Input: What value of x satisfies x^2 + 7/3x - 10/3 = 0

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


Input: Determine x in x^3 - 23/4x^2 - 1205/72x + 425/6 = 0

Output:
x^3 - 23/4x^2 - 1205/72x + 425/6 = 0
(x - 20/3)(x - -15/4)(x - 17/6) = 0
x - 20/3 = 0
x - -15/4 = 0
x - 17/6 = 0
x = 20/3
x = -15/4
x = 17/6


Input:
Solve the system:
5x + 7y = -208/3
3x + 5y = -48

Output:
5x + 7y = -208/3
3x + 5y = -48

Using elimination
3*(5x + 7y = -208/3)
5*(3x + 5y = -48)
15x + 21y = -208
15x + 25y = -240
Subtract equations
-4y = 32
y = 32/-4
y = -8

Substitute y
5x + 7(-8) = -208/3
5x = -40/3
x = -40/3/5
x = -8/3


Input:
Solve the equations:
4x + 2y = -46/5
6x + 9y = -99/5

Output:
4x + 2y = -46/5
6x + 9y = -99/5

Using elimination
6*(4x + 2y = -46/5)
4*(6x + 9y = -99/5)
24x + 12y = -276/5
24x + 36y = -396/5
Subtract equations
-24y = 24
y = 24/-24
y = -1

Substitute y
4x + 2(-1) = -46/5
4x = -36/5
x = -36/5/4
x = -9/5


Input:
Find x and y such that
2x + 6y = -29/6
5x + 5y = 5/12

Output:
2x + 6y = -29/6
5x + 5y = 5/12

Using elimination
5*(2x + 6y = -29/6)
2*(5x + 5y = 5/12)
10x + 30y = -145/6
10x + 10y = 5/6
Subtract equations
20y = -25
y = -25/20
y = -5/4

Substitute y
2x + 6(-5/4) = -29/6
2x = 8/3
x = 8/3/2
x = 4/3


Input: Find the solution to x^2 + 1/5x - 18/5 = 0

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


Input: Solve quickly: x^3 + 59/9x^2 + 16/9x - 28/3 = 0

Output:
x^3 + 59/9x^2 + 16/9x - 28/3 = 0
(x - 1)(x - -6)(x - -14/9) = 0
x - 1 = 0
x - -6 = 0
x - -14/9 = 0
x = 1
x = -6
x = -14/9


Input:
Solve the equations:
5x + 1y = -28
7x + 4y = -378/5

Output:
5x + 1y = -28
7x + 4y = -378/5

Using elimination
7*(5x + 1y = -28)
5*(7x + 4y = -378/5)
35x + 7y = -196
35x + 20y = -378
Subtract equations
-13y = 182
y = 182/-13
y = -14

Substitute y
5x + 1(-14) = -28
5x = -14
x = -14/5
x = -14/5


Input: Find the solution to x^3 + 403/20x^2 + 391/8x - 3179/40 = 0

Output:
x^3 + 403/20x^2 + 391/8x - 3179/40 = 0
(x - -17/4)(x - -17)(x - 11/10) = 0
x - -17/4 = 0
x - -17 = 0
x - 11/10 = 0
x = -17/4
x = -17
x = 11/10


Input:
Solve the system:
1x + 7y = 27/2
5x + 4y = 201/14

Output:
1x + 7y = 27/2
5x + 4y = 201/14

Using elimination
5*(1x + 7y = 27/2)
1*(5x + 4y = 201/14)
5x + 35y = 135/2
5x + 4y = 201/14
Subtract equations
31y = 372/7
y = 372/7/31
y = 12/7

Substitute y
1x + 7(12/7) = 27/2
1x = 3/2
x = 3/2/1
x = 3/2


Input: Determine x in x^2 - 55/3x + 68/3 = 0

Output:
x^2 - 55/3x + 68/3 = 0
(x - 17)(x - 4/3) = 0
x - 17 = 0  or  x - 4/3 = 0
x = 17
x = 4/3


Input: Compute the solution of x^3 + 14/3x^2 - 212/9x - 280/3 = 0

Output:
x^3 + 14/3x^2 - 212/9x - 280/3 = 0
(x - -10/3)(x - -6)(x - 14/3) = 0
x - -10/3 = 0
x - -6 = 0
x - 14/3 = 0
x = -10/3
x = -6
x = 14/3


Input: Solve the equation x^2 - 39/5x + 14 = 0

Output:
x^2 - 39/5x + 14 = 0
(x - 5)(x - 14/5) = 0
x - 5 = 0  or  x - 14/5 = 0
x = 5
x = 14/5


Input:
Find x and y such that
2x + 4y = -16/3
6x + 2y = -98/3

Output:
2x + 4y = -16/3
6x + 2y = -98/3

Using elimination
6*(2x + 4y = -16/3)
2*(6x + 2y = -98/3)
12x + 24y = -32
12x + 4y = -196/3
Subtract equations
20y = 100/3
y = 100/3/20
y = 5/3

Substitute y
2x + 4(5/3) = -16/3
2x = -12
x = -12/2
x = -6


Input: What value of x satisfies x^2 + 43/6x - 20/3 = 0

Output:
x^2 + 43/6x - 20/3 = 0
(x - -8)(x - 5/6) = 0
x - -8 = 0  or  x - 5/6 = 0
x = -8
x = 5/6


Input: Solve the equation x^2 + 71/24x - 143/24 = 0

Output:
x^2 + 71/24x - 143/24 = 0
(x - 11/8)(x - -13/3) = 0
x - 11/8 = 0  or  x - -13/3 = 0
x = 11/8
x = -13/3


Input: Find the solution to x^3 - 169/10x^2 + 731/10x - 133/5 = 0

Output:
x^3 - 169/10x^2 + 731/10x - 133/5 = 0
(x - 2/5)(x - 19/2)(x - 7) = 0
x - 2/5 = 0
x - 19/2 = 0
x - 7 = 0
x = 2/5
x = 19/2
x = 7


Input: Solve the equation x^3 - 11/3x^2 + 10/3x  = 0

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


Input: Find x in 7x + 140/3 = 0

Output:
7x + 140/3 = 0
7x = -140/3
x = -140/3 / 7
x = -20/3


Input:
Solve the system:
1x + 8y = -79/10
7x + 3y = -23/10

Output:
1x + 8y = -79/10
7x + 3y = -23/10

Using elimination
7*(1x + 8y = -79/10)
1*(7x + 3y = -23/10)
7x + 56y = -553/10
7x + 3y = -23/10
Subtract equations
53y = -53
y = -53/53
y = -1

Substitute y
1x + 8(-1) = -79/10
1x = 1/10
x = 1/10/1
x = 1/10


Input: Solve 1x + 8/3 = 0

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


Input: Find x in 2x + 14/5 = 0

Output:
2x + 14/5 = 0
2x = -14/5
x = -14/5 / 2
x = -7/5


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

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


Input: What value of x satisfies x^3 - 163/28x^2 - 375/14x - 459/28 = 0

Output:
x^3 - 163/28x^2 - 375/14x - 459/28 = 0
(x - -3/4)(x - 9)(x - -17/7) = 0
x - -3/4 = 0
x - 9 = 0
x - -17/7 = 0
x = -3/4
x = 9
x = -17/7


Input:
Solve simultaneously:
1x + 9y = -593/10
2x + 10y = -979/15

Output:
1x + 9y = -593/10
2x + 10y = -979/15

Using elimination
2*(1x + 9y = -593/10)
1*(2x + 10y = -979/15)
2x + 18y = -593/5
2x + 10y = -979/15
Subtract equations
8y = -160/3
y = -160/3/8
y = -20/3

Substitute y
1x + 9(-20/3) = -593/10
1x = 7/10
x = 7/10/1
x = 7/10


Input: Solve the equation 10x  = 0

Output:
10x  = 0
10x = 0
x = 0 / 10
x = 0


Input: Find the solution to 4x + 8/7 = 0

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


Input: Compute the solution of x^3 - 14/45x^2 - 373/135x + 28/15 = 0

Output:
x^3 - 14/45x^2 - 373/135x + 28/15 = 0
(x - 4/3)(x - -9/5)(x - 7/9) = 0
x - 4/3 = 0
x - -9/5 = 0
x - 7/9 = 0
x = 4/3
x = -9/5
x = 7/9


Input: Find x for x^2 - 1x - 12 = 0

Output:
x^2 - 1x - 12 = 0
(x - 4)(x - -3) = 0
x - 4 = 0  or  x - -3 = 0
x = 4
x = -3


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

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


Input:
Solve simultaneously:
9x + 9y = -18
1x + 9y = -22/3

Output:
9x + 9y = -18
1x + 9y = -22/3

Using elimination
1*(9x + 9y = -18)
9*(1x + 9y = -22/3)
9x + 9y = -18
9x + 81y = -66
Subtract equations
-72y = 48
y = 48/-72
y = -2/3

Substitute y
9x + 9(-2/3) = -18
9x = -12
x = -12/9
x = -4/3


Input: Solve 7x + 119/3 = 0

Output:
7x + 119/3 = 0
7x = -119/3
x = -119/3 / 7
x = -17/3


Input: Find x for x^3 - 47/60x^2 - 383/120x + 21/8 = 0

Output:
x^3 - 47/60x^2 - 383/120x + 21/8 = 0
(x - -9/5)(x - 5/6)(x - 7/4) = 0
x - -9/5 = 0
x - 5/6 = 0
x - 7/4 = 0
x = -9/5
x = 5/6
x = 7/4


Input: Find the solution to x^3 - 23/7x^2 - 163/7x - 19 = 0

Output:
x^3 - 23/7x^2 - 163/7x - 19 = 0
(x - -19/7)(x - -1)(x - 7) = 0
x - -19/7 = 0
x - -1 = 0
x - 7 = 0
x = -19/7
x = -1
x = 7


Input: Compute the solution of 6x - 36 = 0

Output:
6x - 36 = 0
6x = 36
x = 36 / 6
x = 6


Input: Compute the solution of x^3 + 181/12x^2 - 605/12x + 75/2 = 0

Output:
x^3 + 181/12x^2 - 605/12x + 75/2 = 0
(x - 5/3)(x - -18)(x - 5/4) = 0
x - 5/3 = 0
x - -18 = 0
x - 5/4 = 0
x = 5/3
x = -18
x = 5/4


Input:
Find x and y such that
6x + 9y = -57/4
5x + 4y = -39/8

Output:
6x + 9y = -57/4
5x + 4y = -39/8

Using elimination
5*(6x + 9y = -57/4)
6*(5x + 4y = -39/8)
30x + 45y = -285/4
30x + 24y = -117/4
Subtract equations
21y = -42
y = -42/21
y = -2

Substitute y
6x + 9(-2) = -57/4
6x = 15/4
x = 15/4/6
x = 5/8


Input: What value of x satisfies x^2 + 132/35x + 121/35 = 0

Output:
x^2 + 132/35x + 121/35 = 0
(x - -11/7)(x - -11/5) = 0
x - -11/7 = 0  or  x - -11/5 = 0
x = -11/7
x = -11/5


Input: Compute the solution of x^2 + 151/21x + 208/21 = 0

Output:
x^2 + 151/21x + 208/21 = 0
(x - -13/7)(x - -16/3) = 0
x - -13/7 = 0  or  x - -16/3 = 0
x = -13/7
x = -16/3


Input: Solve the equation 9x - 30 = 0

Output:
9x - 30 = 0
9x = 30
x = 30 / 9
x = 10/3


Input: Solve 6x - 60 = 0

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


Input: Find x for 8x + 24/7 = 0

Output:
8x + 24/7 = 0
8x = -24/7
x = -24/7 / 8
x = -3/7


Input: Solve x^2 - 17/7x - 38/49 = 0

Output:
x^2 - 17/7x - 38/49 = 0
(x - -2/7)(x - 19/7) = 0
x - -2/7 = 0  or  x - 19/7 = 0
x = -2/7
x = 19/7


Input: Solve quickly: x^3 - 19/6x^2 + 87/50x + 19/15 = 0

Output:
x^3 - 19/6x^2 + 87/50x + 19/15 = 0
(x - 19/10)(x - -2/5)(x - 5/3) = 0
x - 19/10 = 0
x - -2/5 = 0
x - 5/3 = 0
x = 19/10
x = -2/5
x = 5/3


Input:
Find x and y such that
2x + 8y = -128/21
8x + 9y = 661/21

Output:
2x + 8y = -128/21
8x + 9y = 661/21

Using elimination
8*(2x + 8y = -128/21)
2*(8x + 9y = 661/21)
16x + 64y = -1024/21
16x + 18y = 1322/21
Subtract equations
46y = -782/7
y = -782/7/46
y = -17/7

Substitute y
2x + 8(-17/7) = -128/21
2x = 40/3
x = 40/3/2
x = 20/3


Input: Solve quickly: 1x - 7/6 = 0

Output:
1x - 7/6 = 0
1x = 7/6
x = 7/6 / 1
x = 7/6


Input: Solve x^2 + 6x - 7 = 0

Output:
x^2 + 6x - 7 = 0
(x - -7)(x - 1) = 0
x - -7 = 0  or  x - 1 = 0
x = -7
x = 1


Input:
Solve the system:
5x + 7y = 283/36
9x + 6y = 293/12

Output:
5x + 7y = 283/36
9x + 6y = 293/12

Using elimination
9*(5x + 7y = 283/36)
5*(9x + 6y = 293/12)
45x + 63y = 283/4
45x + 30y = 1465/12
Subtract equations
33y = -154/3
y = -154/3/33
y = -14/9

Substitute y
5x + 7(-14/9) = 283/36
5x = 75/4
x = 75/4/5
x = 15/4


Input: Solve quickly: x^3 + 21/2x^2 + 35/64x - 1425/32 = 0

Output:
x^3 + 21/2x^2 + 35/64x - 1425/32 = 0
(x - 15/8)(x - -19/8)(x - -10) = 0
x - 15/8 = 0
x - -19/8 = 0
x - -10 = 0
x = 15/8
x = -19/8
x = -10


Input: Compute the solution of 2x - 7/2 = 0

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


Input: What value of x satisfies 5x + 10 = 0

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


Input:
Find x and y such that
6x + 10y = 1/7
3x + 7y = -1/2

Output:
6x + 10y = 1/7
3x + 7y = -1/2

Using elimination
3*(6x + 10y = 1/7)
6*(3x + 7y = -1/2)
18x + 30y = 3/7
18x + 42y = -3
Subtract equations
-12y = 24/7
y = 24/7/-12
y = -2/7

Substitute y
6x + 10(-2/7) = 1/7
6x = 3
x = 3/6
x = 1/2


Input: Determine x in x^3 - 241/30x^2 - 67/5x - 76/15 = 0

Output:
x^3 - 241/30x^2 - 67/5x - 76/15 = 0
(x - 19/2)(x - -2/3)(x - -4/5) = 0
x - 19/2 = 0
x - -2/3 = 0
x - -4/5 = 0
x = 19/2
x = -2/3
x = -4/5


Input: Find x for 6x + 42 = 0

Output:
6x + 42 = 0
6x = -42
x = -42 / 6
x = -7


Input: What value of x satisfies x^3 - 37/14x^2 - 156/49x + 360/49 = 0

Output:
x^3 - 37/14x^2 - 156/49x + 360/49 = 0
(x - 3/2)(x - 20/7)(x - -12/7) = 0
x - 3/2 = 0
x - 20/7 = 0
x - -12/7 = 0
x = 3/2
x = 20/7
x = -12/7


Input: Find the solution to 3x + 39 = 0

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


Input: Solve the equation x^3 - 11/14x^2 - 30/7x  = 0

Output:
x^3 - 11/14x^2 - 30/7x  = 0
(x - 5/2)(x - -12/7)(x - 0) = 0
x - 5/2 = 0
x - -12/7 = 0
x - 0 = 0
x = 5/2
x = -12/7
x = 0


Input: Find x in x^2 - 18/5x - 119/5 = 0

Output:
x^2 - 18/5x - 119/5 = 0
(x - -17/5)(x - 7) = 0
x - -17/5 = 0  or  x - 7 = 0
x = -17/5
x = 7


Input: Determine x in x^3 - 63/4x^2 - 325/4x - 75 = 0

Output:
x^3 - 63/4x^2 - 325/4x - 75 = 0
(x - -3)(x - -5/4)(x - 20) = 0
x - -3 = 0
x - -5/4 = 0
x - 20 = 0
x = -3
x = -5/4
x = 20


