25/2/10
x = 5/4


Input:
Find x and y such that
6x + 1y = -105
9x + 1y = -156

Output:
6x + 1y = -105
9x + 1y = -156

Using elimination
9*(6x + 1y = -105)
6*(9x + 1y = -156)
54x + 9y = -945
54x + 6y = -936
Subtract equations
3y = -9
y = -9/3
y = -3

Substitute y
6x + 1(-3) = -105
6x = -102
x = -102/6
x = -17


Input:
Solve the system:
7x + 7y = -77
7x + 3y = -25

Output:
7x + 7y = -77
7x + 3y = -25

Using elimination
7*(7x + 7y = -77)
7*(7x + 3y = -25)
49x + 49y = -539
49x + 21y = -175
Subtract equations
28y = -364
y = -364/28
y = -13

Substitute y
7x + 7(-13) = -77
7x = 14
x = 14/7
x = 2


Input: Determine x in x^3 + 701/72x^2 + 149/24x - 15/4 = 0

Output:
x^3 + 701/72x^2 + 149/24x - 15/4 = 0
(x - -9)(x - -10/9)(x - 3/8) = 0
x - -9 = 0
x - -10/9 = 0
x - 3/8 = 0
x = -9
x = -10/9
x = 3/8


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

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


Input:
Solve the equations:
4x + 2y = 20/3
6x + 1y = 34/3

Output:
4x + 2y = 20/3
6x + 1y = 34/3

Using elimination
6*(4x + 2y = 20/3)
4*(6x + 1y = 34/3)
24x + 12y = 40
24x + 4y = 136/3
Subtract equations
8y = -16/3
y = -16/3/8
y = -2/3

Substitute y
4x + 2(-2/3) = 20/3
4x = 8
x = 8/4
x = 2


Input: Find x for x^2 - 69/40x - 17/20 = 0

Output:
x^2 - 69/40x - 17/20 = 0
(x - -2/5)(x - 17/8) = 0
x - -2/5 = 0  or  x - 17/8 = 0
x = -2/5
x = 17/8


Input: Find x in x^2 - 23/20x + 3/10 = 0

Output:
x^2 - 23/20x + 3/10 = 0
(x - 2/5)(x - 3/4) = 0
x - 2/5 = 0  or  x - 3/4 = 0
x = 2/5
x = 3/4


Input: Find x for x^3 + 79/15x^2 + 86/15x - 16/5 = 0

Output:
x^3 + 79/15x^2 + 86/15x - 16/5 = 0
(x - -3)(x - -8/3)(x - 2/5) = 0
x - -3 = 0
x - -8/3 = 0
x - 2/5 = 0
x = -3
x = -8/3
x = 2/5


Input: Find x for 5x + 85/3 = 0

Output:
5x + 85/3 = 0
5x = -85/3
x = -85/3 / 5
x = -17/3


Input:
Solve simultaneously:
4x + 5y = 107/2
6x + 9y = 159/2

Output:
4x + 5y = 107/2
6x + 9y = 159/2

Using elimination
6*(4x + 5y = 107/2)
4*(6x + 9y = 159/2)
24x + 30y = 321
24x + 36y = 318
Subtract equations
-6y = 3
y = 3/-6
y = -1/2

Substitute y
4x + 5(-1/2) = 107/2
4x = 56
x = 56/4
x = 14


Input: Find x in x^2 - 113/18x + 8 = 0

Output:
x^2 - 113/18x + 8 = 0
(x - 9/2)(x - 16/9) = 0
x - 9/2 = 0  or  x - 16/9 = 0
x = 9/2
x = 16/9


Input:
Solve the equations:
6x + 10y = -244/5
1x + 7y = -126/5

Output:
6x + 10y = -244/5
1x + 7y = -126/5

Using elimination
1*(6x + 10y = -244/5)
6*(1x + 7y = -126/5)
6x + 10y = -244/5
6x + 42y = -756/5
Subtract equations
-32y = 512/5
y = 512/5/-32
y = -16/5

Substitute y
6x + 10(-16/5) = -244/5
6x = -84/5
x = -84/5/6
x = -14/5


Input: What value of x satisfies x^3 + 17/5x^2 + 32/25x - 28/25 = 0

Output:
x^3 + 17/5x^2 + 32/25x - 28/25 = 0
(x - -14/5)(x - 2/5)(x - -1) = 0
x - -14/5 = 0
x - 2/5 = 0
x - -1 = 0
x = -14/5
x = 2/5
x = -1


Input: Solve x^3 + 11/40x^2 - 51/5x - 27/2 = 0

Output:
x^3 + 11/40x^2 - 51/5x - 27/2 = 0
(x - -15/8)(x - 18/5)(x - -2) = 0
x - -15/8 = 0
x - 18/5 = 0
x - -2 = 0
x = -15/8
x = 18/5
x = -2


Input: Solve quickly: x^3 - 67/36x^2 - 497/108x - 55/54 = 0

Output:
x^3 - 67/36x^2 - 497/108x - 55/54 = 0
(x - 10/3)(x - -1/4)(x - -11/9) = 0
x - 10/3 = 0
x - -1/4 = 0
x - -11/9 = 0
x = 10/3
x = -1/4
x = -11/9


Input: Solve quickly: x^3 - 27/4x^2 - 485/8x - 57/2 = 0

Output:
x^3 - 27/4x^2 - 485/8x - 57/2 = 0
(x - 12)(x - -1/2)(x - -19/4) = 0
x - 12 = 0
x - -1/2 = 0
x - -19/4 = 0
x = 12
x = -1/2
x = -19/4


Input: Find the solution to x^3 - 835/126x^2 + 241/18x - 77/9 = 0

Output:
x^3 - 835/126x^2 + 241/18x - 77/9 = 0
(x - 14/9)(x - 11/7)(x - 7/2) = 0
x - 14/9 = 0
x - 11/7 = 0
x - 7/2 = 0
x = 14/9
x = 11/7
x = 7/2


Input:
Solve the equations:
4x + 2y = -33/5
9x + 8y = -76/5

Output:
4x + 2y = -33/5
9x + 8y = -76/5

Using elimination
9*(4x + 2y = -33/5)
4*(9x + 8y = -76/5)
36x + 18y = -297/5
36x + 32y = -304/5
Subtract equations
-14y = 7/5
y = 7/5/-14
y = -1/10

Substitute y
4x + 2(-1/10) = -33/5
4x = -32/5
x = -32/5/4
x = -8/5


Input:
Find x and y such that
7x + 7y = -28/3
6x + 9y = -6

Output:
7x + 7y = -28/3
6x + 9y = -6

Using elimination
6*(7x + 7y = -28/3)
7*(6x + 9y = -6)
42x + 42y = -56
42x + 63y = -42
Subtract equations
-21y = -14
y = -14/-21
y = 2/3

Substitute y
7x + 7(2/3) = -28/3
7x = -14
x = -14/7
x = -2


Input: Solve x^2 - 13/21x - 190/21 = 0

Output:
x^2 - 13/21x - 190/21 = 0
(x - 10/3)(x - -19/7) = 0
x - 10/3 = 0  or  x - -19/7 = 0
x = 10/3
x = -19/7


Input: Find x for 8x - 8 = 0

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


Input: Determine x in 4x - 52 = 0

Output:
4x - 52 = 0
4x = 52
x = 52 / 4
x = 13


Input:
Solve simultaneously:
1x + 6y = 267/35
7x + 9y = 69/5

Output:
1x + 6y = 267/35
7x + 9y = 69/5

Using elimination
7*(1x + 6y = 267/35)
1*(7x + 9y = 69/5)
7x + 42y = 267/5
7x + 9y = 69/5
Subtract equations
33y = 198/5
y = 198/5/33
y = 6/5

Substitute y
1x + 6(6/5) = 267/35
1x = 3/7
x = 3/7/1
x = 3/7


Input:
Find x and y such that
2x + 5y = 0
1x + 8y = 22

Output:
2x + 5y = 0
1x + 8y = 22

Using elimination
1*(2x + 5y = 0)
2*(1x + 8y = 22)
2x + 5y = 0
2x + 16y = 44
Subtract equations
-11y = -44
y = -44/-11
y = 4

Substitute y
2x + 5(4) = 0
2x = -20
x = -20/2
x = -10


Input: Find the solution to 8x - 11 = 0

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


Input: Solve 7x - 7/2 = 0

Output:
7x - 7/2 = 0
7x = 7/2
x = 7/2 / 7
x = 1/2


Input:
Solve the system:
9x + 10y = -213/8
5x + 5y = -105/8

Output:
9x + 10y = -213/8
5x + 5y = -105/8

Using elimination
5*(9x + 10y = -213/8)
9*(5x + 5y = -105/8)
45x + 50y = -1065/8
45x + 45y = -945/8
Subtract equations
5y = -15
y = -15/5
y = -3

Substitute y
9x + 10(-3) = -213/8
9x = 27/8
x = 27/8/9
x = 3/8


Input: Find x in x^2 + 88/15x + 17/15 = 0

Output:
x^2 + 88/15x + 17/15 = 0
(x - -17/3)(x - -1/5) = 0
x - -17/3 = 0  or  x - -1/5 = 0
x = -17/3
x = -1/5


Input: What value of x satisfies x^3 - 2/5x^2 - 225x + 90 = 0

Output:
x^3 - 2/5x^2 - 225x + 90 = 0
(x - 15)(x - 2/5)(x - -15) = 0
x - 15 = 0
x - 2/5 = 0
x - -15 = 0
x = 15
x = 2/5
x = -15


Input:
Solve the equations:
1x + 9y = 1/3
2x + 7y = 28/9

Output:
1x + 9y = 1/3
2x + 7y = 28/9

Using elimination
2*(1x + 9y = 1/3)
1*(2x + 7y = 28/9)
2x + 18y = 2/3
2x + 7y = 28/9
Subtract equations
11y = -22/9
y = -22/9/11
y = -2/9

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


Input:
Solve the system:
7x + 3y = 103
6x + 10y = 14

Output:
7x + 3y = 103
6x + 10y = 14

Using elimination
6*(7x + 3y = 103)
7*(6x + 10y = 14)
42x + 18y = 618
42x + 70y = 98
Subtract equations
-52y = 520
y = 520/-52
y = -10

Substitute y
7x + 3(-10) = 103
7x = 133
x = 133/7
x = 19


Input:
Find x and y such that
4x + 6y = 10/7
1x + 9y = -50/7

Output:
4x + 6y = 10/7
1x + 9y = -50/7

Using elimination
1*(4x + 6y = 10/7)
4*(1x + 9y = -50/7)
4x + 6y = 10/7
4x + 36y = -200/7
Subtract equations
-30y = 30
y = 30/-30
y = -1

Substitute y
4x + 6(-1) = 10/7
4x = 52/7
x = 52/7/4
x = 13/7


Input: Find x in x^3 - 77/18x^2 - 100/27x + 25/54 = 0

Output:
x^3 - 77/18x^2 - 100/27x + 25/54 = 0
(x - 5)(x - -5/6)(x - 1/9) = 0
x - 5 = 0
x - -5/6 = 0
x - 1/9 = 0
x = 5
x = -5/6
x = 1/9


Input:
Solve the equations:
9x + 4y = 189/5
6x + 2y = 132/5

Output:
9x + 4y = 189/5
6x + 2y = 132/5

Using elimination
6*(9x + 4y = 189/5)
9*(6x + 2y = 132/5)
54x + 24y = 1134/5
54x + 18y = 1188/5
Subtract equations
6y = -54/5
y = -54/5/6
y = -9/5

Substitute y
9x + 4(-9/5) = 189/5
9x = 45
x = 45/9
x = 5


Input: Find x for x^2 + 9x + 18 = 0

Output:
x^2 + 9x + 18 = 0
(x - -3)(x - -6) = 0
x - -3 = 0  or  x - -6 = 0
x = -3
x = -6


Input: Solve the equation 9x + 45/2 = 0

Output:
9x + 45/2 = 0
9x = -45/2
x = -45/2 / 9
x = -5/2


Input: Compute the solution of 10x - 25/4 = 0

Output:
10x - 25/4 = 0
10x = 25/4
x = 25/4 / 10
x = 5/8


Input: Find x for 10x + 20 = 0

Output:
10x + 20 = 0
10x = -20
x = -20 / 10
x = -2


Input:
Solve the system:
4x + 6y = 309/14
9x + 1y = 1081/56

Output:
4x + 6y = 309/14
9x + 1y = 1081/56

Using elimination
9*(4x + 6y = 309/14)
4*(9x + 1y = 1081/56)
36x + 54y = 2781/14
36x + 4y = 1081/14
Subtract equations
50y = 850/7
y = 850/7/50
y = 17/7

Substitute y
4x + 6(17/7) = 309/14
4x = 15/2
x = 15/2/4
x = 15/8


Input: Determine x in x^2 - 11/8x - 19/8 = 0

Output:
x^2 - 11/8x - 19/8 = 0
(x - -1)(x - 19/8) = 0
x - -1 = 0  or  x - 19/8 = 0
x = -1
x = 19/8


Input: Find x for 4x + 12/5 = 0

Output:
4x + 12/5 = 0
4x = -12/5
x = -12/5 / 4
x = -3/5


Input: Find x in x^2 - 1/3x - 154/81 = 0

Output:
x^2 - 1/3x - 154/81 = 0
(x - -11/9)(x - 14/9) = 0
x - -11/9 = 0  or  x - 14/9 = 0
x = -11/9
x = 14/9


Input: What value of x satisfies 1x - 5 = 0

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


Input:
Solve simultaneously:
9x + 2y = 77/5
8x + 10y = 212/9

Output:
9x + 2y = 77/5
8x + 10y = 212/9

Using elimination
8*(9x + 2y = 77/5)
9*(8x + 10y = 212/9)
72x + 16y = 616/5
72x + 90y = 212
Subtract equations
-74y = -444/5
y = -444/5/-74
y = 6/5

Substitute y
9x + 2(6/5) = 77/5
9x = 13
x = 13/9
x = 13/9


Input:
Solve simultaneously:
4x + 7y = -449/5
8x + 9y = -523/5

Output:
4x + 7y = -449/5
8x + 9y = -523/5

Using elimination
8*(4x + 7y = -449/5)
4*(8x + 9y = -523/5)
32x + 56y = -3592/5
32x + 36y = -2092/5
Subtract equations
20y = -300
y = -300/20
y = -15

Substitute y
4x + 7(-15) = -449/5
4x = 76/5
x = 76/5/4
x = 19/5


Input:
Solve the equations:
1x + 6y = -37/3
6x + 8y = -190/9

Output:
1x + 6y = -37/3
6x + 8y = -190/9

Using elimination
6*(1x + 6y = -37/3)
1*(6x + 8y = -190/9)
6x + 36y = -74
6x + 8y = -190/9
Subtract equations
28y = -476/9
y = -476/9/28
y = -17/9

Substitute y
1x + 6(-17/9) = -37/3
1x = -1
x = -1/1
x = -1


Input: Find the solution to 3x + 1/3 = 0

Output:
3x + 1/3 = 0
3x = -1/3
x = -1/3 / 3
x = -1/9


Input: Solve quickly: x^2 - 2/45x - 91/45 = 0

Output:
x^2 - 2/45x - 91/45 = 0
(x - -7/5)(x - 13/9) = 0
x - -7/5 = 0  or  x - 13/9 = 0
x = -7/5
x = 13/9


Input: Compute the solution of x^2 + 5x - 6 = 0

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


Input: Find the solution to x^3 + 11/15x^2 - 12/5x - 32/15 = 0

Output:
x^3 + 11/15x^2 - 12/5x - 32/15 = 0
(x - 8/5)(x - -4/3)(x - -1) = 0
x - 8/5 = 0
x - -4/3 = 0
x - -1 = 0
x = 8/5
x = -4/3
x = -1


Input: What value of x satisfies x^2 - 7/2x + 17/9 = 0

Output:
x^2 - 7/2x + 17/9 = 0
(x - 17/6)(x - 2/3) = 0
x - 17/6 = 0  or  x - 2/3 = 0
x = 17/6
x = 2/3


Input: Solve x^3 - 148/15x^2 - 89/20x + 187/6 = 0

Output:
x^3 - 148/15x^2 - 89/20x + 187/6 = 0
(x - -11/6)(x - 17/10)(x - 10) = 0
x - -11/6 = 0
x - 17/10 = 0
x - 10 = 0
x = -11/6
x = 17/10
x = 10


Input: Solve the equation x^2 - 8/3x - 11/3 = 0

Output:
x^2 - 8/3x - 11/3 = 0
(x - -1)(x - 11/3) = 0
x - -1 = 0  or  x - 11/3 = 0
x = -1
x = 11/3


Input: Solve quickly: x^2 - 76/45x - 1/5 = 0

Output:
x^2 - 76/45x - 1/5 = 0
(x - -1/9)(x - 9/5) = 0
x - -1/9 = 0  or  x - 9/5 = 0
x = -1/9
x = 9/5


Input: Find the solution to 8x - 16 = 0

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


Input: Solve x^2 + 33/4x + 133/8 = 0

Output:
x^2 + 33/4x + 133/8 = 0
(x - -19/4)(x - -7/2) = 0
x - -19/4 = 0  or  x - -7/2 = 0
x = -19/4
x = -7/2


Input:
Solve simultaneously:
2x + 3y = 194/7
5x + 7y = 457/7

Output:
2x + 3y = 194/7
5x + 7y = 457/7

Using elimination
5*(2x + 3y = 194/7)
2*(5x + 7y = 457/7)
10x + 15y = 970/7
10x + 14y = 914/7
Subtract equations
1y = 8
y = 8/1
y = 8

Substitute y
2x + 3(8) = 194/7
2x = 26/7
x = 26/7/2
x = 13/7


Input: Solve x^3 - 191/10x^2 + 57x + 135/2 = 0

Output:
x^3 - 191/10x^2 + 57x + 135/2 = 0
(x - 15)(x - -9/10)(x - 5) = 0
x - 15 = 0
x - -9/10 = 0
x - 5 = 0
x = 15
x = -9/10
x = 5