Input:
Solve the system:
2x + 7y = 67/9
1x + 1y = 11/9

Output:
2x + 7y = 67/9
1x + 1y = 11/9

Using elimination
1*(2x + 7y = 67/9)
2*(1x + 1y = 11/9)
2x + 7y = 67/9
2x + 2y = 22/9
Subtract equations
5y = 5
y = 5/5
y = 1

Substitute y
2x + 7(1) = 67/9
2x = 4/9
x = 4/9/2
x = 2/9


Input: Find the solution to x^3 - 17/2x^2 - 40/9x - 1/2 = 0

Output:
x^3 - 17/2x^2 - 40/9x - 1/2 = 0
(x - -1/6)(x - -1/3)(x - 9) = 0
x - -1/6 = 0
x - -1/3 = 0
x - 9 = 0
x = -1/6
x = -1/3
x = 9


Input: Determine x in 6x + 27 = 0

Output:
6x + 27 = 0
6x = -27
x = -27 / 6
x = -9/2


Input: Solve quickly: x^2 + 18/7x + 11/7 = 0

Output:
x^2 + 18/7x + 11/7 = 0
(x - -1)(x - -11/7) = 0
x - -1 = 0  or  x - -11/7 = 0
x = -1
x = -11/7


Input: Find x for x^2 - 7/4x - 99/8 = 0

Output:
x^2 - 7/4x - 99/8 = 0
(x - 9/2)(x - -11/4) = 0
x - 9/2 = 0  or  x - -11/4 = 0
x = 9/2
x = -11/4


Input: Find x in x^2 - 78/5x - 119/5 = 0

Output:
x^2 - 78/5x - 119/5 = 0
(x - 17)(x - -7/5) = 0
x - 17 = 0  or  x - -7/5 = 0
x = 17
x = -7/5


Input: Determine x in x^3 + 100/9x^2 - 117x - 2584/9 = 0

Output:
x^3 + 100/9x^2 - 117x - 2584/9 = 0
(x - 8)(x - -19/9)(x - -17) = 0
x - 8 = 0
x - -19/9 = 0
x - -17 = 0
x = 8
x = -19/9
x = -17


Input: Find the solution to 4x - 2 = 0

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


Input:
Solve simultaneously:
8x + 1y = -119
9x + 9y = -126

Output:
8x + 1y = -119
9x + 9y = -126

Using elimination
9*(8x + 1y = -119)
8*(9x + 9y = -126)
72x + 9y = -1071
72x + 72y = -1008
Subtract equations
-63y = -63
y = -63/-63
y = 1

Substitute y
8x + 1(1) = -119
8x = -120
x = -120/8
x = -15


Input:
Solve the equations:
9x + 6y = 324/5
1x + 8y = -8/5

Output:
9x + 6y = 324/5
1x + 8y = -8/5

Using elimination
1*(9x + 6y = 324/5)
9*(1x + 8y = -8/5)
9x + 6y = 324/5
9x + 72y = -72/5
Subtract equations
-66y = 396/5
y = 396/5/-66
y = -6/5

Substitute y
9x + 6(-6/5) = 324/5
9x = 72
x = 72/9
x = 8


Input: What value of x satisfies x^2 + 33/8x + 27/8 = 0

Output:
x^2 + 33/8x + 27/8 = 0
(x - -9/8)(x - -3) = 0
x - -9/8 = 0  or  x - -3 = 0
x = -9/8
x = -3


Input: Find the solution to x^3 - 1/6x^2 - 173/3x + 136 = 0

Output:
x^3 - 1/6x^2 - 173/3x + 136 = 0
(x - 8/3)(x - -17/2)(x - 6) = 0
x - 8/3 = 0
x - -17/2 = 0
x - 6 = 0
x = 8/3
x = -17/2
x = 6


Input: Compute the solution of 8x - 88/9 = 0

Output:
8x - 88/9 = 0
8x = 88/9
x = 88/9 / 8
x = 11/9


Input: Determine x in 7x + 21/8 = 0

Output:
7x + 21/8 = 0
7x = -21/8
x = -21/8 / 7
x = -3/8


Input: Solve the equation x^2 - 153/70x + 81/70 = 0

Output:
x^2 - 153/70x + 81/70 = 0
(x - 9/10)(x - 9/7) = 0
x - 9/10 = 0  or  x - 9/7 = 0
x = 9/10
x = 9/7


Input: Solve the equation 7x - 112/9 = 0

Output:
7x - 112/9 = 0
7x = 112/9
x = 112/9 / 7
x = 16/9


Input:
Solve the system:
1x + 6y = 10/3
4x + 2y = 40/3

Output:
1x + 6y = 10/3
4x + 2y = 40/3

Using elimination
4*(1x + 6y = 10/3)
1*(4x + 2y = 40/3)
4x + 24y = 40/3
4x + 2y = 40/3
Subtract equations
22y = 0
y = 0/22
y = 0

Substitute y
1x + 6(0) = 10/3
1x = 10/3
x = 10/3/1
x = 10/3


Input: Determine x in x^3 + 10/3x^2 + 3x + 2/3 = 0

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


Input:
Solve simultaneously:
8x + 9y = -12
4x + 8y = -61/9

Output:
8x + 9y = -12
4x + 8y = -61/9

Using elimination
4*(8x + 9y = -12)
8*(4x + 8y = -61/9)
32x + 36y = -48
32x + 64y = -488/9
Subtract equations
-28y = 56/9
y = 56/9/-28
y = -2/9

Substitute y
8x + 9(-2/9) = -12
8x = -10
x = -10/8
x = -5/4


Input: Solve quickly: x^3 + 15x^2 + 494/9x + 440/9 = 0

Output:
x^3 + 15x^2 + 494/9x + 440/9 = 0
(x - -10)(x - -11/3)(x - -4/3) = 0
x - -10 = 0
x - -11/3 = 0
x - -4/3 = 0
x = -10
x = -11/3
x = -4/3


Input:
Solve the system:
6x + 2y = -22/7
2x + 10y = 114/7

Output:
6x + 2y = -22/7
2x + 10y = 114/7

Using elimination
2*(6x + 2y = -22/7)
6*(2x + 10y = 114/7)
12x + 4y = -44/7
12x + 60y = 684/7
Subtract equations
-56y = -104
y = -104/-56
y = 13/7

Substitute y
6x + 2(13/7) = -22/7
6x = -48/7
x = -48/7/6
x = -8/7


Input: Find x in x^2 - 5/3x - 2/3 = 0

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


Input: Solve the equation x^3 - 83/15x^2 + 32/5x - 16/15 = 0

Output:
x^3 - 83/15x^2 + 32/5x - 16/15 = 0
(x - 4/3)(x - 4)(x - 1/5) = 0
x - 4/3 = 0
x - 4 = 0
x - 1/5 = 0
x = 4/3
x = 4
x = 1/5


Input: Find x in 10x + 5 = 0

Output:
10x + 5 = 0
10x = -5
x = -5 / 10
x = -1/2


Input: Find x in x^3 - 11/15x^2 - 86/15x - 16/5 = 0

Output:
x^3 - 11/15x^2 - 86/15x - 16/5 = 0
(x - -2/3)(x - -8/5)(x - 3) = 0
x - -2/3 = 0
x - -8/5 = 0
x - 3 = 0
x = -2/3
x = -8/5
x = 3


Input: Find the solution to x^2 - 17/3x + 20/3 = 0

Output:
x^2 - 17/3x + 20/3 = 0
(x - 4)(x - 5/3) = 0
x - 4 = 0  or  x - 5/3 = 0
x = 4
x = 5/3


Input: Find the solution to x^3 + 107/20x^2 - 31/40x - 247/10 = 0

Output:
x^3 + 107/20x^2 - 31/40x - 247/10 = 0
(x - -13/4)(x - -4)(x - 19/10) = 0
x - -13/4 = 0
x - -4 = 0
x - 19/10 = 0
x = -13/4
x = -4
x = 19/10


Input: Find the solution to x^2 + 23/18x + 7/18 = 0

Output:
x^2 + 23/18x + 7/18 = 0
(x - -1/2)(x - -7/9) = 0
x - -1/2 = 0  or  x - -7/9 = 0
x = -1/2
x = -7/9


Input: Determine x in x^2 - 1x - 10/9 = 0

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


Input:
Solve the equations:
10x + 3y = 1/2
6x + 9y = 159/10

Output:
10x + 3y = 1/2
6x + 9y = 159/10

Using elimination
6*(10x + 3y = 1/2)
10*(6x + 9y = 159/10)
60x + 18y = 3
60x + 90y = 159
Subtract equations
-72y = -156
y = -156/-72
y = 13/6

Substitute y
10x + 3(13/6) = 1/2
10x = -6
x = -6/10
x = -3/5


Input: Find x for x^2 - 27/10x - 8/5 = 0

Output:
x^2 - 27/10x - 8/5 = 0
(x - -1/2)(x - 16/5) = 0
x - -1/2 = 0  or  x - 16/5 = 0
x = -1/2
x = 16/5


Input: Solve quickly: 6x + 30 = 0

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


Input:
Solve simultaneously:
10x + 6y = -50
6x + 10y = -218/3

Output:
10x + 6y = -50
6x + 10y = -218/3

Using elimination
6*(10x + 6y = -50)
10*(6x + 10y = -218/3)
60x + 36y = -300
60x + 100y = -2180/3
Subtract equations
-64y = 1280/3
y = 1280/3/-64
y = -20/3

Substitute y
10x + 6(-20/3) = -50
10x = -10
x = -10/10
x = -1


Input:
Solve the equations:
2x + 7y = 16
10x + 7y = -4

Output:
2x + 7y = 16
10x + 7y = -4

Using elimination
10*(2x + 7y = 16)
2*(10x + 7y = -4)
20x + 70y = 160
20x + 14y = -8
Subtract equations
56y = 168
y = 168/56
y = 3

Substitute y
2x + 7(3) = 16
2x = -5
x = -5/2
x = -5/2


Input: Find the solution to x^2 + 57/70x - 54/35 = 0

Output:
x^2 + 57/70x - 54/35 = 0
(x - -12/7)(x - 9/10) = 0
x - -12/7 = 0  or  x - 9/10 = 0
x = -12/7
x = 9/10


Input: Solve the equation x^2 + 31/70x - 4/5 = 0

Output:
x^2 + 31/70x - 4/5 = 0
(x - -8/7)(x - 7/10) = 0
x - -8/7 = 0  or  x - 7/10 = 0
x = -8/7
x = 7/10


Input: Find x in 1x + 4 = 0

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


Input: Determine x in 2x + 10 = 0

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


Input:
Solve the system:
2x + 10y = -30
4x + 4y = -108/5

Output:
2x + 10y = -30
4x + 4y = -108/5

Using elimination
4*(2x + 10y = -30)
2*(4x + 4y = -108/5)
8x + 40y = -120
8x + 8y = -216/5
Subtract equations
32y = -384/5
y = -384/5/32
y = -12/5

Substitute y
2x + 10(-12/5) = -30
2x = -6
x = -6/2
x = -3


Input: Solve quickly: x^3 + 31/10x^2 - 62/5x + 22/5 = 0

Output:
x^3 + 31/10x^2 - 62/5x + 22/5 = 0
(x - 2)(x - 2/5)(x - -11/2) = 0
x - 2 = 0
x - 2/5 = 0
x - -11/2 = 0
x = 2
x = 2/5
x = -11/2


Input: Find x for x^3 - 202/15x^2 + 752/15x - 32 = 0

Output:
x^3 - 202/15x^2 + 752/15x - 32 = 0
(x - 20/3)(x - 6)(x - 4/5) = 0
x - 20/3 = 0
x - 6 = 0
x - 4/5 = 0
x = 20/3
x = 6
x = 4/5


Input: Solve the equation x^2 - 5/6x - 28/3 = 0

Output:
x^2 - 5/6x - 28/3 = 0
(x - -8/3)(x - 7/2) = 0
x - -8/3 = 0  or  x - 7/2 = 0
x = -8/3
x = 7/2


Input: Solve the equation x^3 + 68/15x^2 + 4x  = 0

Output:
x^3 + 68/15x^2 + 4x  = 0
(x - -10/3)(x - -6/5)(x - 0) = 0
x - -10/3 = 0
x - -6/5 = 0
x - 0 = 0
x = -10/3
x = -6/5
x = 0


Input: Solve quickly: x^3 + 53/3x^2 + 67/9x - 595/9 = 0

Output:
x^3 + 53/3x^2 + 67/9x - 595/9 = 0
(x - -7/3)(x - -17)(x - 5/3) = 0
x - -7/3 = 0
x - -17 = 0
x - 5/3 = 0
x = -7/3
x = -17
x = 5/3


Input:
Solve simultaneously:
9x + 3y = 16
7x + 3y = 136/9

Output:
9x + 3y = 16
7x + 3y = 136/9

Using elimination
7*(9x + 3y = 16)
9*(7x + 3y = 136/9)
63x + 21y = 112
63x + 27y = 136
Subtract equations
-6y = -24
y = -24/-6
y = 4

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


Input: Find the solution to x^2 + 15/4x + 7/2 = 0

Output:
x^2 + 15/4x + 7/2 = 0
(x - -2)(x - -7/4) = 0
x - -2 = 0  or  x - -7/4 = 0
x = -2
x = -7/4


Input:
Solve simultaneously:
4x + 1y = 95/14
4x + 4y = -26/7

Output:
4x + 1y = 95/14
4x + 4y = -26/7

Using elimination
4*(4x + 1y = 95/14)
4*(4x + 4y = -26/7)
16x + 4y = 190/7
16x + 16y = -104/7
Subtract equations
-12y = 42
y = 42/-12
y = -7/2

Substitute y
4x + 1(-7/2) = 95/14
4x = 72/7
x = 72/7/4
x = 18/7


Input:
Solve the system:
1x + 9y = 44
2x + 10y = 52

Output:
1x + 9y = 44
2x + 10y = 52

Using elimination
2*(1x + 9y = 44)
1*(2x + 10y = 52)
2x + 18y = 88
2x + 10y = 52
Subtract equations
8y = 36
y = 36/8
y = 9/2

Substitute y
1x + 9(9/2) = 44
1x = 7/2
x = 7/2/1
x = 7/2


Input: Find x for x^3 + 28/15x^2 - 1/3x - 2/15 = 0

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


Input: What value of x satisfies x^2 + 7/5x - 198/25 = 0

Output:
x^2 + 7/5x - 198/25 = 0
(x - -18/5)(x - 11/5) = 0
x - -18/5 = 0  or  x - 11/5 = 0
x = -18/5
x = 11/5


Input: Solve quickly: x^2 - 19/10x - 28/5 = 0

Output:
x^2 - 19/10x - 28/5 = 0
(x - 7/2)(x - -8/5) = 0
x - 7/2 = 0  or  x - -8/5 = 0
x = 7/2
x = -8/5


Input:
Solve the system:
2x + 5y = 71/15
6x + 5y = -37/15

Output:
2x + 5y = 71/15
6x + 5y = -37/15

Using elimination
6*(2x + 5y = 71/15)
2*(6x + 5y = -37/15)
12x + 30y = 142/5
12x + 10y = -74/15
Subtract equations
20y = 100/3
y = 100/3/20
y = 5/3

Substitute y
2x + 5(5/3) = 71/15
2x = -18/5
x = -18/5/2
x = -9/5


Input: Find x for x^2 - 46/9x + 40/9 = 0

Output:
x^2 - 46/9x + 40/9 = 0
(x - 4)(x - 10/9) = 0
x - 4 = 0  or  x - 10/9 = 0
x = 4
x = 10/9


Input: Solve quickly: x^2 + 17/4x - 15/4 = 0

Output:
x^2 + 17/4x - 15/4 = 0
(x - 3/4)(x - -5) = 0
x - 3/4 = 0  or  x - -5 = 0
x = 3/4
x = -5


Input: Solve 10x - 90 = 0

Output:
10x - 90 = 0
10x = 90
x = 90 / 10
x = 9


Input:
Find x and y such that
1x + 1y = -37/6
5x + 1y = -109/6

Output:
1x + 1y = -37/6
5x + 1y = -109/6

Using elimination
5*(1x + 1y = -37/6)
1*(5x + 1y = -109/6)
5x + 5y = -185/6
5x + 1y = -109/6
Subtract equations
4y = -38/3
y = -38/3/4
y = -19/6