Input: Find the solution to x^2 - 52/9x + 35/9 = 0

Output:
x^2 - 52/9x + 35/9 = 0
(x - 5)(x - 7/9) = 0
x - 5 = 0  or  x - 7/9 = 0
x = 5
x = 7/9


Input: Determine x in 1x - 11/10 = 0

Output:
1x - 11/10 = 0
1x = 11/10
x = 11/10 / 1
x = 11/10


Input: Find x for x^3 + 35/9x^2 + 34/9x  = 0

Output:
x^3 + 35/9x^2 + 34/9x  = 0
(x - -2)(x - -17/9)(x - 0) = 0
x - -2 = 0
x - -17/9 = 0
x - 0 = 0
x = -2
x = -17/9
x = 0


Input: Find the solution to x^3 - 37/6x^2 - 34/3x + 10 = 0

Output:
x^3 - 37/6x^2 - 34/3x + 10 = 0
(x - 2/3)(x - 15/2)(x - -2) = 0
x - 2/3 = 0
x - 15/2 = 0
x - -2 = 0
x = 2/3
x = 15/2
x = -2


Input: Find the solution to 8x - 2 = 0

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


Input: What value of x satisfies 4x - 52/3 = 0

Output:
4x - 52/3 = 0
4x = 52/3
x = 52/3 / 4
x = 13/3


Input: Solve quickly: x^3 + 79/24x^2 - 46/3x - 85/8 = 0

Output:
x^3 + 79/24x^2 - 46/3x - 85/8 = 0
(x - -5/8)(x - -17/3)(x - 3) = 0
x - -5/8 = 0
x - -17/3 = 0
x - 3 = 0
x = -5/8
x = -17/3
x = 3


Input:
Solve simultaneously:
10x + 1y = 454/63
2x + 5y = -82/63

Output:
10x + 1y = 454/63
2x + 5y = -82/63

Using elimination
2*(10x + 1y = 454/63)
10*(2x + 5y = -82/63)
20x + 2y = 908/63
20x + 50y = -820/63
Subtract equations
-48y = 192/7
y = 192/7/-48
y = -4/7

Substitute y
10x + 1(-4/7) = 454/63
10x = 70/9
x = 70/9/10
x = 7/9


Input: What value of x satisfies 7x + 21/10 = 0

Output:
7x + 21/10 = 0
7x = -21/10
x = -21/10 / 7
x = -3/10


Input: Find x for x^2 - 92/45x - 28/5 = 0

Output:
x^2 - 92/45x - 28/5 = 0
(x - 18/5)(x - -14/9) = 0
x - 18/5 = 0  or  x - -14/9 = 0
x = 18/5
x = -14/9


Input: Solve the equation x^3 + 41/20x^2 - 257/40x - 99/8 = 0

Output:
x^3 + 41/20x^2 - 257/40x - 99/8 = 0
(x - -9/5)(x - -11/4)(x - 5/2) = 0
x - -9/5 = 0
x - -11/4 = 0
x - 5/2 = 0
x = -9/5
x = -11/4
x = 5/2


Input: Find x in x^2 + 28/3x + 64/3 = 0

Output:
x^2 + 28/3x + 64/3 = 0
(x - -4)(x - -16/3) = 0
x - -4 = 0  or  x - -16/3 = 0
x = -4
x = -16/3


Input: Determine x in x^2 - 25x + 100 = 0

Output:
x^2 - 25x + 100 = 0
(x - 20)(x - 5) = 0
x - 20 = 0  or  x - 5 = 0
x = 20
x = 5


Input: Solve quickly: 4x - 18/5 = 0

Output:
4x - 18/5 = 0
4x = 18/5
x = 18/5 / 4
x = 9/10


Input: Solve the equation x^3 + 119/10x^2 + 154/5x - 16/5 = 0

Output:
x^3 + 119/10x^2 + 154/5x - 16/5 = 0
(x - -4)(x - -8)(x - 1/10) = 0
x - -4 = 0
x - -8 = 0
x - 1/10 = 0
x = -4
x = -8
x = 1/10


Input:
Find x and y such that
1x + 4y = 119/18
1x + 8y = 247/18

Output:
1x + 4y = 119/18
1x + 8y = 247/18

Using elimination
1*(1x + 4y = 119/18)
1*(1x + 8y = 247/18)
1x + 4y = 119/18
1x + 8y = 247/18
Subtract equations
-4y = -64/9
y = -64/9/-4
y = 16/9

Substitute y
1x + 4(16/9) = 119/18
1x = -1/2
x = -1/2/1
x = -1/2


Input:
Solve the system:
2x + 6y = -18
6x + 10y = -98/3

Output:
2x + 6y = -18
6x + 10y = -98/3

Using elimination
6*(2x + 6y = -18)
2*(6x + 10y = -98/3)
12x + 36y = -108
12x + 20y = -196/3
Subtract equations
16y = -128/3
y = -128/3/16
y = -8/3

Substitute y
2x + 6(-8/3) = -18
2x = -2
x = -2/2
x = -1


Input: Compute the solution of 10x + 10/3 = 0

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


Input: Find x in 5x - 13 = 0

Output:
5x - 13 = 0
5x = 13
x = 13 / 5
x = 13/5


Input: Solve quickly: x^2 - 40/9x + 13/3 = 0

Output:
x^2 - 40/9x + 13/3 = 0
(x - 13/9)(x - 3) = 0
x - 13/9 = 0  or  x - 3 = 0
x = 13/9
x = 3


Input: Solve the equation x^3 - 844/105x^2 + 1481/105x + 38/5 = 0

Output:
x^3 - 844/105x^2 + 1481/105x + 38/5 = 0
(x - 19/5)(x - 14/3)(x - -3/7) = 0
x - 19/5 = 0
x - 14/3 = 0
x - -3/7 = 0
x = 19/5
x = 14/3
x = -3/7


Input: Find x for 2x + 14/3 = 0

Output:
2x + 14/3 = 0
2x = -14/3
x = -14/3 / 2
x = -7/3


Input: Find x for x^3 + 109/56x^2 - 123/112x - 297/112 = 0

Output:
x^3 + 109/56x^2 - 123/112x - 297/112 = 0
(x - -3/2)(x - -11/7)(x - 9/8) = 0
x - -3/2 = 0
x - -11/7 = 0
x - 9/8 = 0
x = -3/2
x = -11/7
x = 9/8


Input: Determine x in 7x + 7/8 = 0

Output:
7x + 7/8 = 0
7x = -7/8
x = -7/8 / 7
x = -1/8


Input: Find the solution to 1x + 7/8 = 0

Output:
1x + 7/8 = 0
1x = -7/8
x = -7/8 / 1
x = -7/8


Input: Find the solution to x^2 - 11/2x - 63/2 = 0

Output:
x^2 - 11/2x - 63/2 = 0
(x - 9)(x - -7/2) = 0
x - 9 = 0  or  x - -7/2 = 0
x = 9
x = -7/2


Input: Compute the solution of 1x + 5/4 = 0

Output:
1x + 5/4 = 0
1x = -5/4
x = -5/4 / 1
x = -5/4


Input: Solve the equation 1x - 1/6 = 0

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


Input: Find x for x^2 + 115/18x - 25/3 = 0

Output:
x^2 + 115/18x - 25/3 = 0
(x - 10/9)(x - -15/2) = 0
x - 10/9 = 0  or  x - -15/2 = 0
x = 10/9
x = -15/2


Input: Solve x^2 + 1/4x - 7/2 = 0

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


Input:
Find x and y such that
4x + 5y = 33
9x + 10y = 279/4

Output:
4x + 5y = 33
9x + 10y = 279/4

Using elimination
9*(4x + 5y = 33)
4*(9x + 10y = 279/4)
36x + 45y = 297
36x + 40y = 279
Subtract equations
5y = 18
y = 18/5
y = 18/5

Substitute y
4x + 5(18/5) = 33
4x = 15
x = 15/4
x = 15/4


Input: Find the solution to x^2 - 59/30x + 1/2 = 0

Output:
x^2 - 59/30x + 1/2 = 0
(x - 3/10)(x - 5/3) = 0
x - 3/10 = 0  or  x - 5/3 = 0
x = 3/10
x = 5/3


Input: Compute the solution of x^3 - 101/180x^2 - 188/45x + 17/20 = 0

Output:
x^3 - 101/180x^2 - 188/45x + 17/20 = 0
(x - -17/9)(x - 1/5)(x - 9/4) = 0
x - -17/9 = 0
x - 1/5 = 0
x - 9/4 = 0
x = -17/9
x = 1/5
x = 9/4


Input: Solve 3x - 6 = 0

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


Input: Find x in x^3 - 21/8x^2 - 49/16x  = 0

Output:
x^3 - 21/8x^2 - 49/16x  = 0
(x - 7/2)(x - -7/8)(x - 0) = 0
x - 7/2 = 0
x - -7/8 = 0
x - 0 = 0
x = 7/2
x = -7/8
x = 0


Input: Solve quickly: 1x - 19/9 = 0

Output:
1x - 19/9 = 0
1x = 19/9
x = 19/9 / 1
x = 19/9


Input:
Solve the equations:
7x + 10y = 347/15
7x + 4y = 227/15

Output:
7x + 10y = 347/15
7x + 4y = 227/15

Using elimination
7*(7x + 10y = 347/15)
7*(7x + 4y = 227/15)
49x + 70y = 2429/15
49x + 28y = 1589/15
Subtract equations
42y = 56
y = 56/42
y = 4/3

Substitute y
7x + 10(4/3) = 347/15
7x = 49/5
x = 49/5/7
x = 7/5


Input: Solve x^3 - 313/14x^2 + 579/7x - 540/7 = 0

Output:
x^3 - 313/14x^2 + 579/7x - 540/7 = 0
(x - 18)(x - 20/7)(x - 3/2) = 0
x - 18 = 0
x - 20/7 = 0
x - 3/2 = 0
x = 18
x = 20/7
x = 3/2


Input:
Solve simultaneously:
5x + 7y = 23/5
7x + 10y = 33/5

Output:
5x + 7y = 23/5
7x + 10y = 33/5

Using elimination
7*(5x + 7y = 23/5)
5*(7x + 10y = 33/5)
35x + 49y = 161/5
35x + 50y = 33
Subtract equations
-1y = -4/5
y = -4/5/-1
y = 4/5

Substitute y
5x + 7(4/5) = 23/5
5x = -1
x = -1/5
x = -1/5


Input: Determine x in x^3 - 289/30x^2 + 114/5x - 6 = 0

Output:
x^3 - 289/30x^2 + 114/5x - 6 = 0
(x - 3/10)(x - 10/3)(x - 6) = 0
x - 3/10 = 0
x - 10/3 = 0
x - 6 = 0
x = 3/10
x = 10/3
x = 6


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

Output:
1x - 3/2 = 0
1x = 3/2
x = 3/2 / 1
x = 3/2


Input: Find x for x^2 + 43/15x - 42/5 = 0

Output:
x^2 + 43/15x - 42/5 = 0
(x - 9/5)(x - -14/3) = 0
x - 9/5 = 0  or  x - -14/3 = 0
x = 9/5
x = -14/3


Input: Compute the solution of x^3 - 55/18x^2 + 26/9x - 5/6 = 0

Output:
x^3 - 55/18x^2 + 26/9x - 5/6 = 0
(x - 5/9)(x - 3/2)(x - 1) = 0
x - 5/9 = 0
x - 3/2 = 0
x - 1 = 0
x = 5/9
x = 3/2
x = 1


Input:
Solve the system:
2x + 10y = 73/2
6x + 3y = 303/4

Output:
2x + 10y = 73/2
6x + 3y = 303/4

Using elimination
6*(2x + 10y = 73/2)
2*(6x + 3y = 303/4)
12x + 60y = 219
12x + 6y = 303/2
Subtract equations
54y = 135/2
y = 135/2/54
y = 5/4

Substitute y
2x + 10(5/4) = 73/2
2x = 24
x = 24/2
x = 12


Input: Find x in x^3 + 103/10x^2 - 4x - 70 = 0

Output:
x^3 + 103/10x^2 - 4x - 70 = 0
(x - -14/5)(x - 5/2)(x - -10) = 0
x - -14/5 = 0
x - 5/2 = 0
x - -10 = 0
x = -14/5
x = 5/2
x = -10


Input: Find x for 4x - 8/7 = 0

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


Input: Solve x^3 + 71/14x^2 - 45/7x - 36/7 = 0

Output:
x^3 + 71/14x^2 - 45/7x - 36/7 = 0
(x - 3/2)(x - -4/7)(x - -6) = 0
x - 3/2 = 0
x - -4/7 = 0
x - -6 = 0
x = 3/2
x = -4/7
x = -6


Input: Find the solution to x^3 - 41/6x^2 + 25/6x + 25 = 0

Output:
x^3 - 41/6x^2 + 25/6x + 25 = 0
(x - 5)(x - 10/3)(x - -3/2) = 0
x - 5 = 0
x - 10/3 = 0
x - -3/2 = 0
x = 5
x = 10/3
x = -3/2


Input:
Solve the system:
2x + 9y = 13
1x + 4y = 17/3

Output:
2x + 9y = 13
1x + 4y = 17/3

Using elimination
1*(2x + 9y = 13)
2*(1x + 4y = 17/3)
2x + 9y = 13
2x + 8y = 34/3
Subtract equations
1y = 5/3
y = 5/3/1
y = 5/3

Substitute y
2x + 9(5/3) = 13
2x = -2
x = -2/2
x = -1


Input: What value of x satisfies x^3 - 29/12x^2 - 91/24x + 49/8 = 0

Output:
x^3 - 29/12x^2 - 91/24x + 49/8 = 0
(x - -7/4)(x - 3)(x - 7/6) = 0
x - -7/4 = 0
x - 3 = 0
x - 7/6 = 0
x = -7/4
x = 3
x = 7/6


Input: Find the solution to 6x + 24/7 = 0

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


Input: Determine x in x^3 + 43/28x^2 - 145/196x - 13/49 = 0

Output:
x^3 + 43/28x^2 - 145/196x - 13/49 = 0
(x - -1/4)(x - 4/7)(x - -13/7) = 0
x - -1/4 = 0
x - 4/7 = 0
x - -13/7 = 0
x = -1/4
x = 4/7
x = -13/7


Input: Find the solution to x^3 - 271/35x^2 + 11/5x + 21 = 0

Output:
x^3 - 271/35x^2 + 11/5x + 21 = 0
(x - 15/7)(x - -7/5)(x - 7) = 0
x - 15/7 = 0
x - -7/5 = 0
x - 7 = 0
x = 15/7
x = -7/5
x = 7


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

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


Input: Compute the solution of 2x - 17/5 = 0

Output:
2x - 17/5 = 0
2x = 17/5
x = 17/5 / 2
x = 17/10


Input: What value of x satisfies 6x + 15/2 = 0

Output:
6x + 15/2 = 0
6x = -15/2
x = -15/2 / 6
x = -5/4


Input: Solve x^3 + 2/9x^2 - 71/36x - 11/12 = 0

Output:
x^3 + 2/9x^2 - 71/36x - 11/12 = 0
(x - 3/2)(x - -11/9)(x - -1/2) = 0
x - 3/2 = 0
x - -11/9 = 0
x - -1/2 = 0
x = 3/2
x = -11/9
x = -1/2


Input: Find x for x^2 + 11/6x - 91/3 = 0

Output:
x^2 + 11/6x - 91/3 = 0
(x - -13/2)(x - 14/3) = 0
x - -13/2 = 0  or  x - 14/3 = 0
x = -13/2
x = 14/3


Input:
Solve the system:
8x + 1y = -535/8
2x + 2y = -59/4

Output:
8x + 1y = -535/8
2x + 2y = -59/4

Using elimination
2*(8x + 1y = -535/8)
8*(2x + 2y = -59/4)
16x + 2y = -535/4
16x + 16y = -118
Subtract equations
-14y = -63/4
y = -63/4/-14
y = 9/8

Substitute y
8x + 1(9/8) = -535/8
8x = -68
x = -68/8
x = -17/2


Input: What value of x satisfies 4x + 4 = 0

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


Input: Find x for 8x - 48 = 0

Output:
8x - 48 = 0
8x = 48
x = 48 / 8
x = 6


Input: Find x for x^3 + 9/7x^2 - 202/49x - 240/49 = 0

Output:
x^3 + 9/7x^2 - 202/49x - 240/49 = 0
(x - -8/7)(x - -15/7)(x - 2) = 0
x - -8/7 = 0
x - -15/7 = 0
x - 2 = 0
x = -8/7
x = -15/7
x = 2


Input: Solve the equation 10x - 8 = 0

Output:
10x - 8 = 0
10x = 8
x = 8 / 10
x = 4/5


Input:
Solve the equations:
4x + 6y = -158/9
3x + 6y = -53/3

Output:
4x + 6y = -158/9
3x + 6y = -53/3

Using elimination
3*(4x + 6y = -158/9)
4*(3x + 6y = -53/3)
12x + 18y = -158/3
12x + 24y = -212/3
Subtract equations
-6y = 18
y = 18/-6
y = -3

Substitute y
4x + 6(-3) = -158/9
4x = 4/9
x = 4/9/4
x = 1/9


Input: Solve the equation x^3 - 43/3x^2 + 39x - 77/3 = 0

Output:
x^3 - 43/3x^2 + 39x - 77/3 = 0
(x - 7/3)(x - 1)(x - 11) = 0
x - 7/3 = 0
x - 1 = 0
x - 11 = 0
x = 7/3
x = 1
x = 11


Input: Find x in 7x - 133/10 = 0

Output:
7x - 133/10 = 0
7x = 133/10
x = 133/10 / 7
x = 19/10


Input: Find x in x^3 - 11/18x^2 - 241/54x + 110/27 = 0

Output:
x^3 - 11/18x^2 - 241/54x + 110/27 = 0
(x - 11/6)(x - 1)(x - -20/9) = 0
x - 11/6 = 0
x - 1 = 0
x - -20/9 = 0
x = 11/6
x = 1
x = -20/9