Substitute y
1x + 1(-19/6) = -37/6
1x = -3
x = -3/1
x = -3


Input: Find the solution to 2x + 14/5 = 0

Output:
2x + 14/5 = 0
2x = -14/5
x = -14/5 / 2
x = -7/5


Input: Determine x in x^2 + 33/7x + 36/7 = 0

Output:
x^2 + 33/7x + 36/7 = 0
(x - -12/7)(x - -3) = 0
x - -12/7 = 0  or  x - -3 = 0
x = -12/7
x = -3


Input: Find the solution to 2x + 6 = 0

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


Input: Find the solution to 6x + 6 = 0

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


Input: Determine x in x^3 - 241/90x^2 - 371/90x + 196/45 = 0

Output:
x^3 - 241/90x^2 - 371/90x + 196/45 = 0
(x - 7/9)(x - 7/2)(x - -8/5) = 0
x - 7/9 = 0
x - 7/2 = 0
x - -8/5 = 0
x = 7/9
x = 7/2
x = -8/5


Input: Find x for x^3 + 185/24x^2 + 173/12x + 35/8 = 0

Output:
x^3 + 185/24x^2 + 173/12x + 35/8 = 0
(x - -3/8)(x - -7/3)(x - -5) = 0
x - -3/8 = 0
x - -7/3 = 0
x - -5 = 0
x = -3/8
x = -7/3
x = -5


Input: Solve x^2 - 86/63x - 5/3 = 0

Output:
x^2 - 86/63x - 5/3 = 0
(x - -7/9)(x - 15/7) = 0
x - -7/9 = 0  or  x - 15/7 = 0
x = -7/9
x = 15/7


Input: Find x for 8x + 8 = 0

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


Input:
Solve the system:
7x + 7y = -119/4
2x + 3y = -25/4

Output:
7x + 7y = -119/4
2x + 3y = -25/4

Using elimination
2*(7x + 7y = -119/4)
7*(2x + 3y = -25/4)
14x + 14y = -119/2
14x + 21y = -175/4
Subtract equations
-7y = -63/4
y = -63/4/-7
y = 9/4

Substitute y
7x + 7(9/4) = -119/4
7x = -91/2
x = -91/2/7
x = -13/2


Input: Determine x in x^3 - 5x^2 - 13x - 7 = 0

Output:
x^3 - 5x^2 - 13x - 7 = 0
(x - 7)(x - -1)(x - -1) = 0
x - 7 = 0
x - -1 = 0
x - -1 = 0
x = 7
x = -1
x = -1


Input: Solve the equation x^3 - 49/8x^2  + 225/8 = 0

Output:
x^3 - 49/8x^2  + 225/8 = 0
(x - -15/8)(x - 5)(x - 3) = 0
x - -15/8 = 0
x - 5 = 0
x - 3 = 0
x = -15/8
x = 5
x = 3


Input: Find the solution to 9x - 153/4 = 0

Output:
9x - 153/4 = 0
9x = 153/4
x = 153/4 / 9
x = 17/4


Input: What value of x satisfies x^3 - 7/5x^2 - 58/5x + 24/5 = 0

Output:
x^3 - 7/5x^2 - 58/5x + 24/5 = 0
(x - -3)(x - 4)(x - 2/5) = 0
x - -3 = 0
x - 4 = 0
x - 2/5 = 0
x = -3
x = 4
x = 2/5


Input: Compute the solution of x^2 + 104/21x + 4/3 = 0

Output:
x^2 + 104/21x + 4/3 = 0
(x - -2/7)(x - -14/3) = 0
x - -2/7 = 0  or  x - -14/3 = 0
x = -2/7
x = -14/3


Input: Solve quickly: x^2 + 5/9x - 4/9 = 0

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


Input: Find x for x^2 + 6x - 16 = 0

Output:
x^2 + 6x - 16 = 0
(x - -8)(x - 2) = 0
x - -8 = 0  or  x - 2 = 0
x = -8
x = 2


Input: Find x in x^3 - 3/56x^2 - 243/56x + 95/28 = 0

Output:
x^3 - 3/56x^2 - 243/56x + 95/28 = 0
(x - -19/8)(x - 1)(x - 10/7) = 0
x - -19/8 = 0
x - 1 = 0
x - 10/7 = 0
x = -19/8
x = 1
x = 10/7


Input: Find x for x^2 + 47/6x + 19/2 = 0

Output:
x^2 + 47/6x + 19/2 = 0
(x - -19/3)(x - -3/2) = 0
x - -19/3 = 0  or  x - -3/2 = 0
x = -19/3
x = -3/2


Input:
Solve simultaneously:
3x + 4y = -73/8
8x + 5y = -9/2

Output:
3x + 4y = -73/8
8x + 5y = -9/2

Using elimination
8*(3x + 4y = -73/8)
3*(8x + 5y = -9/2)
24x + 32y = -73
24x + 15y = -27/2
Subtract equations
17y = -119/2
y = -119/2/17
y = -7/2

Substitute y
3x + 4(-7/2) = -73/8
3x = 39/8
x = 39/8/3
x = 13/8


Input: Compute the solution of x^2 + 157/8x - 15/2 = 0

Output:
x^2 + 157/8x - 15/2 = 0
(x - 3/8)(x - -20) = 0
x - 3/8 = 0  or  x - -20 = 0
x = 3/8
x = -20


Input: Solve x^2 + 2/45x - 112/45 = 0

Output:
x^2 + 2/45x - 112/45 = 0
(x - -8/5)(x - 14/9) = 0
x - -8/5 = 0  or  x - 14/9 = 0
x = -8/5
x = 14/9


Input:
Solve simultaneously:
4x + 6y = -100/3
1x + 7y = -139/18

Output:
4x + 6y = -100/3
1x + 7y = -139/18

Using elimination
1*(4x + 6y = -100/3)
4*(1x + 7y = -139/18)
4x + 6y = -100/3
4x + 28y = -278/9
Subtract equations
-22y = -22/9
y = -22/9/-22
y = 1/9

Substitute y
4x + 6(1/9) = -100/3
4x = -34
x = -34/4
x = -17/2


Input: Find x in x^3 + 1/10x^2 - 9/10x  = 0

Output:
x^3 + 1/10x^2 - 9/10x  = 0
(x - -1)(x - 0)(x - 9/10) = 0
x - -1 = 0
x - 0 = 0
x - 9/10 = 0
x = -1
x = 0
x = 9/10


Input: What value of x satisfies x^2 + 73/90x - 247/90 = 0

Output:
x^2 + 73/90x - 247/90 = 0
(x - 13/10)(x - -19/9) = 0
x - 13/10 = 0  or  x - -19/9 = 0
x = 13/10
x = -19/9


Input: Solve quickly: 8x + 52 = 0

Output:
8x + 52 = 0
8x = -52
x = -52 / 8
x = -13/2


Input:
Solve the equations:
5x + 5y = -36
3x + 9y = -114/5

Output:
5x + 5y = -36
3x + 9y = -114/5

Using elimination
3*(5x + 5y = -36)
5*(3x + 9y = -114/5)
15x + 15y = -108
15x + 45y = -114
Subtract equations
-30y = 6
y = 6/-30
y = -1/5

Substitute y
5x + 5(-1/5) = -36
5x = -35
x = -35/5
x = -7


Input: Solve the equation x^3 + 21/2x^2 + 27/2x  = 0

Output:
x^3 + 21/2x^2 + 27/2x  = 0
(x - 0)(x - -9)(x - -3/2) = 0
x - 0 = 0
x - -9 = 0
x - -3/2 = 0
x = 0
x = -9
x = -3/2


Input: Solve the equation 7x + 28/3 = 0

Output:
7x + 28/3 = 0
7x = -28/3
x = -28/3 / 7
x = -4/3


Input: Find the solution to x^3 - 89/8x^2 + 81/4x - 81/8 = 0

Output:
x^3 - 89/8x^2 + 81/4x - 81/8 = 0
(x - 9/8)(x - 1)(x - 9) = 0
x - 9/8 = 0
x - 1 = 0
x - 9 = 0
x = 9/8
x = 1
x = 9


Input: Find x for x^2 + 34/7x + 40/7 = 0

Output:
x^2 + 34/7x + 40/7 = 0
(x - -20/7)(x - -2) = 0
x - -20/7 = 0  or  x - -2 = 0
x = -20/7
x = -2


Input:
Solve the system:
8x + 2y = 12/7
4x + 8y = 97/7

Output:
8x + 2y = 12/7
4x + 8y = 97/7

Using elimination
4*(8x + 2y = 12/7)
8*(4x + 8y = 97/7)
32x + 8y = 48/7
32x + 64y = 776/7
Subtract equations
-56y = -104
y = -104/-56
y = 13/7

Substitute y
8x + 2(13/7) = 12/7
8x = -2
x = -2/8
x = -1/4


Input:
Solve the equations:
3x + 3y = -39/10
8x + 7y = -51/5

Output:
3x + 3y = -39/10
8x + 7y = -51/5

Using elimination
8*(3x + 3y = -39/10)
3*(8x + 7y = -51/5)
24x + 24y = -156/5
24x + 21y = -153/5
Subtract equations
3y = -3/5
y = -3/5/3
y = -1/5

Substitute y
3x + 3(-1/5) = -39/10
3x = -33/10
x = -33/10/3
x = -11/10


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

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

Using elimination
1*(3x + 3y = -3/10)
3*(1x + 3y = -7/10)
3x + 3y = -3/10
3x + 9y = -21/10
Subtract equations
-6y = 9/5
y = 9/5/-6
y = -3/10

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


Input: Compute the solution of x^2 - 8x - 153 = 0

Output:
x^2 - 8x - 153 = 0
(x - 17)(x - -9) = 0
x - 17 = 0  or  x - -9 = 0
x = 17
x = -9


Input: Find x in x^3 - 1/30x^2 - 217/150x - 49/75 = 0

Output:
x^3 - 1/30x^2 - 217/150x - 49/75 = 0
(x - 7/5)(x - -2/3)(x - -7/10) = 0
x - 7/5 = 0
x - -2/3 = 0
x - -7/10 = 0
x = 7/5
x = -2/3
x = -7/10


Input: Find the solution to x^3 + 1/4x^2 - 117/8x + 81/4 = 0

Output:
x^3 + 1/4x^2 - 117/8x + 81/4 = 0
(x - 9/4)(x - 2)(x - -9/2) = 0
x - 9/4 = 0
x - 2 = 0
x - -9/2 = 0
x = 9/4
x = 2
x = -9/2


Input: Determine x in x^2 + 5/12x - 25/24 = 0

Output:
x^2 + 5/12x - 25/24 = 0
(x - -5/4)(x - 5/6) = 0
x - -5/4 = 0  or  x - 5/6 = 0
x = -5/4
x = 5/6


Input:
Solve the equations:
6x + 1y = 551/35
5x + 4y = 95/7

Output:
6x + 1y = 551/35
5x + 4y = 95/7

Using elimination
5*(6x + 1y = 551/35)
6*(5x + 4y = 95/7)
30x + 5y = 551/7
30x + 24y = 570/7
Subtract equations
-19y = -19/7
y = -19/7/-19
y = 1/7

Substitute y
6x + 1(1/7) = 551/35
6x = 78/5
x = 78/5/6
x = 13/5


Input:
Solve simultaneously:
5x + 2y = -19/3
5x + 1y = -22/3

Output:
5x + 2y = -19/3
5x + 1y = -22/3

Using elimination
5*(5x + 2y = -19/3)
5*(5x + 1y = -22/3)
25x + 10y = -95/3
25x + 5y = -110/3
Subtract equations
5y = 5
y = 5/5
y = 1

Substitute y
5x + 2(1) = -19/3
5x = -25/3
x = -25/3/5
x = -5/3


Input: Solve the equation x^3 + 107/5x^2 + 134/5x - 24 = 0

Output:
x^3 + 107/5x^2 + 134/5x - 24 = 0
(x - -20)(x - -2)(x - 3/5) = 0
x - -20 = 0
x - -2 = 0
x - 3/5 = 0
x = -20
x = -2
x = 3/5


Input: Compute the solution of 5x + 15 = 0

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


Input: Compute the solution of 2x - 14/9 = 0

Output:
2x - 14/9 = 0
2x = 14/9
x = 14/9 / 2
x = 7/9


Input: Compute the solution of x^3 + 139/20x^2 + 269/20x + 33/5 = 0

Output:
x^3 + 139/20x^2 + 269/20x + 33/5 = 0
(x - -11/5)(x - -3/4)(x - -4) = 0
x - -11/5 = 0
x - -3/4 = 0
x - -4 = 0
x = -11/5
x = -3/4
x = -4


Input:
Solve simultaneously:
4x + 9y = -217/10
1x + 7y = -21/10

Output:
4x + 9y = -217/10
1x + 7y = -21/10

Using elimination
1*(4x + 9y = -217/10)
4*(1x + 7y = -21/10)
4x + 9y = -217/10
4x + 28y = -42/5
Subtract equations
-19y = -133/10
y = -133/10/-19
y = 7/10

Substitute y
4x + 9(7/10) = -217/10
4x = -28
x = -28/4
x = -7


Input: Determine x in 7x + 49 = 0

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


Input: Find the solution to 6x + 2 = 0

Output:
6x + 2 = 0
6x = -2
x = -2 / 6
x = -1/3


Input: Find x for x^3 + 8/5x^2 - 23/5x - 26/5 = 0

Output:
x^3 + 8/5x^2 - 23/5x - 26/5 = 0
(x - 2)(x - -13/5)(x - -1) = 0
x - 2 = 0
x - -13/5 = 0
x - -1 = 0
x = 2
x = -13/5
x = -1


Input: What value of x satisfies x^3 - 277/18x^2 + 277/9x + 65/18 = 0

Output:
x^3 - 277/18x^2 + 277/9x + 65/18 = 0
(x - -1/9)(x - 5/2)(x - 13) = 0
x - -1/9 = 0
x - 5/2 = 0
x - 13 = 0
x = -1/9
x = 5/2
x = 13


Input: Find the solution to 10x - 18 = 0

Output:
10x - 18 = 0
10x = 18
x = 18 / 10
x = 9/5


Input: Solve x^2 - 35/12x + 25/12 = 0

Output:
x^2 - 35/12x + 25/12 = 0
(x - 5/4)(x - 5/3) = 0
x - 5/4 = 0  or  x - 5/3 = 0
x = 5/4
x = 5/3


Input: Find the solution to 7x + 21/5 = 0

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


Input: Solve the equation 5x + 95 = 0

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


Input: Find the solution to 9x + 54 = 0

Output:
9x + 54 = 0
9x = -54
x = -54 / 9
x = -6


Input: Solve the equation x^2 - 2x + 32/81 = 0

Output:
x^2 - 2x + 32/81 = 0
(x - 16/9)(x - 2/9) = 0
x - 16/9 = 0  or  x - 2/9 = 0
x = 16/9
x = 2/9


Input:
Find x and y such that
7x + 5y = -2/3
2x + 1y = 2/3

Output:
7x + 5y = -2/3
2x + 1y = 2/3

Using elimination
2*(7x + 5y = -2/3)
7*(2x + 1y = 2/3)
14x + 10y = -4/3
14x + 7y = 14/3
Subtract equations
3y = -6
y = -6/3
y = -2

Substitute y
7x + 5(-2) = -2/3
7x = 28/3
x = 28/3/7
x = 4/3


Input:
Solve the equations:
10x + 1y = -94/3
4x + 10y = 196/15

Output:
10x + 1y = -94/3
4x + 10y = 196/15

Using elimination
4*(10x + 1y = -94/3)
10*(4x + 10y = 196/15)
40x + 4y = -376/3
40x + 100y = 392/3
Subtract equations
-96y = -256
y = -256/-96
y = 8/3

Substitute y
10x + 1(8/3) = -94/3
10x = -34
x = -34/10
x = -17/5


Input: Solve quickly: x^2 + 33/8x + 17/4 = 0

Output:
x^2 + 33/8x + 17/4 = 0
(x - -2)(x - -17/8) = 0
x - -2 = 0  or  x - -17/8 = 0
x = -2
x = -17/8


Input: Solve 6x + 90 = 0

Output:
6x + 90 = 0
6x = -90
x = -90 / 6
x = -15


Input: What value of x satisfies 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: What value of x satisfies x^3 - 25/18x^2 - 659/144x + 95/16 = 0

Output:
x^3 - 25/18x^2 - 659/144x + 95/16 = 0
(x - -19/9)(x - 9/4)(x - 5/4) = 0
x - -19/9 = 0
x - 9/4 = 0
x - 5/4 = 0
x = -19/9
x = 9/4
x = 5/4


Input:
Solve the system:
7x + 1y = -13/3
7x + 9y = -61/3

Output:
7x + 1y = -13/3
7x + 9y = -61/3

Using elimination
7*(7x + 1y = -13/3)
7*(7x + 9y = -61/3)
49x + 7y = -91/3
49x + 63y = -427/3
Subtract equations
-56y = 112
y = 112/-56
y = -2

Substitute y
7x + 1(-2) = -13/3
7x = -7/3
x = -7/3/7
x = -1/3


Input: Determine x in x^2 + 25/9x - 44/9 = 0

Output:
x^2 + 25/9x - 44/9 = 0
(x - 11/9)(x - -4) = 0
x - 11/9 = 0  or  x - -4 = 0
x = 11/9
x = -4


Input: Solve quickly: x^2 - 43/9x - 340/27 = 0

Output:
x^2 - 43/9x - 340/27 = 0
(x - 20/3)(x - -17/9) = 0
x - 20/3 = 0  or  x - -17/9 = 0
x = 20/3
x = -17/9


Input: Solve x^2 - 18/35x - 8/35 = 0

Output:
x^2 - 18/35x - 8/35 = 0
(x - -2/7)(x - 4/5) = 0
x - -2/7 = 0  or  x - 4/5 = 0
x = -2/7
x = 4/5


Input: Find the solution to x^3 - 33/14x^2 + 2/7x + 6/7 = 0

Output:
x^3 - 33/14x^2 + 2/7x + 6/7 = 0
(x - 2)(x - 6/7)(x - -1/2) = 0
x - 2 = 0
x - 6/7 = 0
x - -1/2 = 0
x = 2
x = 6/7
x = -1/2


Input: Solve the equation x^3 + 64/15x^2 + 1787/300x + 273/100 = 0

Output:
x^3 + 64/15x^2 + 1787/300x + 273/100 = 0
(x - -7/6)(x - -13/10)(x - -9/5) = 0
x - -7/6 = 0
x - -13/10 = 0
x - -9/5 = 0
x = -7/6
x = -13/10
x = -9/5


Input: What value of x satisfies x^2 - 17/20x - 11/40 = 0

Output:
x^2 - 17/20x - 11/40 = 0
(x - -1/4)(x - 11/10) = 0
x - -1/4 = 0  or  x - 11/10 = 0
x = -1/4
x = 11/10


Input: Find x for 4x - 48 = 0

Output:
4x - 48 = 0
4x = 48
x = 48 / 4
x = 12


Input:
Solve the equations:
5x + 6y = 355/12
1x + 4y = 67/6

Output:
5x + 6y = 355/12
1x + 4y = 67/6

Using elimination
1*(5x + 6y = 355/12)
5*(1x + 4y = 67/6)
5x + 6y = 355/12
5x + 20y = 335/6
Subtract equations
-14y = -105/4
y = -105/4/-14
y = 15/8

Substitute y
5x + 6(15/8) = 355/12
5x = 55/3
x = 55/3/5
x = 11/3


Input:
Solve simultaneously:
5x + 3y = -57/8
1x + 3y = -189/40

Output:
5x + 3y = -57/8
1x + 3y = -189/40

Using elimination
1*(5x + 3y = -57/8)
5*(1x + 3y = -189/40)
5x + 3y = -57/8
5x + 15y = -189/8
Subtract equations
-12y = 33/2
y = 33/2/-12
y = -11/8

Substitute y
5x + 3(-11/8) = -57/8
5x = -3
x = -3/5
x = -3/5


Input:
Solve simultaneously:
8x + 2y = -60
7x + 10y = -36

Output:
8x + 2y = -60
7x + 10y = -36

Using elimination
7*(8x + 2y = -60)
8*(7x + 10y = -36)
56x + 14y = -420
56x + 80y = -288
Subtract equations
-66y = -132
y = -132/-66
y = 2

Substitute y
8x + 2(2) = -60
8x = -64
x = -64/8
x = -8


Input:
Solve the system:
3x + 2y = -46
2x + 5y = -93

Output:
3x + 2y = -46
2x + 5y = -93

Using elimination
2*(3x + 2y = -46)
3*(2x + 5y = -93)
6x + 4y = -92
6x + 15y = -279
Subtract equations
-11y = 187
y = 187/-11
y = -17

Substitute y
3x + 2(-17) = -46
3x = -12
x = -12/3
x = -4


Input:
Solve simultaneously:
6x + 8y = -49/4
2x + 5y = -7/2

Output:
6x + 8y = -49/4
2x + 5y = -7/2

Using elimination
2*(6x + 8y = -49/4)
6*(2x + 5y = -7/2)
12x + 16y = -49/2
12x + 30y = -21
Subtract equations
-14y = -7/2
y = -7/2/-14
y = 1/4

Substitute y
6x + 8(1/4) = -49/4
6x = -57/4
x = -57/4/6
x = -19/8


Input: Solve quickly: 1x  = 0

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


Input: What value of x satisfies 7x - 35/6 = 0

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


Input: Solve quickly: x^3 + 2x^2 - 37/9x + 10/9 = 0

Output:
x^3 + 2x^2 - 37/9x + 10/9 = 0
(x - 1)(x - 1/3)(x - -10/3) = 0
x - 1 = 0
x - 1/3 = 0
x - -10/3 = 0
x = 1
x = 1/3
x = -10/3


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

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


Input: Solve quickly: 5x - 15 = 0

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


Input: Determine x in x^3 - 61/28x^2 + 1/4x + 3/14 = 0

Output:
x^3 - 61/28x^2 + 1/4x + 3/14 = 0
(x - 3/7)(x - -1/4)(x - 2) = 0
x - 3/7 = 0
x - -1/4 = 0
x - 2 = 0
x = 3/7
x = -1/4
x = 2


Input:
Solve the equations:
3x + 7y = -5
7x + 3y = 15

Output:
3x + 7y = -5
7x + 3y = 15

Using elimination
7*(3x + 7y = -5)
3*(7x + 3y = 15)
21x + 49y = -35
21x + 9y = 45
Subtract equations
40y = -80
y = -80/40
y = -2

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


Input:
Find x and y such that
3x + 3y = 18/5
8x + 9y = 63/5

Output:
3x + 3y = 18/5
8x + 9y = 63/5

Using elimination
8*(3x + 3y = 18/5)
3*(8x + 9y = 63/5)
24x + 24y = 144/5
24x + 27y = 189/5
Subtract equations
-3y = -9
y = -9/-3
y = 3

Substitute y
3x + 3(3) = 18/5
3x = -27/5
x = -27/5/3
x = -9/5


Input: Compute the solution of x^3 - 39/7x^2 + 530/63x - 200/63 = 0

Output:
x^3 - 39/7x^2 + 530/63x - 200/63 = 0
(x - 10/3)(x - 4/7)(x - 5/3) = 0
x - 10/3 = 0
x - 4/7 = 0
x - 5/3 = 0
x = 10/3
x = 4/7
x = 5/3


Input: Solve quickly: x^3 + 7/9x^2 - 91/36x - 4/3 = 0

Output:
x^3 + 7/9x^2 - 91/36x - 4/3 = 0
(x - -1/2)(x - -16/9)(x - 3/2) = 0
x - -1/2 = 0
x - -16/9 = 0
x - 3/2 = 0
x = -1/2
x = -16/9
x = 3/2


Input: Find x in x^2 + 46/5x + 77/5 = 0

Output:
x^2 + 46/5x + 77/5 = 0
(x - -11/5)(x - -7) = 0
x - -11/5 = 0  or  x - -7 = 0
x = -11/5
x = -7


Input: Compute the solution of 7x + 7/3 = 0

Output:
7x + 7/3 = 0
7x = -7/3
x = -7/3 / 7
x = -1/3


Input: Compute the solution of x^3 + 21/8x^2 - 499/16x - 63/16 = 0

Output:
x^3 + 21/8x^2 - 499/16x - 63/16 = 0
(x - -7)(x - -1/8)(x - 9/2) = 0
x - -7 = 0
x - -1/8 = 0
x - 9/2 = 0
x = -7
x = -1/8
x = 9/2


Input:
Find x and y such that
10x + 7y = -293/10
10x + 9y = -291/10

Output:
10x + 7y = -293/10
10x + 9y = -291/10

Using elimination
10*(10x + 7y = -293/10)
10*(10x + 9y = -291/10)
100x + 70y = -293
100x + 90y = -291
Subtract equations
-20y = -2
y = -2/-20
y = 1/10

Substitute y
10x + 7(1/10) = -293/10
10x = -30
x = -30/10
x = -3


Input:
Solve simultaneously:
3x + 7y = 946/63
5x + 1y = 382/63

Output:
3x + 7y = 946/63
5x + 1y = 382/63

Using elimination
5*(3x + 7y = 946/63)
3*(5x + 1y = 382/63)
15x + 35y = 4730/63
15x + 3y = 382/21
Subtract equations
32y = 512/9
y = 512/9/32
y = 16/9

Substitute y
3x + 7(16/9) = 946/63
3x = 18/7
x = 18/7/3
x = 6/7


Input:
Solve the system:
8x + 3y = 4
8x + 9y = 24

Output:
8x + 3y = 4
8x + 9y = 24

Using elimination
8*(8x + 3y = 4)
8*(8x + 9y = 24)
64x + 24y = 32
64x + 72y = 192
Subtract equations
-48y = -160
y = -160/-48
y = 10/3

Substitute y
8x + 3(10/3) = 4
8x = -6
x = -6/8
x = -3/4


Input: Compute the solution of x^3 + 7/18x^2 - 161/225x + 11/150 = 0

Output:
x^3 + 7/18x^2 - 161/225x + 11/150 = 0
(x - -11/10)(x - 1/9)(x - 3/5) = 0
x - -11/10 = 0
x - 1/9 = 0
x - 3/5 = 0
x = -11/10
x = 1/9
x = 3/5


Input: Determine x in x^3 - 148/15x^2 - 13/3x + 30 = 0

Output:
x^3 - 148/15x^2 - 13/3x + 30 = 0
(x - 5/3)(x - -9/5)(x - 10) = 0
x - 5/3 = 0
x - -9/5 = 0
x - 10 = 0
x = 5/3
x = -9/5
x = 10


Input: Compute the solution of x^3 - 7/2x^2 - 7/2x + 6 = 0

Output:
x^3 - 7/2x^2 - 7/2x + 6 = 0
(x - -3/2)(x - 1)(x - 4) = 0
x - -3/2 = 0
x - 1 = 0
x - 4 = 0
x = -3/2
x = 1
x = 4


Input: Solve quickly: 9x + 18 = 0

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


Input: Determine x in 1x - 6 = 0

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


Input: Solve quickly: x^2 - 46/7x - 3 = 0

Output:
x^2 - 46/7x - 3 = 0
(x - 7)(x - -3/7) = 0
x - 7 = 0  or  x - -3/7 = 0
x = 7
x = -3/7


Input: Solve quickly: 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: Solve x^3 - 37/2x^2 + 629/16x + 11 = 0

Output:
x^3 - 37/2x^2 + 629/16x + 11 = 0
(x - -1/4)(x - 11/4)(x - 16) = 0
x - -1/4 = 0
x - 11/4 = 0
x - 16 = 0
x = -1/4
x = 11/4
x = 16


Input: Solve the equation x^2 - 87/35x + 22/35 = 0

Output:
x^2 - 87/35x + 22/35 = 0
(x - 2/7)(x - 11/5) = 0
x - 2/7 = 0  or  x - 11/5 = 0
x = 2/7
x = 11/5


Input: Determine x in 7x - 70 = 0

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


Input: Find the solution to x^2 - 25/4x + 17/2 = 0

Output:
x^2 - 25/4x + 17/2 = 0
(x - 17/4)(x - 2) = 0
x - 17/4 = 0  or  x - 2 = 0
x = 17/4
x = 2


Input:
Find x and y such that
1x + 5y = -11/10
7x + 10y = -101/5

Output:
1x + 5y = -11/10
7x + 10y = -101/5

Using elimination
7*(1x + 5y = -11/10)
1*(7x + 10y = -101/5)
7x + 35y = -77/10
7x + 10y = -101/5
Subtract equations
25y = 25/2
y = 25/2/25
y = 1/2

Substitute y
1x + 5(1/2) = -11/10
1x = -18/5
x = -18/5/1
x = -18/5


Input: Solve quickly: 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: Find x for x^3 - 142/21x^2 + 83/7x - 68/21 = 0

Output:
x^3 - 142/21x^2 + 83/7x - 68/21 = 0
(x - 17/7)(x - 1/3)(x - 4) = 0
x - 17/7 = 0
x - 1/3 = 0
x - 4 = 0
x = 17/7
x = 1/3
x = 4


Input:
Solve simultaneously:
2x + 3y = -9/2
10x + 9y = -23/2

Output:
2x + 3y = -9/2
10x + 9y = -23/2

Using elimination
10*(2x + 3y = -9/2)
2*(10x + 9y = -23/2)
20x + 30y = -45
20x + 18y = -23
Subtract equations
12y = -22
y = -22/12
y = -11/6

Substitute y
2x + 3(-11/6) = -9/2
2x = 1
x = 1/2
x = 1/2


Input:
Solve simultaneously:
7x + 1y = -40/3
8x + 9y = -35/9

Output:
7x + 1y = -40/3
8x + 9y = -35/9

Using elimination
8*(7x + 1y = -40/3)
7*(8x + 9y = -35/9)
56x + 8y = -320/3
56x + 63y = -245/9
Subtract equations
-55y = -715/9
y = -715/9/-55
y = 13/9

Substitute y
7x + 1(13/9) = -40/3
7x = -133/9
x = -133/9/7
x = -19/9


Input: Find x for x^2 + 207/56x + 81/28 = 0

Output:
x^2 + 207/56x + 81/28 = 0
(x - -9/8)(x - -18/7) = 0
x - -9/8 = 0  or  x - -18/7 = 0
x = -9/8
x = -18/7


Input: Find x for x^2 + 23/12x - 13/24 = 0

Output:
x^2 + 23/12x - 13/24 = 0
(x - 1/4)(x - -13/6) = 0
x - 1/4 = 0  or  x - -13/6 = 0
x = 1/4
x = -13/6


Input: Find x for x^3 - 121/45x^2 - 436/75x + 228/25 = 0

Output:
x^3 - 121/45x^2 - 436/75x + 228/25 = 0
(x - -19/9)(x - 18/5)(x - 6/5) = 0
x - -19/9 = 0
x - 18/5 = 0
x - 6/5 = 0
x = -19/9
x = 18/5
x = 6/5


Input: What value of x satisfies 9x + 117/10 = 0

Output:
9x + 117/10 = 0
9x = -117/10
x = -117/10 / 9
x = -13/10


Input: Find x in 9x + 3 = 0

Output:
9x + 3 = 0
9x = -3
x = -3 / 9
x = -1/3


Input:
Solve the equations:
10x + 7y = -191/14
9x + 1y = -209/14

Output:
10x + 7y = -191/14
9x + 1y = -209/14

Using elimination
9*(10x + 7y = -191/14)
10*(9x + 1y = -209/14)
90x + 63y = -1719/14
90x + 10y = -1045/7
Subtract equations
53y = 53/2
y = 53/2/53
y = 1/2

Substitute y
10x + 7(1/2) = -191/14
10x = -120/7
x = -120/7/10
x = -12/7


Input:
Solve the equations:
10x + 4y = 197/6
2x + 2y = 13/6

Output:
10x + 4y = 197/6
2x + 2y = 13/6

Using elimination
2*(10x + 4y = 197/6)
10*(2x + 2y = 13/6)
20x + 8y = 197/3
20x + 20y = 65/3
Subtract equations
-12y = 44
y = 44/-12
y = -11/3

Substitute y
10x + 4(-11/3) = 197/6
10x = 95/2
x = 95/2/10
x = 19/4


Input: Solve x^2 - 51/4x - 135/4 = 0

Output:
x^2 - 51/4x - 135/4 = 0
(x - -9/4)(x - 15) = 0
x - -9/4 = 0  or  x - 15 = 0
x = -9/4
x = 15


Input:
Solve the system:
4x + 8y = 1204/45
3x + 1y = 46/15

Output:
4x + 8y = 1204/45
3x + 1y = 46/15

Using elimination
3*(4x + 8y = 1204/45)
4*(3x + 1y = 46/15)
12x + 24y = 1204/15
12x + 4y = 184/15
Subtract equations
20y = 68
y = 68/20
y = 17/5