Input: Compute the solution of x^3 - 55/7x^2 + 568/49x - 132/49 = 0

Output:
x^3 - 55/7x^2 + 568/49x - 132/49 = 0
(x - 2/7)(x - 6)(x - 11/7) = 0
x - 2/7 = 0
x - 6 = 0
x - 11/7 = 0
x = 2/7
x = 6
x = 11/7


Input: Solve x^3 + 169/180x^2 - 2077/180x + 323/30 = 0

Output:
x^3 + 169/180x^2 - 2077/180x + 323/30 = 0
(x - 19/9)(x - -17/4)(x - 6/5) = 0
x - 19/9 = 0
x - -17/4 = 0
x - 6/5 = 0
x = 19/9
x = -17/4
x = 6/5


Input: Find x in x^2 - 3x - 304 = 0

Output:
x^2 - 3x - 304 = 0
(x - -16)(x - 19) = 0
x - -16 = 0  or  x - 19 = 0
x = -16
x = 19


Input: Solve quickly: 1x - 17/6 = 0

Output:
1x - 17/6 = 0
1x = 17/6
x = 17/6 / 1
x = 17/6


Input: Find the solution to x^2 + 21/4x + 5/4 = 0

Output:
x^2 + 21/4x + 5/4 = 0
(x - -1/4)(x - -5) = 0
x - -1/4 = 0  or  x - -5 = 0
x = -1/4
x = -5


Input: Solve the equation 5x - 8 = 0

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


Input: Find x for 2x + 36 = 0

Output:
2x + 36 = 0
2x = -36
x = -36 / 2
x = -18


Input:
Solve the system:
6x + 5y = 37
2x + 1y = 9

Output:
6x + 5y = 37
2x + 1y = 9

Using elimination
2*(6x + 5y = 37)
6*(2x + 1y = 9)
12x + 10y = 74
12x + 6y = 54
Subtract equations
4y = 20
y = 20/4
y = 5

Substitute y
6x + 5(5) = 37
6x = 12
x = 12/6
x = 2


Input: Find the solution to x^3 + 15/2x^2 + 81/16x - 595/16 = 0

Output:
x^3 + 15/2x^2 + 81/16x - 595/16 = 0
(x - 7/4)(x - -17/4)(x - -5) = 0
x - 7/4 = 0
x - -17/4 = 0
x - -5 = 0
x = 7/4
x = -17/4
x = -5


Input: Solve the equation x^3 + 59/30x^2 - 29/10x - 17/3 = 0

Output:
x^3 + 59/30x^2 - 29/10x - 17/3 = 0
(x - 17/10)(x - -2)(x - -5/3) = 0
x - 17/10 = 0
x - -2 = 0
x - -5/3 = 0
x = 17/10
x = -2
x = -5/3


Input: Compute the solution of x^3 + 18/5x^2 + 233/100x - 21/20 = 0

Output:
x^3 + 18/5x^2 + 233/100x - 21/20 = 0
(x - -5/2)(x - -7/5)(x - 3/10) = 0
x - -5/2 = 0
x - -7/5 = 0
x - 3/10 = 0
x = -5/2
x = -7/5
x = 3/10


Input: Solve quickly: 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: Solve the equation x^2 - 196/45x + 196/45 = 0

Output:
x^2 - 196/45x + 196/45 = 0
(x - 14/5)(x - 14/9) = 0
x - 14/5 = 0  or  x - 14/9 = 0
x = 14/5
x = 14/9


Input:
Solve the equations:
10x + 3y = 8
5x + 3y = 8

Output:
10x + 3y = 8
5x + 3y = 8

Using elimination
5*(10x + 3y = 8)
10*(5x + 3y = 8)
50x + 15y = 40
50x + 30y = 80
Subtract equations
-15y = -40
y = -40/-15
y = 8/3

Substitute y
10x + 3(8/3) = 8
10x = 0
x = 0/10
x = 0


Input: Solve quickly: x^3 + 19/2x^2 + 27x + 45/2 = 0

Output:
x^3 + 19/2x^2 + 27x + 45/2 = 0
(x - -5)(x - -3/2)(x - -3) = 0
x - -5 = 0
x - -3/2 = 0
x - -3 = 0
x = -5
x = -3/2
x = -3


Input: What value of x satisfies x^2 - 37/45x + 2/15 = 0

Output:
x^2 - 37/45x + 2/15 = 0
(x - 2/9)(x - 3/5) = 0
x - 2/9 = 0  or  x - 3/5 = 0
x = 2/9
x = 3/5


Input: Solve the equation x^2 - 7/6x - 10/3 = 0

Output:
x^2 - 7/6x - 10/3 = 0
(x - -4/3)(x - 5/2) = 0
x - -4/3 = 0  or  x - 5/2 = 0
x = -4/3
x = 5/2


Input:
Find x and y such that
1x + 9y = -58/7
7x + 6y = 50/7

Output:
1x + 9y = -58/7
7x + 6y = 50/7

Using elimination
7*(1x + 9y = -58/7)
1*(7x + 6y = 50/7)
7x + 63y = -58
7x + 6y = 50/7
Subtract equations
57y = -456/7
y = -456/7/57
y = -8/7

Substitute y
1x + 9(-8/7) = -58/7
1x = 2
x = 2/1
x = 2


Input: Solve the equation x^2  - 25/16 = 0

Output:
x^2  - 25/16 = 0
(x - -5/4)(x - 5/4) = 0
x - -5/4 = 0  or  x - 5/4 = 0
x = -5/4
x = 5/4


Input: Solve quickly: x^3 - 59/10x^2 + 242/25x - 112/25 = 0

Output:
x^3 - 59/10x^2 + 242/25x - 112/25 = 0
(x - 8/5)(x - 7/2)(x - 4/5) = 0
x - 8/5 = 0
x - 7/2 = 0
x - 4/5 = 0
x = 8/5
x = 7/2
x = 4/5


Input: Find the solution to 9x + 6 = 0

Output:
9x + 6 = 0
9x = -6
x = -6 / 9
x = -2/3


Input:
Find x and y such that
3x + 5y = 444/7
3x + 3y = 426/7

Output:
3x + 5y = 444/7
3x + 3y = 426/7

Using elimination
3*(3x + 5y = 444/7)
3*(3x + 3y = 426/7)
9x + 15y = 1332/7
9x + 9y = 1278/7
Subtract equations
6y = 54/7
y = 54/7/6
y = 9/7

Substitute y
3x + 5(9/7) = 444/7
3x = 57
x = 57/3
x = 19


Input:
Solve the system:
3x + 8y = 171/28
10x + 3y = 1/14

Output:
3x + 8y = 171/28
10x + 3y = 1/14

Using elimination
10*(3x + 8y = 171/28)
3*(10x + 3y = 1/14)
30x + 80y = 855/14
30x + 9y = 3/14
Subtract equations
71y = 426/7
y = 426/7/71
y = 6/7

Substitute y
3x + 8(6/7) = 171/28
3x = -3/4
x = -3/4/3
x = -1/4


Input: Solve quickly: x^3 - 412/21x^2 - 96/7x + 2560/21 = 0

Output:
x^3 - 412/21x^2 - 96/7x + 2560/21 = 0
(x - 16/7)(x - -8/3)(x - 20) = 0
x - 16/7 = 0
x - -8/3 = 0
x - 20 = 0
x = 16/7
x = -8/3
x = 20


Input: What value of x satisfies x^2 - 145/56x + 3/2 = 0

Output:
x^2 - 145/56x + 3/2 = 0
(x - 7/8)(x - 12/7) = 0
x - 7/8 = 0  or  x - 12/7 = 0
x = 7/8
x = 12/7


Input: Find x for x^3 - 7/9x^2 - 34/9x + 32/9 = 0

Output:
x^3 - 7/9x^2 - 34/9x + 32/9 = 0
(x - 1)(x - 16/9)(x - -2) = 0
x - 1 = 0
x - 16/9 = 0
x - -2 = 0
x = 1
x = 16/9
x = -2


Input: Find x in 5x - 10 = 0

Output:
5x - 10 = 0
5x = 10
x = 10 / 5
x = 2


Input: Find x in x^3 + 509/252x^2 - 505/252x - 13/3 = 0

Output:
x^3 + 509/252x^2 - 505/252x - 13/3 = 0
(x - -12/7)(x - 13/9)(x - -7/4) = 0
x - -12/7 = 0
x - 13/9 = 0
x - -7/4 = 0
x = -12/7
x = 13/9
x = -7/4


Input: Solve x^3 + 311/18x^2 + 287/6x + 245/9 = 0

Output:
x^3 + 311/18x^2 + 287/6x + 245/9 = 0
(x - -14)(x - -7/9)(x - -5/2) = 0
x - -14 = 0
x - -7/9 = 0
x - -5/2 = 0
x = -14
x = -7/9
x = -5/2


Input: Compute the solution of x^3 - 9/7x^2 - 10/49x + 24/49 = 0

Output:
x^3 - 9/7x^2 - 10/49x + 24/49 = 0
(x - -4/7)(x - 6/7)(x - 1) = 0
x - -4/7 = 0
x - 6/7 = 0
x - 1 = 0
x = -4/7
x = 6/7
x = 1