Substitute y
4x + 8(17/5) = 1204/45
4x = -4/9
x = -4/9/4
x = -1/9


Input:
Solve the equations:
9x + 6y = -85/2
6x + 6y = -35

Output:
9x + 6y = -85/2
6x + 6y = -35

Using elimination
6*(9x + 6y = -85/2)
9*(6x + 6y = -35)
54x + 36y = -255
54x + 54y = -315
Subtract equations
-18y = 60
y = 60/-18
y = -10/3

Substitute y
9x + 6(-10/3) = -85/2
9x = -45/2
x = -45/2/9
x = -5/2


Input: Find the solution to x^2 + 13/4x - 99/8 = 0

Output:
x^2 + 13/4x - 99/8 = 0
(x - -11/2)(x - 9/4) = 0
x - -11/2 = 0  or  x - 9/4 = 0
x = -11/2
x = 9/4


Input: Find x for x^2 + 45/4x + 26 = 0

Output:
x^2 + 45/4x + 26 = 0
(x - -13/4)(x - -8) = 0
x - -13/4 = 0  or  x - -8 = 0
x = -13/4
x = -8


Input:
Solve the equations:
8x + 9y = 119
10x + 3y = 157

Output:
8x + 9y = 119
10x + 3y = 157

Using elimination
10*(8x + 9y = 119)
8*(10x + 3y = 157)
80x + 90y = 1190
80x + 24y = 1256
Subtract equations
66y = -66
y = -66/66
y = -1

Substitute y
8x + 9(-1) = 119
8x = 128
x = 128/8
x = 16


Input: Compute the solution of 1x + 6/5 = 0

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


Input: Find the solution to x^3 + 167/12x^2 + 695/24x - 275/8 = 0

Output:
x^3 + 167/12x^2 + 695/24x - 275/8 = 0
(x - 5/6)(x - -11)(x - -15/4) = 0
x - 5/6 = 0
x - -11 = 0
x - -15/4 = 0
x = 5/6
x = -11
x = -15/4


Input: Compute the solution of x^3 + 103/28x^2 + 27/28x - 45/14 = 0

Output:
x^3 + 103/28x^2 + 27/28x - 45/14 = 0
(x - 3/4)(x - -10/7)(x - -3) = 0
x - 3/4 = 0
x - -10/7 = 0
x - -3 = 0
x = 3/4
x = -10/7
x = -3


Input: Determine x in x^2 + 11/7x - 18/7 = 0

Output:
x^2 + 11/7x - 18/7 = 0
(x - 1)(x - -18/7) = 0
x - 1 = 0  or  x - -18/7 = 0
x = 1
x = -18/7


Input: What value of x satisfies x^2 - 48/5x + 64/5 = 0

Output:
x^2 - 48/5x + 64/5 = 0
(x - 8/5)(x - 8) = 0
x - 8/5 = 0  or  x - 8 = 0
x = 8/5
x = 8


Input: Solve the equation 5x - 11 = 0

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


Input: Solve the equation x^3 - 2x^2 - 25/4x + 25/2 = 0

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


Input: Solve the equation x^2 - 3x - 18 = 0

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


Input:
Solve the equations:
9x + 1y = 54/5
3x + 4y = -129/10

Output:
9x + 1y = 54/5
3x + 4y = -129/10

Using elimination
3*(9x + 1y = 54/5)
9*(3x + 4y = -129/10)
27x + 3y = 162/5
27x + 36y = -1161/10
Subtract equations
-33y = 297/2
y = 297/2/-33
y = -9/2

Substitute y
9x + 1(-9/2) = 54/5
9x = 153/10
x = 153/10/9
x = 17/10


Input: Solve 1x - 13/8 = 0

Output:
1x - 13/8 = 0
1x = 13/8
x = 13/8 / 1
x = 13/8


Input:
Find x and y such that
7x + 3y = 31
7x + 7y = 63

Output:
7x + 3y = 31
7x + 7y = 63

Using elimination
7*(7x + 3y = 31)
7*(7x + 7y = 63)
49x + 21y = 217
49x + 49y = 441
Subtract equations
-28y = -224
y = -224/-28
y = 8

Substitute y
7x + 3(8) = 31
7x = 7
x = 7/7
x = 1


Input: Find x in x^2 + 67/45x + 8/15 = 0

Output:
x^2 + 67/45x + 8/15 = 0
(x - -3/5)(x - -8/9) = 0
x - -3/5 = 0  or  x - -8/9 = 0
x = -3/5
x = -8/9


Input:
Solve simultaneously:
4x + 8y = -34/5
8x + 1y = -197/20

Output:
4x + 8y = -34/5
8x + 1y = -197/20

Using elimination
8*(4x + 8y = -34/5)
4*(8x + 1y = -197/20)
32x + 64y = -272/5
32x + 4y = -197/5
Subtract equations
60y = -15
y = -15/60
y = -1/4

Substitute y
4x + 8(-1/4) = -34/5
4x = -24/5
x = -24/5/4
x = -6/5


Input: Determine x in 6x - 33/5 = 0

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


Input: Find the solution to x^2 - 19x + 70 = 0

Output:
x^2 - 19x + 70 = 0
(x - 5)(x - 14) = 0
x - 5 = 0  or  x - 14 = 0
x = 5
x = 14


Input: Find x for x^3 - 481/140x^2 - 13/35x + 48/7 = 0

Output:
x^3 - 481/140x^2 - 13/35x + 48/7 = 0
(x - -5/4)(x - 16/7)(x - 12/5) = 0
x - -5/4 = 0
x - 16/7 = 0
x - 12/5 = 0
x = -5/4
x = 16/7
x = 12/5


Input: Solve quickly: x^3 + 87/20x^2 + 11/10x - 6/5 = 0

Output:
x^3 + 87/20x^2 + 11/10x - 6/5 = 0
(x - -3/4)(x - 2/5)(x - -4) = 0
x - -3/4 = 0
x - 2/5 = 0
x - -4 = 0
x = -3/4
x = 2/5
x = -4


Input: Solve the equation x^2 + 103/24x + 55/24 = 0

Output:
x^2 + 103/24x + 55/24 = 0
(x - -5/8)(x - -11/3) = 0
x - -5/8 = 0  or  x - -11/3 = 0
x = -5/8
x = -11/3


Input: Solve quickly: 10x - 140/3 = 0

Output:
10x - 140/3 = 0
10x = 140/3
x = 140/3 / 10
x = 14/3


Input: Solve x^3 + 77/24x^2 + 7/12x - 1/8 = 0

Output:
x^3 + 77/24x^2 + 7/12x - 1/8 = 0
(x - -1/3)(x - 1/8)(x - -3) = 0
x - -1/3 = 0
x - 1/8 = 0
x - -3 = 0
x = -1/3
x = 1/8
x = -3


Input: Solve the equation x^3 + 127/60x^2 - 683/120x + 13/8 = 0

Output:
x^3 + 127/60x^2 - 683/120x + 13/8 = 0
(x - 13/10)(x - -15/4)(x - 1/3) = 0
x - 13/10 = 0
x - -15/4 = 0
x - 1/3 = 0
x = 13/10
x = -15/4
x = 1/3


Input: Find x for 2x + 28 = 0

Output:
2x + 28 = 0
2x = -28
x = -28 / 2
x = -14


Input:
Solve simultaneously:
8x + 1y = 47/2
4x + 8y = 23

Output:
8x + 1y = 47/2
4x + 8y = 23

Using elimination
4*(8x + 1y = 47/2)
8*(4x + 8y = 23)
32x + 4y = 94
32x + 64y = 184
Subtract equations
-60y = -90
y = -90/-60
y = 3/2

Substitute y
8x + 1(3/2) = 47/2
8x = 22
x = 22/8
x = 11/4


Input: Compute the solution of x^3 + 9/10x^2 - 93/25x - 76/25 = 0

Output:
x^3 + 9/10x^2 - 93/25x - 76/25 = 0
(x - -2)(x - 19/10)(x - -4/5) = 0
x - -2 = 0
x - 19/10 = 0
x - -4/5 = 0
x = -2
x = 19/10
x = -4/5


Input:
Find x and y such that
8x + 7y = 536/5
10x + 5y = 74

Output:
8x + 7y = 536/5
10x + 5y = 74

Using elimination
10*(8x + 7y = 536/5)
8*(10x + 5y = 74)
80x + 70y = 1072
80x + 40y = 592
Subtract equations
30y = 480
y = 480/30
y = 16

Substitute y
8x + 7(16) = 536/5
8x = -24/5
x = -24/5/8
x = -3/5


Input: Find the solution to 1x + 19/2 = 0

Output:
1x + 19/2 = 0
1x = -19/2
x = -19/2 / 1
x = -19/2


Input: Determine x in x^3 + 25/21x^2 - 82/21x - 104/21 = 0

Output:
x^3 + 25/21x^2 - 82/21x - 104/21 = 0
(x - -13/7)(x - 2)(x - -4/3) = 0
x - -13/7 = 0
x - 2 = 0
x - -4/3 = 0
x = -13/7
x = 2
x = -4/3


Input: Solve quickly: x^3 + 7/18x^2 - 31/9x - 8/3 = 0

Output:
x^3 + 7/18x^2 - 31/9x - 8/3 = 0
(x - -3/2)(x - -8/9)(x - 2) = 0
x - -3/2 = 0
x - -8/9 = 0
x - 2 = 0
x = -3/2
x = -8/9
x = 2


Input: Solve quickly: x^3 - 9/2x^2 - 171/16x + 81/8 = 0

Output:
x^3 - 9/2x^2 - 171/16x + 81/8 = 0
(x - 6)(x - 3/4)(x - -9/4) = 0
x - 6 = 0
x - 3/4 = 0
x - -9/4 = 0
x = 6
x = 3/4
x = -9/4


Input: What value of x satisfies 3x + 9/4 = 0

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


Input:
Solve the system:
6x + 8y = 44/3
8x + 2y = 50/3

Output:
6x + 8y = 44/3
8x + 2y = 50/3

Using elimination
8*(6x + 8y = 44/3)
6*(8x + 2y = 50/3)
48x + 64y = 352/3
48x + 12y = 100
Subtract equations
52y = 52/3
y = 52/3/52
y = 1/3

Substitute y
6x + 8(1/3) = 44/3
6x = 12
x = 12/6
x = 2


Input:
Solve the equations:
7x + 4y = -33/4
5x + 1y = -5/4

Output:
7x + 4y = -33/4
5x + 1y = -5/4

Using elimination
5*(7x + 4y = -33/4)
7*(5x + 1y = -5/4)
35x + 20y = -165/4
35x + 7y = -35/4
Subtract equations
13y = -65/2
y = -65/2/13
y = -5/2

Substitute y
7x + 4(-5/2) = -33/4
7x = 7/4
x = 7/4/7
x = 1/4


Input: Solve 2x + 15 = 0

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


Input: Solve quickly: 10x + 35/4 = 0

Output:
10x + 35/4 = 0
10x = -35/4
x = -35/4 / 10
x = -7/8


Input:
Find x and y such that
6x + 1y = 121/40
4x + 7y = 239/40

Output:
6x + 1y = 121/40
4x + 7y = 239/40

Using elimination
4*(6x + 1y = 121/40)
6*(4x + 7y = 239/40)
24x + 4y = 121/10
24x + 42y = 717/20
Subtract equations
-38y = -95/4
y = -95/4/-38
y = 5/8

Substitute y
6x + 1(5/8) = 121/40
6x = 12/5
x = 12/5/6
x = 2/5


Input: Find x in x^2 - 51/5x + 133/20 = 0

Output:
x^2 - 51/5x + 133/20 = 0
(x - 7/10)(x - 19/2) = 0
x - 7/10 = 0  or  x - 19/2 = 0
x = 7/10
x = 19/2


Input:
Solve the system:
7x + 1y = -33/7
6x + 2y = -10/7

Output:
7x + 1y = -33/7
6x + 2y = -10/7

Using elimination
6*(7x + 1y = -33/7)
7*(6x + 2y = -10/7)
42x + 6y = -198/7
42x + 14y = -10
Subtract equations
-8y = -128/7
y = -128/7/-8
y = 16/7

Substitute y
7x + 1(16/7) = -33/7
7x = -7
x = -7/7
x = -1


Input: Solve x^2 + 2x  = 0

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


Input:
Find x and y such that
3x + 8y = -293/10
1x + 10y = -391/10

Output:
3x + 8y = -293/10
1x + 10y = -391/10

Using elimination
1*(3x + 8y = -293/10)
3*(1x + 10y = -391/10)
3x + 8y = -293/10
3x + 30y = -1173/10
Subtract equations
-22y = 88
y = 88/-22
y = -4

Substitute y
3x + 8(-4) = -293/10
3x = 27/10
x = 27/10/3
x = 9/10


Input:
Find x and y such that
1x + 4y = 4/3
4x + 10y = 28/3

Output:
1x + 4y = 4/3
4x + 10y = 28/3

Using elimination
4*(1x + 4y = 4/3)
1*(4x + 10y = 28/3)
4x + 16y = 16/3
4x + 10y = 28/3
Subtract equations
6y = -4
y = -4/6
y = -2/3

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


Input: Solve 1x - 3 = 0

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


Input: What value of x satisfies x^2 - 27/5x + 28/5 = 0

Output:
x^2 - 27/5x + 28/5 = 0
(x - 7/5)(x - 4) = 0
x - 7/5 = 0  or  x - 4 = 0
x = 7/5
x = 4


Input: Compute the solution of x^3 + 77/8x^2 + 189/8x + 45/4 = 0

Output:
x^3 + 77/8x^2 + 189/8x + 45/4 = 0
(x - -6)(x - -3)(x - -5/8) = 0
x - -6 = 0
x - -3 = 0
x - -5/8 = 0
x = -6
x = -3
x = -5/8


Input:
Solve the system:
8x + 2y = 126/5
4x + 3y = 53/5

Output:
8x + 2y = 126/5
4x + 3y = 53/5

Using elimination
4*(8x + 2y = 126/5)
8*(4x + 3y = 53/5)
32x + 8y = 504/5
32x + 24y = 424/5
Subtract equations
-16y = 16
y = 16/-16
y = -1

Substitute y
8x + 2(-1) = 126/5
8x = 136/5
x = 136/5/8
x = 17/5


Input:
Solve the equations:
9x + 1y = 227/15
10x + 3y = 25

Output:
9x + 1y = 227/15
10x + 3y = 25

Using elimination
10*(9x + 1y = 227/15)
9*(10x + 3y = 25)
90x + 10y = 454/3
90x + 27y = 225
Subtract equations
-17y = -221/3
y = -221/3/-17
y = 13/3

Substitute y
9x + 1(13/3) = 227/15
9x = 54/5
x = 54/5/9
x = 6/5


Input: Find x in x^2 + 149/40x + 117/40 = 0

Output:
x^2 + 149/40x + 117/40 = 0
(x - -9/8)(x - -13/5) = 0
x - -9/8 = 0  or  x - -13/5 = 0
x = -9/8
x = -13/5


Input:
Find x and y such that
5x + 2y = -739/63
6x + 5y = -1087/63

Output:
5x + 2y = -739/63
6x + 5y = -1087/63

Using elimination
6*(5x + 2y = -739/63)
5*(6x + 5y = -1087/63)
30x + 12y = -1478/21
30x + 25y = -5435/63
Subtract equations
-13y = 143/9
y = 143/9/-13
y = -11/9

Substitute y
5x + 2(-11/9) = -739/63
5x = -65/7
x = -65/7/5
x = -13/7


Input:
Solve the equations:
5x + 2y = 209/3
5x + 3y = 67

Output:
5x + 2y = 209/3
5x + 3y = 67

Using elimination
5*(5x + 2y = 209/3)
5*(5x + 3y = 67)
25x + 10y = 1045/3
25x + 15y = 335
Subtract equations
-5y = 40/3
y = 40/3/-5
y = -8/3

Substitute y
5x + 2(-8/3) = 209/3
5x = 75
x = 75/5
x = 15


Input:
Solve the equations:
3x + 4y = 151/30
6x + 6y = 37/5

Output:
3x + 4y = 151/30
6x + 6y = 37/5

Using elimination
6*(3x + 4y = 151/30)
3*(6x + 6y = 37/5)
18x + 24y = 151/5
18x + 18y = 111/5
Subtract equations
6y = 8
y = 8/6
y = 4/3

Substitute y
3x + 4(4/3) = 151/30
3x = -3/10
x = -3/10/3
x = -1/10


Input: Compute the solution of 3x + 3 = 0

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


Input:
Solve the equations:
8x + 7y = 137/2
7x + 5y = 103/2

Output:
8x + 7y = 137/2
7x + 5y = 103/2

Using elimination
7*(8x + 7y = 137/2)
8*(7x + 5y = 103/2)
56x + 49y = 959/2
56x + 40y = 412
Subtract equations
9y = 135/2
y = 135/2/9
y = 15/2