Input: Find x in 7x + 91/10 = 0

Output:
7x + 91/10 = 0
7x = -91/10
x = -91/10 / 7
x = -13/10


Input: Find x in x^3 - 35/18x^2 - 2407/450x - 11/5 = 0

Output:
x^3 - 35/18x^2 - 2407/450x - 11/5 = 0
(x - -5/9)(x - 18/5)(x - -11/10) = 0
x - -5/9 = 0
x - 18/5 = 0
x - -11/10 = 0
x = -5/9
x = 18/5
x = -11/10


Input: Solve x^2 + 37/10x + 7/10 = 0

Output:
x^2 + 37/10x + 7/10 = 0
(x - -1/5)(x - -7/2) = 0
x - -1/5 = 0  or  x - -7/2 = 0
x = -1/5
x = -7/2


Input:
Solve simultaneously:
4x + 9y = 1
6x + 3y = -9

Output:
4x + 9y = 1
6x + 3y = -9

Using elimination
6*(4x + 9y = 1)
4*(6x + 3y = -9)
24x + 54y = 6
24x + 12y = -36
Subtract equations
42y = 42
y = 42/42
y = 1

Substitute y
4x + 9(1) = 1
4x = -8
x = -8/4
x = -2


Input:
Solve the equations:
9x + 8y = 83/5
8x + 3y = 323/40

Output:
9x + 8y = 83/5
8x + 3y = 323/40

Using elimination
8*(9x + 8y = 83/5)
9*(8x + 3y = 323/40)
72x + 64y = 664/5
72x + 27y = 2907/40
Subtract equations
37y = 481/8
y = 481/8/37
y = 13/8

Substitute y
9x + 8(13/8) = 83/5
9x = 18/5
x = 18/5/9
x = 2/5


Input: Solve quickly: x^3 - 17/30x^2 - 71/6x + 57/5 = 0

Output:
x^3 - 17/30x^2 - 71/6x + 57/5 = 0
(x - -18/5)(x - 19/6)(x - 1) = 0
x - -18/5 = 0
x - 19/6 = 0
x - 1 = 0
x = -18/5
x = 19/6
x = 1


Input: What value of x satisfies 4x - 16 = 0

Output:
4x - 16 = 0
4x = 16
x = 16 / 4
x = 4


Input: Find the solution to x^2 - 4x + 187/49 = 0

Output:
x^2 - 4x + 187/49 = 0
(x - 11/7)(x - 17/7) = 0
x - 11/7 = 0  or  x - 17/7 = 0
x = 11/7
x = 17/7


Input: Solve the equation x^3 - 88/105x^2 - 449/105x - 8/5 = 0

Output:
x^3 - 88/105x^2 - 449/105x - 8/5 = 0
(x - -3/7)(x - -7/5)(x - 8/3) = 0
x - -3/7 = 0
x - -7/5 = 0
x - 8/3 = 0
x = -3/7
x = -7/5
x = 8/3


Input:
Solve the system:
8x + 7y = 56/5
4x + 5y = 256/35

Output:
8x + 7y = 56/5
4x + 5y = 256/35

Using elimination
4*(8x + 7y = 56/5)
8*(4x + 5y = 256/35)
32x + 28y = 224/5
32x + 40y = 2048/35
Subtract equations
-12y = -96/7
y = -96/7/-12
y = 8/7

Substitute y
8x + 7(8/7) = 56/5
8x = 16/5
x = 16/5/8
x = 2/5


Input: Find x for x^3 - 67/12x^2 + 23/12x + 5 = 0

Output:
x^3 - 67/12x^2 + 23/12x + 5 = 0
(x - 5)(x - 4/3)(x - -3/4) = 0
x - 5 = 0
x - 4/3 = 0
x - -3/4 = 0
x = 5
x = 4/3
x = -3/4


Input: Solve quickly: x^2 - 11/40x - 1/20 = 0

Output:
x^2 - 11/40x - 1/20 = 0
(x - -1/8)(x - 2/5) = 0
x - -1/8 = 0  or  x - 2/5 = 0
x = -1/8
x = 2/5


Input:
Solve the equations:
1x + 3y = 67/2
7x + 4y = 129/2

Output:
1x + 3y = 67/2
7x + 4y = 129/2

Using elimination
7*(1x + 3y = 67/2)
1*(7x + 4y = 129/2)
7x + 21y = 469/2
7x + 4y = 129/2
Subtract equations
17y = 170
y = 170/17
y = 10

Substitute y
1x + 3(10) = 67/2
1x = 7/2
x = 7/2/1
x = 7/2


Input: Find the solution to 1x + 3/2 = 0

Output:
1x + 3/2 = 0
1x = -3/2
x = -3/2 / 1
x = -3/2


Input: Solve quickly: x^2 - 7x + 6 = 0

Output:
x^2 - 7x + 6 = 0
(x - 1)(x - 6) = 0
x - 1 = 0  or  x - 6 = 0
x = 1
x = 6


Input: Find the solution to x^3 + 175/18x^2 + 1279/54x + 380/27 = 0

Output:
x^3 + 175/18x^2 + 1279/54x + 380/27 = 0
(x - -19/3)(x - -8/9)(x - -5/2) = 0
x - -19/3 = 0
x - -8/9 = 0
x - -5/2 = 0
x = -19/3
x = -8/9
x = -5/2


Input: What value of x satisfies x^3 - 1139/70x^2 + 23/10x + 1144/35 = 0

Output:
x^3 - 1139/70x^2 + 23/10x + 1144/35 = 0
(x - -13/10)(x - 16)(x - 11/7) = 0
x - -13/10 = 0
x - 16 = 0
x - 11/7 = 0
x = -13/10
x = 16
x = 11/7


Input: Find x in x^3 + 23/56x^2 - 843/392x - 297/196 = 0

Output:
x^3 + 23/56x^2 - 843/392x - 297/196 = 0
(x - -6/7)(x - -9/8)(x - 11/7) = 0
x - -6/7 = 0
x - -9/8 = 0
x - 11/7 = 0
x = -6/7
x = -9/8
x = 11/7


Input: What value of x satisfies 4x + 24 = 0

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


Input: Solve x^2 + 77/10x - 171/10 = 0

Output:
x^2 + 77/10x - 171/10 = 0
(x - 9/5)(x - -19/2) = 0
x - 9/5 = 0  or  x - -19/2 = 0
x = 9/5
x = -19/2


Input: Determine x in x^3 + 12x^2 + 153/4x + 135/4 = 0

Output:
x^3 + 12x^2 + 153/4x + 135/4 = 0
(x - -3/2)(x - -3)(x - -15/2) = 0
x - -3/2 = 0
x - -3 = 0
x - -15/2 = 0
x = -3/2
x = -3
x = -15/2


Input:
Solve the equations:
10x + 2y = 34/3
10x + 3y = 31/3

Output:
10x + 2y = 34/3
10x + 3y = 31/3

Using elimination
10*(10x + 2y = 34/3)
10*(10x + 3y = 31/3)
100x + 20y = 340/3
100x + 30y = 310/3
Subtract equations
-10y = 10
y = 10/-10
y = -1

Substitute y
10x + 2(-1) = 34/3
10x = 40/3
x = 40/3/10
x = 4/3


Input: Compute the solution of x^3 + 55/3x^2 + 439/9x - 55/3 = 0

Output:
x^3 + 55/3x^2 + 439/9x - 55/3 = 0
(x - -15)(x - 1/3)(x - -11/3) = 0
x - -15 = 0
x - 1/3 = 0
x - -11/3 = 0
x = -15
x = 1/3
x = -11/3


Input:
Solve the system:
1x + 9y = -3
9x + 1y = 133

Output:
1x + 9y = -3
9x + 1y = 133

Using elimination
9*(1x + 9y = -3)
1*(9x + 1y = 133)
9x + 81y = -27
9x + 1y = 133
Subtract equations
80y = -160
y = -160/80
y = -2

Substitute y
1x + 9(-2) = -3
1x = 15
x = 15/1
x = 15


Input: Compute the solution of x^2 - 72/35x - 128/35 = 0

Output:
x^2 - 72/35x - 128/35 = 0
(x - 16/5)(x - -8/7) = 0
x - 16/5 = 0  or  x - -8/7 = 0
x = 16/5
x = -8/7


Input: Find x for x^2 - 46/7x + 72/7 = 0

Output:
x^2 - 46/7x + 72/7 = 0
(x - 18/7)(x - 4) = 0
x - 18/7 = 0  or  x - 4 = 0
x = 18/7
x = 4


Input:
Solve simultaneously:
2x + 4y = 534/35
7x + 2y = 729/35

Output:
2x + 4y = 534/35
7x + 2y = 729/35

Using elimination
7*(2x + 4y = 534/35)
2*(7x + 2y = 729/35)
14x + 28y = 534/5
14x + 4y = 1458/35
Subtract equations
24y = 456/7
y = 456/7/24
y = 19/7