Substitute y
8x + 7(15/2) = 137/2
8x = 16
x = 16/8
x = 2


Input: Find x in 6x - 24/5 = 0

Output:
6x - 24/5 = 0
6x = 24/5
x = 24/5 / 6
x = 4/5


Input:
Find x and y such that
1x + 2y = -32/5
3x + 5y = -177/10

Output:
1x + 2y = -32/5
3x + 5y = -177/10

Using elimination
3*(1x + 2y = -32/5)
1*(3x + 5y = -177/10)
3x + 6y = -96/5
3x + 5y = -177/10
Subtract equations
1y = -3/2
y = -3/2/1
y = -3/2

Substitute y
1x + 2(-3/2) = -32/5
1x = -17/5
x = -17/5/1
x = -17/5


Input: Determine x in 5x - 16 = 0

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


Input:
Solve the system:
5x + 8y = -31/12
6x + 3y = 29/2

Output:
5x + 8y = -31/12
6x + 3y = 29/2

Using elimination
6*(5x + 8y = -31/12)
5*(6x + 3y = 29/2)
30x + 48y = -31/2
30x + 15y = 145/2
Subtract equations
33y = -88
y = -88/33
y = -8/3

Substitute y
5x + 8(-8/3) = -31/12
5x = 75/4
x = 75/4/5
x = 15/4


Input: Solve 1x - 16/3 = 0

Output:
1x - 16/3 = 0
1x = 16/3
x = 16/3 / 1
x = 16/3


Input:
Find x and y such that
7x + 8y = 92
4x + 8y = 80

Output:
7x + 8y = 92
4x + 8y = 80

Using elimination
4*(7x + 8y = 92)
7*(4x + 8y = 80)
28x + 32y = 368
28x + 56y = 560
Subtract equations
-24y = -192
y = -192/-24
y = 8

Substitute y
7x + 8(8) = 92
7x = 28
x = 28/7
x = 4


Input:
Find x and y such that
8x + 5y = -170/9
1x + 3y = -64/9

Output:
8x + 5y = -170/9
1x + 3y = -64/9

Using elimination
1*(8x + 5y = -170/9)
8*(1x + 3y = -64/9)
8x + 5y = -170/9
8x + 24y = -512/9
Subtract equations
-19y = 38
y = 38/-19
y = -2

Substitute y
8x + 5(-2) = -170/9
8x = -80/9
x = -80/9/8
x = -10/9


Input:
Solve simultaneously:
9x + 8y = 19
4x + 5y = 7

Output:
9x + 8y = 19
4x + 5y = 7

Using elimination
4*(9x + 8y = 19)
9*(4x + 5y = 7)
36x + 32y = 76
36x + 45y = 63
Subtract equations
-13y = 13
y = 13/-13
y = -1

Substitute y
9x + 8(-1) = 19
9x = 27
x = 27/9
x = 3


Input: Find x in x^2 - 1/6x - 1/3 = 0

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


Input: What value of x satisfies 1x - 3/7 = 0

Output:
1x - 3/7 = 0
1x = 3/7
x = 3/7 / 1
x = 3/7


Input: Find x in x^2 + 11/3x - 20/3 = 0

Output:
x^2 + 11/3x - 20/3 = 0
(x - 4/3)(x - -5) = 0
x - 4/3 = 0  or  x - -5 = 0
x = 4/3
x = -5


Input:
Solve simultaneously:
9x + 8y = -51
10x + 6y = -118/3

Output:
9x + 8y = -51
10x + 6y = -118/3

Using elimination
10*(9x + 8y = -51)
9*(10x + 6y = -118/3)
90x + 80y = -510
90x + 54y = -354
Subtract equations
26y = -156
y = -156/26
y = -6

Substitute y
9x + 8(-6) = -51
9x = -3
x = -3/9
x = -1/3


Input:
Find x and y such that
6x + 8y = 194/7
8x + 7y = 389/14

Output:
6x + 8y = 194/7
8x + 7y = 389/14

Using elimination
8*(6x + 8y = 194/7)
6*(8x + 7y = 389/14)
48x + 64y = 1552/7
48x + 42y = 1167/7
Subtract equations
22y = 55
y = 55/22
y = 5/2

Substitute y
6x + 8(5/2) = 194/7
6x = 54/7
x = 54/7/6
x = 9/7


Input:
Solve the equations:
1x + 2y = -12
5x + 3y = -127/2

Output:
1x + 2y = -12
5x + 3y = -127/2

Using elimination
5*(1x + 2y = -12)
1*(5x + 3y = -127/2)
5x + 10y = -60
5x + 3y = -127/2
Subtract equations
7y = 7/2
y = 7/2/7
y = 1/2

Substitute y
1x + 2(1/2) = -12
1x = -13
x = -13/1
x = -13


Input:
Solve the equations:
5x + 7y = -151/6
8x + 8y = -92/3

Output:
5x + 7y = -151/6
8x + 8y = -92/3

Using elimination
8*(5x + 7y = -151/6)
5*(8x + 8y = -92/3)
40x + 56y = -604/3
40x + 40y = -460/3
Subtract equations
16y = -48
y = -48/16
y = -3

Substitute y
5x + 7(-3) = -151/6
5x = -25/6
x = -25/6/5
x = -5/6


Input:
Solve the system:
1x + 5y = 506/63
4x + 7y = 122/9

Output:
1x + 5y = 506/63
4x + 7y = 122/9

Using elimination
4*(1x + 5y = 506/63)
1*(4x + 7y = 122/9)
4x + 20y = 2024/63
4x + 7y = 122/9
Subtract equations
13y = 130/7
y = 130/7/13
y = 10/7

Substitute y
1x + 5(10/7) = 506/63
1x = 8/9
x = 8/9/1
x = 8/9


Input: Find the solution to x^3 - 11/10x^2 - 2x + 114/125 = 0

Output:
x^3 - 11/10x^2 - 2x + 114/125 = 0
(x - 2/5)(x - -6/5)(x - 19/10) = 0
x - 2/5 = 0
x - -6/5 = 0
x - 19/10 = 0
x = 2/5
x = -6/5
x = 19/10


Input: Compute the solution of x^2 + 20/63x - 1/21 = 0

Output:
x^2 + 20/63x - 1/21 = 0
(x - -3/7)(x - 1/9) = 0
x - -3/7 = 0  or  x - 1/9 = 0
x = -3/7
x = 1/9


Input: Solve x^3 + 271/60x^2 + 16/3x + 16/15 = 0

Output:
x^3 + 271/60x^2 + 16/3x + 16/15 = 0
(x - -8/3)(x - -8/5)(x - -1/4) = 0
x - -8/3 = 0
x - -8/5 = 0
x - -1/4 = 0
x = -8/3
x = -8/5
x = -1/4


Input: Determine x in 8x - 24 = 0

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


Input:
Find x and y such that
1x + 1y = 4
8x + 5y = 26

Output:
1x + 1y = 4
8x + 5y = 26

Using elimination
8*(1x + 1y = 4)
1*(8x + 5y = 26)
8x + 8y = 32
8x + 5y = 26
Subtract equations
3y = 6
y = 6/3
y = 2

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


Input: Determine x in x^3 + 23/9x^2 - 40/9x - 28/3 = 0

Output:
x^3 + 23/9x^2 - 40/9x - 28/3 = 0
(x - -3)(x - -14/9)(x - 2) = 0
x - -3 = 0
x - -14/9 = 0
x - 2 = 0
x = -3
x = -14/9
x = 2


Input: Solve quickly: x^2 + 37/12x - 12 = 0

Output:
x^2 + 37/12x - 12 = 0
(x - 9/4)(x - -16/3) = 0
x - 9/4 = 0  or  x - -16/3 = 0
x = 9/4
x = -16/3


Input: Solve the equation x^2 + 63/4x - 4 = 0

Output:
x^2 + 63/4x - 4 = 0
(x - 1/4)(x - -16) = 0
x - 1/4 = 0  or  x - -16 = 0
x = 1/4
x = -16


Input: Determine x in x^2 + 7x + 68/9 = 0

Output:
x^2 + 7x + 68/9 = 0
(x - -17/3)(x - -4/3) = 0
x - -17/3 = 0  or  x - -4/3 = 0
x = -17/3
x = -4/3


Input: Solve quickly: x^2 + 31/5x + 6/5 = 0

Output:
x^2 + 31/5x + 6/5 = 0
(x - -1/5)(x - -6) = 0
x - -1/5 = 0  or  x - -6 = 0
x = -1/5
x = -6


Input: Solve the equation x^2 + 51/40x - 27/10 = 0

Output:
x^2 + 51/40x - 27/10 = 0
(x - -12/5)(x - 9/8) = 0
x - -12/5 = 0  or  x - 9/8 = 0
x = -12/5
x = 9/8


Input: Compute the solution of x^2 + 104/7x - 15/7 = 0

Output:
x^2 + 104/7x - 15/7 = 0
(x - 1/7)(x - -15) = 0
x - 1/7 = 0  or  x - -15 = 0
x = 1/7
x = -15


Input: Find the solution to x^2 + 125/63x - 68/63 = 0

Output:
x^2 + 125/63x - 68/63 = 0
(x - -17/7)(x - 4/9) = 0
x - -17/7 = 0  or  x - 4/9 = 0
x = -17/7
x = 4/9


Input: Find x for x^2 - 58/3x + 247/3 = 0

Output:
x^2 - 58/3x + 247/3 = 0
(x - 19/3)(x - 13) = 0
x - 19/3 = 0  or  x - 13 = 0
x = 19/3
x = 13


Input: Solve x^2 - 43/15x - 44/15 = 0

Output:
x^2 - 43/15x - 44/15 = 0
(x - 11/3)(x - -4/5) = 0
x - 11/3 = 0  or  x - -4/5 = 0
x = 11/3
x = -4/5


Input: Find x for x^2 - 40/9x + 128/27 = 0

Output:
x^2 - 40/9x + 128/27 = 0
(x - 16/9)(x - 8/3) = 0
x - 16/9 = 0  or  x - 8/3 = 0
x = 16/9
x = 8/3


Input: Solve 8x + 80/3 = 0

Output:
8x + 80/3 = 0
8x = -80/3
x = -80/3 / 8
x = -10/3


Input:
Solve simultaneously:
10x + 9y = -194
10x + 10y = -580/3

Output:
10x + 9y = -194
10x + 10y = -580/3

Using elimination
10*(10x + 9y = -194)
10*(10x + 10y = -580/3)
100x + 90y = -1940
100x + 100y = -5800/3
Subtract equations
-10y = -20/3
y = -20/3/-10
y = 2/3

Substitute y
10x + 9(2/3) = -194
10x = -200
x = -200/10
x = -20


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

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


Input: Find the solution to 8x + 32/3 = 0

Output:
8x + 32/3 = 0
8x = -32/3
x = -32/3 / 8
x = -4/3


Input:
Solve simultaneously:
10x + 9y = -82/3
4x + 5y = -44/3

Output:
10x + 9y = -82/3
4x + 5y = -44/3

Using elimination
4*(10x + 9y = -82/3)
10*(4x + 5y = -44/3)
40x + 36y = -328/3
40x + 50y = -440/3
Subtract equations
-14y = 112/3
y = 112/3/-14
y = -8/3

Substitute y
10x + 9(-8/3) = -82/3
10x = -10/3
x = -10/3/10
x = -1/3


Input: Compute the solution of 1x - 17/7 = 0

Output:
1x - 17/7 = 0
1x = 17/7
x = 17/7 / 1
x = 17/7


Input: Find x in x^2 + 173/9x - 140/9 = 0

Output:
x^2 + 173/9x - 140/9 = 0
(x - 7/9)(x - -20) = 0
x - 7/9 = 0  or  x - -20 = 0
x = 7/9
x = -20


Input: Solve x^2 - 7/4x + 3/8 = 0

Output:
x^2 - 7/4x + 3/8 = 0
(x - 3/2)(x - 1/4) = 0
x - 3/2 = 0  or  x - 1/4 = 0
x = 3/2
x = 1/4


Input:
Solve the system:
5x + 8y = 37
3x + 6y = 24

Output:
5x + 8y = 37
3x + 6y = 24

Using elimination
3*(5x + 8y = 37)
5*(3x + 6y = 24)
15x + 24y = 111
15x + 30y = 120
Subtract equations
-6y = -9
y = -9/-6
y = 3/2

Substitute y
5x + 8(3/2) = 37
5x = 25
x = 25/5
x = 5


Input: Solve the equation x^2 + 87/8x - 11/8 = 0

Output:
x^2 + 87/8x - 11/8 = 0
(x - -11)(x - 1/8) = 0
x - -11 = 0  or  x - 1/8 = 0
x = -11
x = 1/8


Input:
Find x and y such that
6x + 5y = -51/7
6x + 4y = -52/7

Output:
6x + 5y = -51/7
6x + 4y = -52/7

Using elimination
6*(6x + 5y = -51/7)
6*(6x + 4y = -52/7)
36x + 30y = -306/7
36x + 24y = -312/7
Subtract equations
6y = 6/7
y = 6/7/6
y = 1/7

Substitute y
6x + 5(1/7) = -51/7
6x = -8
x = -8/6
x = -4/3


Input: Solve quickly: 7x - 133/4 = 0

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


Input: What value of x satisfies 1x + 6/7 = 0

Output:
1x + 6/7 = 0
1x = -6/7
x = -6/7 / 1
x = -6/7


Input: Find the solution to x^2 - 69/20x - 17/5 = 0

Output:
x^2 - 69/20x - 17/5 = 0
(x - -4/5)(x - 17/4) = 0
x - -4/5 = 0  or  x - 17/4 = 0
x = -4/5
x = 17/4


Input:
Find x and y such that
2x + 6y = 2/35
1x + 10y = 281/35

Output:
2x + 6y = 2/35
1x + 10y = 281/35

Using elimination
1*(2x + 6y = 2/35)
2*(1x + 10y = 281/35)
2x + 6y = 2/35
2x + 20y = 562/35
Subtract equations
-14y = -16
y = -16/-14
y = 8/7

Substitute y
2x + 6(8/7) = 2/35
2x = -34/5
x = -34/5/2
x = -17/5


Input: Determine x in 2x - 6 = 0

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


Input: Find the solution to 2x + 30/7 = 0

Output:
2x + 30/7 = 0
2x = -30/7
x = -30/7 / 2
x = -15/7


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

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

Using elimination
1*(6x + 4y = 4)
6*(1x + 8y = -7/6)
6x + 4y = 4
6x + 48y = -7
Subtract equations
-44y = 11
y = 11/-44
y = -1/4

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


Input:
Solve the system:
3x + 4y = 19/3
6x + 1y = 52/3

Output:
3x + 4y = 19/3
6x + 1y = 52/3

Using elimination
6*(3x + 4y = 19/3)
3*(6x + 1y = 52/3)
18x + 24y = 38
18x + 3y = 52
Subtract equations
21y = -14
y = -14/21
y = -2/3

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


Input: Determine x in x^3 - 917/45x^2 + 1199/45x - 133/15 = 0

Output:
x^3 - 917/45x^2 + 1199/45x - 133/15 = 0
(x - 7/9)(x - 19)(x - 3/5) = 0
x - 7/9 = 0
x - 19 = 0
x - 3/5 = 0
x = 7/9
x = 19
x = 3/5


Input: What value of x satisfies x^2 + 68/35x + 32/35 = 0

Output:
x^2 + 68/35x + 32/35 = 0
(x - -8/7)(x - -4/5) = 0
x - -8/7 = 0  or  x - -4/5 = 0
x = -8/7
x = -4/5


Input: Solve x^3 + 4/3x^2 - 20/3x  = 0

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


Input: What value of x satisfies x^3 - 97/30x^2 - 73/30x + 7 = 0

Output:
x^3 - 97/30x^2 - 73/30x + 7 = 0
(x - 10/3)(x - 7/5)(x - -3/2) = 0
x - 10/3 = 0
x - 7/5 = 0
x - -3/2 = 0
x = 10/3
x = 7/5
x = -3/2


Input:
Solve the system:
6x + 1y = 3/2
4x + 6y = 9

Output:
6x + 1y = 3/2
4x + 6y = 9

Using elimination
4*(6x + 1y = 3/2)
6*(4x + 6y = 9)
24x + 4y = 6
24x + 36y = 54
Subtract equations
-32y = -48
y = -48/-32
y = 3/2