Substitute y
2x + 4(19/7) = 534/35
2x = 22/5
x = 22/5/2
x = 11/5


Input: Find x in 3x - 45/4 = 0

Output:
3x - 45/4 = 0
3x = 45/4
x = 45/4 / 3
x = 15/4


Input: What value of x satisfies x^3 + 325/84x^2 + 113/28x + 20/21 = 0

Output:
x^3 + 325/84x^2 + 113/28x + 20/21 = 0
(x - -16/7)(x - -1/3)(x - -5/4) = 0
x - -16/7 = 0
x - -1/3 = 0
x - -5/4 = 0
x = -16/7
x = -1/3
x = -5/4


Input: Find x for x^2 - 9/2x - 5/2 = 0

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


Input: Solve quickly: x^2 - 5x + 21/4 = 0

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


Input: Determine x in 3x + 2/3 = 0

Output:
3x + 2/3 = 0
3x = -2/3
x = -2/3 / 3
x = -2/9


Input: Find x in x^2 + 21/5x + 16/5 = 0

Output:
x^2 + 21/5x + 16/5 = 0
(x - -1)(x - -16/5) = 0
x - -1 = 0  or  x - -16/5 = 0
x = -1
x = -16/5


Input: Find x in x^3 + 3x^2 + 2x  = 0

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


Input: Find x for x^3 - 149/30x^2 + 41/5x - 9/2 = 0

Output:
x^3 - 149/30x^2 + 41/5x - 9/2 = 0
(x - 3/2)(x - 5/3)(x - 9/5) = 0
x - 3/2 = 0
x - 5/3 = 0
x - 9/5 = 0
x = 3/2
x = 5/3
x = 9/5


Input: Find the solution to x^3 - 7/8x^2 - 77/32x + 5/16 = 0

Output:
x^3 - 7/8x^2 - 77/32x + 5/16 = 0
(x - 1/8)(x - 2)(x - -5/4) = 0
x - 1/8 = 0
x - 2 = 0
x - -5/4 = 0
x = 1/8
x = 2
x = -5/4


Input: Find the solution to 7x + 14/9 = 0

Output:
7x + 14/9 = 0
7x = -14/9
x = -14/9 / 7
x = -2/9


Input: Compute the solution of x^3 + 70/9x^2 + 121/27x - 182/27 = 0

Output:
x^3 + 70/9x^2 + 121/27x - 182/27 = 0
(x - 2/3)(x - -13/9)(x - -7) = 0
x - 2/3 = 0
x - -13/9 = 0
x - -7 = 0
x = 2/3
x = -13/9
x = -7


Input:
Solve the system:
4x + 1y = -287/30
9x + 2y = -311/15

Output:
4x + 1y = -287/30
9x + 2y = -311/15

Using elimination
9*(4x + 1y = -287/30)
4*(9x + 2y = -311/15)
36x + 9y = -861/10
36x + 8y = -1244/15
Subtract equations
1y = -19/6
y = -19/6/1
y = -19/6

Substitute y
4x + 1(-19/6) = -287/30
4x = -32/5
x = -32/5/4
x = -8/5


Input:
Solve the system:
9x + 2y = -31/63
1x + 8y = -439/63

Output:
9x + 2y = -31/63
1x + 8y = -439/63

Using elimination
1*(9x + 2y = -31/63)
9*(1x + 8y = -439/63)
9x + 2y = -31/63
9x + 72y = -439/7
Subtract equations
-70y = 560/9
y = 560/9/-70
y = -8/9

Substitute y
9x + 2(-8/9) = -31/63
9x = 9/7
x = 9/7/9
x = 1/7


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

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


Input: Determine x in x^3 + 123/14x^2 + 73/14x - 60/7 = 0

Output:
x^3 + 123/14x^2 + 73/14x - 60/7 = 0
(x - -3/2)(x - 5/7)(x - -8) = 0
x - -3/2 = 0
x - 5/7 = 0
x - -8 = 0
x = -3/2
x = 5/7
x = -8


Input: Compute the solution of x^3 + 97/6x^2 - 91/6x - 17 = 0

Output:
x^3 + 97/6x^2 - 91/6x - 17 = 0
(x - 3/2)(x - -17)(x - -2/3) = 0
x - 3/2 = 0
x - -17 = 0
x - -2/3 = 0
x = 3/2
x = -17
x = -2/3


Input:
Solve simultaneously:
6x + 9y = 5
9x + 3y = -10

Output:
6x + 9y = 5
9x + 3y = -10

Using elimination
9*(6x + 9y = 5)
6*(9x + 3y = -10)
54x + 81y = 45
54x + 18y = -60
Subtract equations
63y = 105
y = 105/63
y = 5/3

Substitute y
6x + 9(5/3) = 5
6x = -10
x = -10/6
x = -5/3


Input: Compute the solution of x^2 + 8x + 16 = 0

Output:
x^2 + 8x + 16 = 0
(x - -4)(x - -4) = 0
x - -4 = 0  or  x - -4 = 0
x = -4
x = -4


Input: Solve quickly: x^3 - 21/4x^2 + 67/8x - 33/8 = 0

Output:
x^3 - 21/4x^2 + 67/8x - 33/8 = 0
(x - 1)(x - 11/4)(x - 3/2) = 0
x - 1 = 0
x - 11/4 = 0
x - 3/2 = 0
x = 1
x = 11/4
x = 3/2


Input: Find the solution to x^2 + 83/8x - 39/2 = 0

Output:
x^2 + 83/8x - 39/2 = 0
(x - 13/8)(x - -12) = 0
x - 13/8 = 0  or  x - -12 = 0
x = 13/8
x = -12


Input: Find x in 6x - 21 = 0

Output:
6x - 21 = 0
6x = 21
x = 21 / 6
x = 7/2


Input: Find x for x^3 - 49/6x^2 - 15/2x + 119/3 = 0

Output:
x^3 - 49/6x^2 - 15/2x + 119/3 = 0
(x - -7/3)(x - 17/2)(x - 2) = 0
x - -7/3 = 0
x - 17/2 = 0
x - 2 = 0
x = -7/3
x = 17/2
x = 2


Input:
Solve the system:
9x + 9y = -18
8x + 2y = -28

Output:
9x + 9y = -18
8x + 2y = -28

Using elimination
8*(9x + 9y = -18)
9*(8x + 2y = -28)
72x + 72y = -144
72x + 18y = -252
Subtract equations
54y = 108
y = 108/54
y = 2

Substitute y
9x + 9(2) = -18
9x = -36
x = -36/9
x = -4


Input: Find the solution to 5x - 90 = 0

Output:
5x - 90 = 0
5x = 90
x = 90 / 5
x = 18


Input: What value of x satisfies x^3 - 7/2x^2 + 179/64x + 13/32 = 0

Output:
x^3 - 7/2x^2 + 179/64x + 13/32 = 0
(x - -1/8)(x - 2)(x - 13/8) = 0
x - -1/8 = 0
x - 2 = 0
x - 13/8 = 0
x = -1/8
x = 2
x = 13/8


Input: Find x in x^3 + 89/6x^2 + 149/3x - 40 = 0

Output:
x^3 + 89/6x^2 + 149/3x - 40 = 0
(x - -15/2)(x - -8)(x - 2/3) = 0
x - -15/2 = 0
x - -8 = 0
x - 2/3 = 0
x = -15/2
x = -8
x = 2/3


Input: Find the solution to x^3 - 151/90x^2 - 641/54x - 1309/135 = 0

Output:
x^3 - 151/90x^2 - 641/54x - 1309/135 = 0
(x - 14/3)(x - -17/9)(x - -11/10) = 0
x - 14/3 = 0
x - -17/9 = 0
x - -11/10 = 0
x = 14/3
x = -17/9
x = -11/10


Input: Find x in x^3 + 4/3x^2 - 25/9x - 28/27 = 0

Output:
x^3 + 4/3x^2 - 25/9x - 28/27 = 0
(x - -7/3)(x - 4/3)(x - -1/3) = 0
x - -7/3 = 0
x - 4/3 = 0
x - -1/3 = 0
x = -7/3
x = 4/3
x = -1/3


Input: Compute the solution of x^3 - 23/3x^2 - 200/9x - 100/9 = 0

Output:
x^3 - 23/3x^2 - 200/9x - 100/9 = 0
(x - -5/3)(x - -2/3)(x - 10) = 0
x - -5/3 = 0
x - -2/3 = 0
x - 10 = 0
x = -5/3
x = -2/3
x = 10


Input: Solve the equation x^2 + 101/45x + 52/45 = 0

Output:
x^2 + 101/45x + 52/45 = 0
(x - -4/5)(x - -13/9) = 0
x - -4/5 = 0  or  x - -13/9 = 0
x = -4/5
x = -13/9


Input: What value of x satisfies x^3 + 91/5x^2 + 462/5x + 432/5 = 0

Output:
x^3 + 91/5x^2 + 462/5x + 432/5 = 0
(x - -9)(x - -6/5)(x - -8) = 0
x - -9 = 0
x - -6/5 = 0
x - -8 = 0
x = -9
x = -6/5
x = -8


Input: Solve x^2 - 7/10x - 13/5 = 0

Output:
x^2 - 7/10x - 13/5 = 0
(x - 2)(x - -13/10) = 0
x - 2 = 0  or  x - -13/10 = 0
x = 2
x = -13/10


Input:
Find x and y such that
10x + 4y = 16
4x + 6y = 13

Output:
10x + 4y = 16
4x + 6y = 13

Using elimination
4*(10x + 4y = 16)
10*(4x + 6y = 13)
40x + 16y = 64
40x + 60y = 130
Subtract equations
-44y = -66
y = -66/-44
y = 3/2

Substitute y
10x + 4(3/2) = 16
10x = 10
x = 10/10
x = 1


Input: Compute the solution of x^2 + 7/6x - 1/2 = 0

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


Input: What value of x satisfies x^2 - 5/2x - 25/2 = 0

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


Input: Compute the solution of x^2 + 62/35x - 32/7 = 0

Output:
x^2 + 62/35x - 32/7 = 0
(x - 10/7)(x - -16/5) = 0
x - 10/7 = 0  or  x - -16/5 = 0
x = 10/7
x = -16/5


Input: What value of x satisfies x^2  - 16 = 0

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


Input:
Find x and y such that
6x + 3y = -111/4
9x + 8y = -25

Output:
6x + 3y = -111/4
9x + 8y = -25

Using elimination
9*(6x + 3y = -111/4)
6*(9x + 8y = -25)
54x + 27y = -999/4
54x + 48y = -150
Subtract equations
-21y = -399/4
y = -399/4/-21
y = 19/4

Substitute y
6x + 3(19/4) = -111/4
6x = -42
x = -42/6
x = -7


Input: What value of x satisfies x^3 + 47/5x^2 + 2/5x - 144/5 = 0

Output:
x^3 + 47/5x^2 + 2/5x - 144/5 = 0
(x - -9)(x - 8/5)(x - -2) = 0
x - -9 = 0
x - 8/5 = 0
x - -2 = 0
x = -9
x = 8/5
x = -2


Input: Solve the equation 4x + 5 = 0

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


Input: Solve x^2 - 7/4x + 5/8 = 0

Output:
x^2 - 7/4x + 5/8 = 0
(x - 5/4)(x - 1/2) = 0
x - 5/4 = 0  or  x - 1/2 = 0
x = 5/4
x = 1/2


Input: Find x for 2x - 10/3 = 0

Output:
2x - 10/3 = 0
2x = 10/3
x = 10/3 / 2
x = 5/3


Input: Find the solution to x^3 - 5/6x^2 - 46x - 30 = 0

Output:
x^3 - 5/6x^2 - 46x - 30 = 0
(x - -6)(x - 15/2)(x - -2/3) = 0
x - -6 = 0
x - 15/2 = 0
x - -2/3 = 0
x = -6
x = 15/2
x = -2/3


Input: Find the solution to x^2 + 5/3x  = 0

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


Input: Determine x in x^3 - 61/8x^2 - 67/8x + 255/32 = 0

Output:
x^3 - 61/8x^2 - 67/8x + 255/32 = 0
(x - -3/2)(x - 5/8)(x - 17/2) = 0
x - -3/2 = 0
x - 5/8 = 0
x - 17/2 = 0
x = -3/2
x = 5/8
x = 17/2


Input: Find x in x^2 - 23x + 90 = 0

Output:
x^2 - 23x + 90 = 0
(x - 18)(x - 5) = 0
x - 18 = 0  or  x - 5 = 0
x = 18
x = 5


Input: Find the solution to x^2 - 99/5x + 238/5 = 0

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


Input: Solve x^2 + 97/40x + 13/10 = 0

Output:
x^2 + 97/40x + 13/10 = 0
(x - -4/5)(x - -13/8) = 0
x - -4/5 = 0  or  x - -13/8 = 0
x = -4/5
x = -13/8


Input:
Solve simultaneously:
5x + 3y = 119/12
6x + 7y = 17/4

Output:
5x + 3y = 119/12
6x + 7y = 17/4

Using elimination
6*(5x + 3y = 119/12)
5*(6x + 7y = 17/4)
30x + 18y = 119/2
30x + 35y = 85/4
Subtract equations
-17y = 153/4
y = 153/4/-17
y = -9/4

Substitute y
5x + 3(-9/4) = 119/12
5x = 50/3
x = 50/3/5
x = 10/3


Input: Compute the solution of x^3 + 131/40x^2 + 69/20x + 189/160 = 0

Output:
x^3 + 131/40x^2 + 69/20x + 189/160 = 0
(x - -7/8)(x - -9/10)(x - -3/2) = 0
x - -7/8 = 0
x - -9/10 = 0
x - -3/2 = 0
x = -7/8
x = -9/10
x = -3/2


Input: What value of x satisfies x^2 - 25/6x + 25/9 = 0

Output:
x^2 - 25/6x + 25/9 = 0
(x - 10/3)(x - 5/6) = 0
x - 10/3 = 0  or  x - 5/6 = 0
x = 10/3
x = 5/6


Input: What value of x satisfies x^3 - 87/28x^2 + 723/448x + 19/64 = 0

Output:
x^3 - 87/28x^2 + 723/448x + 19/64 = 0
(x - 7/8)(x - -1/7)(x - 19/8) = 0
x - 7/8 = 0
x - -1/7 = 0
x - 19/8 = 0
x = 7/8
x = -1/7
x = 19/8


Input: Determine x in x^2 + 63/40x + 9/20 = 0

Output:
x^2 + 63/40x + 9/20 = 0
(x - -6/5)(x - -3/8) = 0
x - -6/5 = 0  or  x - -3/8 = 0
x = -6/5
x = -3/8


Input: Find x in 5x + 45 = 0

Output:
5x + 45 = 0
5x = -45
x = -45 / 5
x = -9


Input: Find x for 10x  = 0

Output:
10x  = 0
10x = 0
x = 0 / 10
x = 0


Input: Find the solution to x^3 - 599/45x^2 + 718/45x - 8/3 = 0

Output:
x^3 - 599/45x^2 + 718/45x - 8/3 = 0
(x - 12)(x - 10/9)(x - 1/5) = 0
x - 12 = 0
x - 10/9 = 0
x - 1/5 = 0
x = 12
x = 10/9
x = 1/5


Input: Compute the solution of x^2 + 179/90x + 17/90 = 0

Output:
x^2 + 179/90x + 17/90 = 0
(x - -1/10)(x - -17/9) = 0
x - -1/10 = 0  or  x - -17/9 = 0
x = -1/10
x = -17/9


Input: Solve quickly: x^3 + 11/7x^2 - 100/7x + 100/7 = 0

Output:
x^3 + 11/7x^2 - 100/7x + 100/7 = 0
(x - 2)(x - 10/7)(x - -5) = 0
x - 2 = 0
x - 10/7 = 0
x - -5 = 0
x = 2
x = 10/7
x = -5


Input: Solve x^3 + 203/30x^2 + 107/10x + 21/5 = 0

Output:
x^3 + 203/30x^2 + 107/10x + 21/5 = 0
(x - -3/2)(x - -3/5)(x - -14/3) = 0
x - -3/2 = 0
x - -3/5 = 0
x - -14/3 = 0
x = -3/2
x = -3/5
x = -14/3


Input: Solve quickly: x^2 + 2/21x - 55/21 = 0

Output:
x^2 + 2/21x - 55/21 = 0
(x - -5/3)(x - 11/7) = 0
x - -5/3 = 0  or  x - 11/7 = 0
x = -5/3
x = 11/7


Input: Find x for x^3 - 109/24x^2 - 313/24x - 15/2 = 0

Output:
x^3 - 109/24x^2 - 313/24x - 15/2 = 0
(x - 20/3)(x - -1)(x - -9/8) = 0
x - 20/3 = 0
x - -1 = 0
x - -9/8 = 0
x = 20/3
x = -1
x = -9/8


Input: Find x for x^2 - 13/10x - 169/50 = 0

Output:
x^2 - 13/10x - 169/50 = 0
(x - 13/5)(x - -13/10) = 0
x - 13/5 = 0  or  x - -13/10 = 0
x = 13/5
x = -13/10


Input: Find x in x^2 - 43/2x + 30 = 0

Output:
x^2 - 43/2x + 30 = 0
(x - 3/2)(x - 20) = 0
x - 3/2 = 0  or  x - 20 = 0
x = 3/2
x = 20


Input: Find x in x^3 + 55/12x^2 + 13/4x - 9/2 = 0

Output:
x^3 + 55/12x^2 + 13/4x - 9/2 = 0
(x - -3)(x - 2/3)(x - -9/4) = 0
x - -3 = 0
x - 2/3 = 0
x - -9/4 = 0
x = -3
x = 2/3
x = -9/4


Input:
Solve the system:
7x + 7y = 63/4
10x + 8y = 41/2

Output:
7x + 7y = 63/4
10x + 8y = 41/2

Using elimination
10*(7x + 7y = 63/4)
7*(10x + 8y = 41/2)
70x + 70y = 315/2
70x + 56y = 287/2
Subtract equations
14y = 14
y = 14/14
y = 1

Substitute y
7x + 7(1) = 63/4
7x = 35/4
x = 35/4/7
x = 5/4


Input: Compute the solution of x^2 - 16/21x + 1/7 = 0

Output:
x^2 - 16/21x + 1/7 = 0
(x - 3/7)(x - 1/3) = 0
x - 3/7 = 0  or  x - 1/3 = 0
x = 3/7
x = 1/3