Substitute y
6x + 1(3/2) = 3/2
6x = 0
x = 0/6
x = 0


Input:
Solve simultaneously:
1x + 7y = 59/3
7x + 7y = 161/3

Output:
1x + 7y = 59/3
7x + 7y = 161/3

Using elimination
7*(1x + 7y = 59/3)
1*(7x + 7y = 161/3)
7x + 49y = 413/3
7x + 7y = 161/3
Subtract equations
42y = 84
y = 84/42
y = 2

Substitute y
1x + 7(2) = 59/3
1x = 17/3
x = 17/3/1
x = 17/3


Input:
Find x and y such that
6x + 2y = 82/15
3x + 4y = 194/15

Output:
6x + 2y = 82/15
3x + 4y = 194/15

Using elimination
3*(6x + 2y = 82/15)
6*(3x + 4y = 194/15)
18x + 6y = 82/5
18x + 24y = 388/5
Subtract equations
-18y = -306/5
y = -306/5/-18
y = 17/5

Substitute y
6x + 2(17/5) = 82/15
6x = -4/3
x = -4/3/6
x = -2/9


Input: Solve quickly: 1x - 7/10 = 0

Output:
1x - 7/10 = 0
1x = 7/10
x = 7/10 / 1
x = 7/10


Input: Solve 4x + 56/5 = 0

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


Input: Solve the equation 2x - 16/5 = 0

Output:
2x - 16/5 = 0
2x = 16/5
x = 16/5 / 2
x = 8/5


Input: Compute the solution of x^2 - 17/4x - 15/4 = 0

Output:
x^2 - 17/4x - 15/4 = 0
(x - 5)(x - -3/4) = 0
x - 5 = 0  or  x - -3/4 = 0
x = 5
x = -3/4


Input: Determine x in 1x + 6 = 0

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


Input: Find the solution to x^3 + 83/7x^2 - 116/7x - 156/7 = 0

Output:
x^3 + 83/7x^2 - 116/7x - 156/7 = 0
(x - 2)(x - -6/7)(x - -13) = 0
x - 2 = 0
x - -6/7 = 0
x - -13 = 0
x = 2
x = -6/7
x = -13


Input:
Solve simultaneously:
8x + 10y = -70/3
5x + 6y = -43/3

Output:
8x + 10y = -70/3
5x + 6y = -43/3

Using elimination
5*(8x + 10y = -70/3)
8*(5x + 6y = -43/3)
40x + 50y = -350/3
40x + 48y = -344/3
Subtract equations
2y = -2
y = -2/2
y = -1

Substitute y
8x + 10(-1) = -70/3
8x = -40/3
x = -40/3/8
x = -5/3


Input: Find x in x^3 - 4x^2 - 35/4x + 75/4 = 0

Output:
x^3 - 4x^2 - 35/4x + 75/4 = 0
(x - 3/2)(x - -5/2)(x - 5) = 0
x - 3/2 = 0
x - -5/2 = 0
x - 5 = 0
x = 3/2
x = -5/2
x = 5


Input: Determine x in x^3 - 583/56x^2 - 135/7x + 18/7 = 0

Output:
x^3 - 583/56x^2 - 135/7x + 18/7 = 0
(x - 12)(x - -12/7)(x - 1/8) = 0
x - 12 = 0
x - -12/7 = 0
x - 1/8 = 0
x = 12
x = -12/7
x = 1/8


Input: Solve 5x - 8 = 0

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


Input: Determine x in 2x + 2/3 = 0

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


Input: Solve quickly: x^2 - 24/7x + 80/49 = 0

Output:
x^2 - 24/7x + 80/49 = 0
(x - 4/7)(x - 20/7) = 0
x - 4/7 = 0  or  x - 20/7 = 0
x = 4/7
x = 20/7


Input: Solve the equation x^3 - 7x^2 - 35/4x + 75/2 = 0

Output:
x^3 - 7x^2 - 35/4x + 75/2 = 0
(x - -5/2)(x - 2)(x - 15/2) = 0
x - -5/2 = 0
x - 2 = 0
x - 15/2 = 0
x = -5/2
x = 2
x = 15/2


Input: Find the solution to x^3 - 8x^2 + 17x - 10 = 0

Output:
x^3 - 8x^2 + 17x - 10 = 0
(x - 1)(x - 2)(x - 5) = 0
x - 1 = 0
x - 2 = 0
x - 5 = 0
x = 1
x = 2
x = 5


Input: Solve 9x + 21/2 = 0

Output:
9x + 21/2 = 0
9x = -21/2
x = -21/2 / 9
x = -7/6


Input:
Solve simultaneously:
9x + 1y = 19/2
1x + 4y = 53/6

Output:
9x + 1y = 19/2
1x + 4y = 53/6

Using elimination
1*(9x + 1y = 19/2)
9*(1x + 4y = 53/6)
9x + 1y = 19/2
9x + 36y = 159/2
Subtract equations
-35y = -70
y = -70/-35
y = 2

Substitute y
9x + 1(2) = 19/2
9x = 15/2
x = 15/2/9
x = 5/6


Input: Find x in x^2 + 24/5x + 128/25 = 0

Output:
x^2 + 24/5x + 128/25 = 0
(x - -8/5)(x - -16/5) = 0
x - -8/5 = 0  or  x - -16/5 = 0
x = -8/5
x = -16/5


Input:
Find x and y such that
5x + 8y = 931/15
6x + 5y = 57

Output:
5x + 8y = 931/15
6x + 5y = 57

Using elimination
6*(5x + 8y = 931/15)
5*(6x + 5y = 57)
30x + 48y = 1862/5
30x + 25y = 285
Subtract equations
23y = 437/5
y = 437/5/23
y = 19/5

Substitute y
5x + 8(19/5) = 931/15
5x = 95/3
x = 95/3/5
x = 19/3


Input:
Solve the equations:
9x + 5y = 570/7
4x + 9y = 172/7

Output:
9x + 5y = 570/7
4x + 9y = 172/7

Using elimination
4*(9x + 5y = 570/7)
9*(4x + 9y = 172/7)
36x + 20y = 2280/7
36x + 81y = 1548/7
Subtract equations
-61y = 732/7
y = 732/7/-61
y = -12/7

Substitute y
9x + 5(-12/7) = 570/7
9x = 90
x = 90/9
x = 10


Input:
Solve simultaneously:
1x + 3y = 23/10
8x + 4y = 282/5

Output:
1x + 3y = 23/10
8x + 4y = 282/5

Using elimination
8*(1x + 3y = 23/10)
1*(8x + 4y = 282/5)
8x + 24y = 92/5
8x + 4y = 282/5
Subtract equations
20y = -38
y = -38/20
y = -19/10

Substitute y
1x + 3(-19/10) = 23/10
1x = 8
x = 8/1
x = 8


Input: Find the solution to 5x - 11 = 0

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


Input: Solve 6x + 4 = 0

Output:
6x + 4 = 0
6x = -4
x = -4 / 6
x = -2/3


Input:
Find x and y such that
6x + 9y = 261/20
4x + 4y = 41/5

Output:
6x + 9y = 261/20
4x + 4y = 41/5

Using elimination
4*(6x + 9y = 261/20)
6*(4x + 4y = 41/5)
24x + 36y = 261/5
24x + 24y = 246/5
Subtract equations
12y = 3
y = 3/12
y = 1/4

Substitute y
6x + 9(1/4) = 261/20
6x = 54/5
x = 54/5/6
x = 9/5


Input:
Solve the equations:
10x + 7y = 9/2
3x + 9y = -9

Output:
10x + 7y = 9/2
3x + 9y = -9

Using elimination
3*(10x + 7y = 9/2)
10*(3x + 9y = -9)
30x + 21y = 27/2
30x + 90y = -90
Subtract equations
-69y = 207/2
y = 207/2/-69
y = -3/2

Substitute y
10x + 7(-3/2) = 9/2
10x = 15
x = 15/10
x = 3/2


Input: Find x for x^3 - 1/2x^2 - 255x + 1404 = 0

Output:
x^3 - 1/2x^2 - 255x + 1404 = 0
(x - -18)(x - 13/2)(x - 12) = 0
x - -18 = 0
x - 13/2 = 0
x - 12 = 0
x = -18
x = 13/2
x = 12


Input: Compute the solution of 7x - 21/2 = 0

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


Input: Solve x^3 - 10/7x^2 - 397/175x - 68/175 = 0

Output:
x^3 - 10/7x^2 - 397/175x - 68/175 = 0
(x - -1/5)(x - 17/7)(x - -4/5) = 0
x - -1/5 = 0
x - 17/7 = 0
x - -4/5 = 0
x = -1/5
x = 17/7
x = -4/5


Input:
Solve the system:
9x + 9y = -261/10
6x + 5y = -31/2

Output:
9x + 9y = -261/10
6x + 5y = -31/2

Using elimination
6*(9x + 9y = -261/10)
9*(6x + 5y = -31/2)
54x + 54y = -783/5
54x + 45y = -279/2
Subtract equations
9y = -171/10
y = -171/10/9
y = -19/10

Substitute y
9x + 9(-19/10) = -261/10
9x = -9
x = -9/9
x = -1


Input:
Solve the equations:
7x + 5y = 149/14
6x + 1y = 31/7

Output:
7x + 5y = 149/14
6x + 1y = 31/7

Using elimination
6*(7x + 5y = 149/14)
7*(6x + 1y = 31/7)
42x + 30y = 447/7
42x + 7y = 31
Subtract equations
23y = 230/7
y = 230/7/23
y = 10/7

Substitute y
7x + 5(10/7) = 149/14
7x = 7/2
x = 7/2/7
x = 1/2


Input:
Find x and y such that
4x + 8y = -16/7
10x + 3y = 232/7

Output:
4x + 8y = -16/7
10x + 3y = 232/7

Using elimination
10*(4x + 8y = -16/7)
4*(10x + 3y = 232/7)
40x + 80y = -160/7
40x + 12y = 928/7
Subtract equations
68y = -1088/7
y = -1088/7/68
y = -16/7

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


Input:
Solve the equations:
5x + 10y = -7
3x + 2y = 19/5

Output:
5x + 10y = -7
3x + 2y = 19/5

Using elimination
3*(5x + 10y = -7)
5*(3x + 2y = 19/5)
15x + 30y = -21
15x + 10y = 19
Subtract equations
20y = -40
y = -40/20
y = -2

Substitute y
5x + 10(-2) = -7
5x = 13
x = 13/5
x = 13/5


Input: Solve x^2 + 18/7x  = 0

Output:
x^2 + 18/7x  = 0
(x - 0)(x - -18/7) = 0
x - 0 = 0  or  x - -18/7 = 0
x = 0
x = -18/7


Input:
Solve the equations:
7x + 3y = -23/8
5x + 7y = -133/8

Output:
7x + 3y = -23/8
5x + 7y = -133/8

Using elimination
5*(7x + 3y = -23/8)
7*(5x + 7y = -133/8)
35x + 15y = -115/8
35x + 49y = -931/8
Subtract equations
-34y = 102
y = 102/-34
y = -3

Substitute y
7x + 3(-3) = -23/8
7x = 49/8
x = 49/8/7
x = 7/8


Input: Solve quickly: x^3 + 5/18x^2 - 28/9x + 2/3 = 0

Output:
x^3 + 5/18x^2 - 28/9x + 2/3 = 0
(x - 2/9)(x - -2)(x - 3/2) = 0
x - 2/9 = 0
x - -2 = 0
x - 3/2 = 0
x = 2/9
x = -2
x = 3/2


Input: Solve quickly: 9x + 180/7 = 0

Output:
9x + 180/7 = 0
9x = -180/7
x = -180/7 / 9
x = -20/7


Input: Find x for x^3 - 129/40x^2 + 1107/400x - 119/400 = 0

Output:
x^3 - 129/40x^2 + 1107/400x - 119/400 = 0
(x - 17/10)(x - 1/8)(x - 7/5) = 0
x - 17/10 = 0
x - 1/8 = 0
x - 7/5 = 0
x = 17/10
x = 1/8
x = 7/5


Input: What value of x satisfies x^2 + 41/6x - 76/3 = 0

Output:
x^2 + 41/6x - 76/3 = 0
(x - -19/2)(x - 8/3) = 0
x - -19/2 = 0  or  x - 8/3 = 0
x = -19/2
x = 8/3


Input:
Solve the system:
3x + 10y = -12
1x + 4y = -68/15

Output:
3x + 10y = -12
1x + 4y = -68/15

Using elimination
1*(3x + 10y = -12)
3*(1x + 4y = -68/15)
3x + 10y = -12
3x + 12y = -68/5
Subtract equations
-2y = 8/5
y = 8/5/-2
y = -4/5

Substitute y
3x + 10(-4/5) = -12
3x = -4
x = -4/3
x = -4/3


Input:
Solve the equations:
1x + 6y = 113/8
10x + 1y = 17/2

Output:
1x + 6y = 113/8
10x + 1y = 17/2

Using elimination
10*(1x + 6y = 113/8)
1*(10x + 1y = 17/2)
10x + 60y = 565/4
10x + 1y = 17/2
Subtract equations
59y = 531/4
y = 531/4/59
y = 9/4

Substitute y
1x + 6(9/4) = 113/8
1x = 5/8
x = 5/8/1
x = 5/8


Input: Find the solution to x^3 - 6x^2 + 8x  = 0

Output:
x^3 - 6x^2 + 8x  = 0
(x - 0)(x - 2)(x - 4) = 0
x - 0 = 0
x - 2 = 0
x - 4 = 0
x = 0
x = 2
x = 4


Input: Compute the solution of x^2 - 177/10x + 136/5 = 0

Output:
x^2 - 177/10x + 136/5 = 0
(x - 16)(x - 17/10) = 0
x - 16 = 0  or  x - 17/10 = 0
x = 16
x = 17/10


Input:
Solve the equations:
10x + 9y = 19/2
6x + 6y = 27/5

Output:
10x + 9y = 19/2
6x + 6y = 27/5

Using elimination
6*(10x + 9y = 19/2)
10*(6x + 6y = 27/5)
60x + 54y = 57
60x + 60y = 54
Subtract equations
-6y = 3
y = 3/-6
y = -1/2

Substitute y
10x + 9(-1/2) = 19/2
10x = 14
x = 14/10
x = 7/5


Input:
Solve simultaneously:
5x + 8y = -92/7
1x + 2y = -89/28

Output:
5x + 8y = -92/7
1x + 2y = -89/28

Using elimination
1*(5x + 8y = -92/7)
5*(1x + 2y = -89/28)
5x + 8y = -92/7
5x + 10y = -445/28
Subtract equations
-2y = 11/4
y = 11/4/-2
y = -11/8

Substitute y
5x + 8(-11/8) = -92/7
5x = -15/7
x = -15/7/5
x = -3/7


Input:
Solve the system:
6x + 1y = 66
4x + 5y = 70

Output:
6x + 1y = 66
4x + 5y = 70

Using elimination
4*(6x + 1y = 66)
6*(4x + 5y = 70)
24x + 4y = 264
24x + 30y = 420
Subtract equations
-26y = -156
y = -156/-26
y = 6

Substitute y
6x + 1(6) = 66
6x = 60
x = 60/6
x = 10


Input: What value of x satisfies x^3 - 63/10x^2 - 11/2x + 21/5 = 0

Output:
x^3 - 63/10x^2 - 11/2x + 21/5 = 0
(x - 1/2)(x - -6/5)(x - 7) = 0
x - 1/2 = 0
x - -6/5 = 0
x - 7 = 0
x = 1/2
x = -6/5
x = 7


Input: Determine x in x^3 + 127/168x^2 - 103/24x + 15/7 = 0

Output:
x^3 + 127/168x^2 - 103/24x + 15/7 = 0
(x - 9/7)(x - -8/3)(x - 5/8) = 0
x - 9/7 = 0
x - -8/3 = 0
x - 5/8 = 0
x = 9/7
x = -8/3
x = 5/8


Input: Determine x in x^2 - 19/5x + 84/25 = 0

Output:
x^2 - 19/5x + 84/25 = 0
(x - 12/5)(x - 7/5) = 0
x - 12/5 = 0  or  x - 7/5 = 0
x = 12/5
x = 7/5


Input: Solve the equation 3x - 24 = 0

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


Input: Solve the equation x^3 + 24/7x^2 + 101/49x - 78/49 = 0

Output:
x^3 + 24/7x^2 + 101/49x - 78/49 = 0
(x - 3/7)(x - -13/7)(x - -2) = 0
x - 3/7 = 0
x - -13/7 = 0
x - -2 = 0
x = 3/7
x = -13/7
x = -2


Input: Solve the equation x^2 - 43/10x + 39/10 = 0

Output:
x^2 - 43/10x + 39/10 = 0
(x - 13/10)(x - 3) = 0
x - 13/10 = 0  or  x - 3 = 0
x = 13/10
x = 3


Input: Compute the solution of x^3 + 601/42x^2 - 79/3x + 80/7 = 0

Output:
x^3 + 601/42x^2 - 79/3x + 80/7 = 0
(x - 6/7)(x - -16)(x - 5/6) = 0
x - 6/7 = 0
x - -16 = 0
x - 5/6 = 0
x = 6/7
x = -16
x = 5/6


Input: Find the solution to 3x - 42 = 0

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


Input:
Find x and y such that
2x + 8y = 141/2
6x + 3y = 45/2

Output:
2x + 8y = 141/2
6x + 3y = 45/2

Using elimination
6*(2x + 8y = 141/2)
2*(6x + 3y = 45/2)
12x + 48y = 423
12x + 6y = 45
Subtract equations
42y = 378
y = 378/42
y = 9

Substitute y
2x + 8(9) = 141/2
2x = -3/2
x = -3/2/2
x = -3/4


Input:
Solve simultaneously:
1x + 10y = -787/12
6x + 1y = -119/6

Output:
1x + 10y = -787/12
6x + 1y = -119/6

Using elimination
6*(1x + 10y = -787/12)
1*(6x + 1y = -119/6)
6x + 60y = -787/2
6x + 1y = -119/6
Subtract equations
59y = -1121/3
y = -1121/3/59
y = -19/3

Substitute y
1x + 10(-19/3) = -787/12
1x = -9/4
x = -9/4/1
x = -9/4


Input:
Find x and y such that
4x + 6y = -32/5
10x + 4y = -16

Output:
4x + 6y = -32/5
10x + 4y = -16

Using elimination
10*(4x + 6y = -32/5)
4*(10x + 4y = -16)
40x + 60y = -64
40x + 16y = -64
Subtract equations
44y = 0
y = 0/44
y = 0

Substitute y
4x + 6(0) = -32/5
4x = -32/5
x = -32/5/4
x = -8/5


Input: What value of x satisfies x^3 + 1/2x^2 - 18x + 45/2 = 0

Output:
x^3 + 1/2x^2 - 18x + 45/2 = 0
(x - -5)(x - 3)(x - 3/2) = 0
x - -5 = 0
x - 3 = 0
x - 3/2 = 0
x = -5
x = 3
x = 3/2


Input: Solve x^3 - 38/9x^2 - 121/12x + 605/36 = 0

Output:
x^3 - 38/9x^2 - 121/12x + 605/36 = 0
(x - 11/2)(x - 11/9)(x - -5/2) = 0
x - 11/2 = 0
x - 11/9 = 0
x - -5/2 = 0
x = 11/2
x = 11/9
x = -5/2


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

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


Input: Determine x in x^2 - 223/56x + 45/14 = 0

Output:
x^2 - 223/56x + 45/14 = 0
(x - 20/7)(x - 9/8) = 0
x - 20/7 = 0  or  x - 9/8 = 0
x = 20/7
x = 9/8


Input: Determine x in x^2 - 33/8x - 121/16 = 0

Output:
x^2 - 33/8x - 121/16 = 0
(x - -11/8)(x - 11/2) = 0
x - -11/8 = 0  or  x - 11/2 = 0
x = -11/8
x = 11/2


Input: Compute the solution of x^3 - 484/45x^2 + 247/15x - 6 = 0

Output:
x^3 - 484/45x^2 + 247/15x - 6 = 0
(x - 5/9)(x - 9)(x - 6/5) = 0
x - 5/9 = 0
x - 9 = 0
x - 6/5 = 0
x = 5/9
x = 9
x = 6/5


Input: Determine x in x^3 + 53/5x^2 + 337/20x - 17/2 = 0

Output:
x^3 + 53/5x^2 + 337/20x - 17/2 = 0
(x - 2/5)(x - -5/2)(x - -17/2) = 0
x - 2/5 = 0
x - -5/2 = 0
x - -17/2 = 0
x = 2/5
x = -5/2
x = -17/2


Input:
Find x and y such that
10x + 8y = 544/9
2x + 4y = 92/9

Output:
10x + 8y = 544/9
2x + 4y = 92/9

Using elimination
2*(10x + 8y = 544/9)
10*(2x + 4y = 92/9)
20x + 16y = 1088/9
20x + 40y = 920/9
Subtract equations
-24y = 56/3
y = 56/3/-24
y = -7/9

Substitute y
10x + 8(-7/9) = 544/9
10x = 200/3
x = 200/3/10
x = 20/3


Input: Find x in x^3 - 59/30x^2 + 53/150x + 28/75 = 0

Output:
x^3 - 59/30x^2 + 53/150x + 28/75 = 0
(x - 8/5)(x - -1/3)(x - 7/10) = 0
x - 8/5 = 0
x - -1/3 = 0
x - 7/10 = 0
x = 8/5
x = -1/3
x = 7/10


Input: What value of x satisfies x^3 - 5/28x^2 - 1997/448x + 855/224 = 0

Output:
x^3 - 5/28x^2 - 1997/448x + 855/224 = 0
(x - 10/7)(x - 9/8)(x - -19/8) = 0
x - 10/7 = 0
x - 9/8 = 0
x - -19/8 = 0
x = 10/7
x = 9/8
x = -19/8


Input:
Solve simultaneously:
8x + 5y = 53/8
10x + 5y = 85/8

Output:
8x + 5y = 53/8
10x + 5y = 85/8

Using elimination
10*(8x + 5y = 53/8)
8*(10x + 5y = 85/8)
80x + 50y = 265/4
80x + 40y = 85
Subtract equations
10y = -75/4
y = -75/4/10
y = -15/8

Substitute y
8x + 5(-15/8) = 53/8
8x = 16
x = 16/8
x = 2


Input: Find the solution to x^2 - 3/10x - 7/10 = 0

Output:
x^2 - 3/10x - 7/10 = 0
(x - -7/10)(x - 1) = 0
x - -7/10 = 0  or  x - 1 = 0
x = -7/10
x = 1


Input:
Find x and y such that
9x + 10y = 4
8x + 5y = 11/2

Output:
9x + 10y = 4
8x + 5y = 11/2

Using elimination
8*(9x + 10y = 4)
9*(8x + 5y = 11/2)
72x + 80y = 32
72x + 45y = 99/2
Subtract equations
35y = -35/2
y = -35/2/35
y = -1/2

Substitute y
9x + 10(-1/2) = 4
9x = 9
x = 9/9
x = 1


Input: Solve x^2 - 11/12x - 121/12 = 0

Output:
x^2 - 11/12x - 121/12 = 0
(x - 11/3)(x - -11/4) = 0
x - 11/3 = 0  or  x - -11/4 = 0
x = 11/3
x = -11/4


Input: Solve quickly: 3x - 33/2 = 0

Output:
3x - 33/2 = 0
3x = 33/2
x = 33/2 / 3
x = 11/2


Input: Find x for x^2 - 8/15x - 16/15 = 0

Output:
x^2 - 8/15x - 16/15 = 0
(x - 4/3)(x - -4/5) = 0
x - 4/3 = 0  or  x - -4/5 = 0
x = 4/3
x = -4/5


Input:
Find x and y such that
9x + 2y = 48/5
4x + 4y = 164/45

Output:
9x + 2y = 48/5
4x + 4y = 164/45

Using elimination
4*(9x + 2y = 48/5)
9*(4x + 4y = 164/45)
36x + 8y = 192/5
36x + 36y = 164/5
Subtract equations
-28y = 28/5
y = 28/5/-28
y = -1/5

Substitute y
9x + 2(-1/5) = 48/5
9x = 10
x = 10/9
x = 10/9


Input: What value of x satisfies x^2 - 63/10x + 81/10 = 0

Output:
x^2 - 63/10x + 81/10 = 0
(x - 9/2)(x - 9/5) = 0
x - 9/2 = 0  or  x - 9/5 = 0
x = 9/2
x = 9/5


Input: Solve quickly: x^3 - 157/42x^2 - 173/42x - 1 = 0

Output:
x^3 - 157/42x^2 - 173/42x - 1 = 0
(x - 14/3)(x - -1/2)(x - -3/7) = 0
x - 14/3 = 0
x - -1/2 = 0
x - -3/7 = 0
x = 14/3
x = -1/2
x = -3/7


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

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


Input: Solve quickly: 7x + 49/6 = 0

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


Input: Solve quickly: x^2 - 22/5x + 96/25 = 0

Output:
x^2 - 22/5x + 96/25 = 0
(x - 16/5)(x - 6/5) = 0
x - 16/5 = 0  or  x - 6/5 = 0
x = 16/5
x = 6/5


Input: Find the solution to x^2 - 1/24x - 133/24 = 0

Output:
x^2 - 1/24x - 133/24 = 0
(x - 19/8)(x - -7/3) = 0
x - 19/8 = 0  or  x - -7/3 = 0
x = 19/8
x = -7/3


Input: What value of x satisfies x^2 + 11/8x  = 0

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


Input: Find x in x^3 + 2/9x^2 - 19/36x - 7/36 = 0

Output:
x^3 + 2/9x^2 - 19/36x - 7/36 = 0
(x - -1/2)(x - 7/9)(x - -1/2) = 0
x - -1/2 = 0
x - 7/9 = 0
x - -1/2 = 0
x = -1/2
x = 7/9
x = -1/2


Input:
Find x and y such that
2x + 2y = -52/9
7x + 10y = -317/9

Output:
2x + 2y = -52/9
7x + 10y = -317/9

Using elimination
7*(2x + 2y = -52/9)
2*(7x + 10y = -317/9)
14x + 14y = -364/9
14x + 20y = -634/9
Subtract equations
-6y = 30
y = 30/-6
y = -5

Substitute y
2x + 2(-5) = -52/9
2x = 38/9
x = 38/9/2
x = 19/9


Input: What value of x satisfies 4x + 64 = 0

Output:
4x + 64 = 0
4x = -64
x = -64 / 4
x = -16


Input: Solve quickly: 1x + 17 = 0

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


Input: Find x in x^3 - 3/5x^2 - 9/5x + 7/5 = 0

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


Input: Find x in 1x + 1/5 = 0

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


Input: Find the solution to 5x - 14 = 0

Output:
5x - 14 = 0
5x = 14
x = 14 / 5
x = 14/5


Input: Find x in x^3 - 7/2x^2 - 47/2x + 26 = 0

Output:
x^3 - 7/2x^2 - 47/2x + 26 = 0
(x - -4)(x - 1)(x - 13/2) = 0
x - -4 = 0
x - 1 = 0
x - 13/2 = 0
x = -4
x = 1
x = 13/2


Input: Find x for 3x + 15/7 = 0

Output:
3x + 15/7 = 0
3x = -15/7
x = -15/7 / 3
x = -5/7


Input:
Solve simultaneously:
8x + 4y = -68/3
1x + 7y = -17/6

Output:
8x + 4y = -68/3
1x + 7y = -17/6

Using elimination
1*(8x + 4y = -68/3)
8*(1x + 7y = -17/6)
8x + 4y = -68/3
8x + 56y = -68/3
Subtract equations
-52y = 0
y = 0/-52
y = 0

Substitute y
8x + 4(0) = -68/3
8x = -68/3
x = -68/3/8
x = -17/6


Input: Compute the solution of x^2 + 13/3x + 4 = 0

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


Input:
Find x and y such that
6x + 2y = -272/15
2x + 9y = -58/5

Output:
6x + 2y = -272/15
2x + 9y = -58/5

Using elimination
2*(6x + 2y = -272/15)
6*(2x + 9y = -58/5)
12x + 4y = -544/15
12x + 54y = -348/5
Subtract equations
-50y = 100/3
y = 100/3/-50
y = -2/3

Substitute y
6x + 2(-2/3) = -272/15
6x = -84/5
x = -84/5/6
x = -14/5


Input:
Solve the system:
7x + 10y = 235/42
8x + 3y = -68/21

Output:
7x + 10y = 235/42
8x + 3y = -68/21

Using elimination
8*(7x + 10y = 235/42)
7*(8x + 3y = -68/21)
56x + 80y = 940/21
56x + 21y = -68/3
Subtract equations
59y = 472/7
y = 472/7/59
y = 8/7

Substitute y
7x + 10(8/7) = 235/42
7x = -35/6
x = -35/6/7
x = -5/6


Input: Solve the equation 1x + 1/9 = 0

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


Input: Find x for x^3 - 121/40x^2 + 197/80x - 21/80 = 0

Output:
x^3 - 121/40x^2 + 197/80x - 21/80 = 0
(x - 7/5)(x - 1/8)(x - 3/2) = 0
x - 7/5 = 0
x - 1/8 = 0
x - 3/2 = 0
x = 7/5
x = 1/8
x = 3/2


Input: Find the solution to x^3 - 77/36x^2 - 71/72x + 35/12 = 0

Output:
x^3 - 77/36x^2 - 71/72x + 35/12 = 0
(x - 3/2)(x - -10/9)(x - 7/4) = 0
x - 3/2 = 0
x - -10/9 = 0
x - 7/4 = 0
x = 3/2
x = -10/9
x = 7/4


Input:
Solve the system:
4x + 8y = 4/3
3x + 2y = -41/3

Output:
4x + 8y = 4/3
3x + 2y = -41/3

Using elimination
3*(4x + 8y = 4/3)
4*(3x + 2y = -41/3)
12x + 24y = 4
12x + 8y = -164/3
Subtract equations
16y = 176/3
y = 176/3/16
y = 11/3

Substitute y
4x + 8(11/3) = 4/3
4x = -28
x = -28/4
x = -7


Input: Find x in 9x + 5 = 0

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


Input: Compute the solution of x^2 + 39/4x + 19/8 = 0

Output:
x^2 + 39/4x + 19/8 = 0
(x - -1/4)(x - -19/2) = 0
x - -1/4 = 0  or  x - -19/2 = 0
x = -1/4
x = -19/2


Input: Solve quickly: x^2 - 17/12x + 1/2 = 0

Output:
x^2 - 17/12x + 1/2 = 0
(x - 2/3)(x - 3/4) = 0
x - 2/3 = 0  or  x - 3/4 = 0
x = 2/3
x = 3/4


Input:
Solve the system:
4x + 10y = 190/9
4x + 7y = 187/9

Output:
4x + 10y = 190/9
4x + 7y = 187/9

Using elimination
4*(4x + 10y = 190/9)
4*(4x + 7y = 187/9)
16x + 40y = 760/9
16x + 28y = 748/9
Subtract equations
12y = 4/3
y = 4/3/12
y = 1/9

Substitute y
4x + 10(1/9) = 190/9
4x = 20
x = 20/4
x = 5


Input: Compute the solution of 4x + 76/9 = 0

Output:
4x + 76/9 = 0
4x = -76/9
x = -76/9 / 4
x = -19/9


Input: Find x in 3x + 51/4 = 0

Output:
3x + 51/4 = 0
3x = -51/4
x = -51/4 / 3
x = -17/4


Input: Compute the solution of 1x - 11/2 = 0

Output:
1x - 11/2 = 0
1x = 11/2
x = 11/2 / 1
x = 11/2


Input: Find x in x^3 + 4/35x^2 - 15/49x - 18/245 = 0

Output:
x^3 + 4/35x^2 - 15/49x - 18/245 = 0
(x - -3/7)(x - 3/5)(x - -2/7) = 0
x - -3/7 = 0
x - 3/5 = 0
x - -2/7 = 0
x = -3/7
x = 3/5
x = -2/7


Input: Determine x in 8x + 3 = 0

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


Input: Find the solution to x^3 + 247/36x^2 + 91/36x - 95/6 = 0

Output:
x^3 + 247/36x^2 + 91/36x - 95/6 = 0
(x - 5/4)(x - -6)(x - -19/9) = 0
x - 5/4 = 0
x - -6 = 0
x - -19/9 = 0
x = 5/4
x = -6
x = -19/9


Input:
Solve the system:
6x + 5y = -467/7
1x + 4y = -366/7

Output:
6x + 5y = -467/7
1x + 4y = -366/7

Using elimination
1*(6x + 5y = -467/7)
6*(1x + 4y = -366/7)
6x + 5y = -467/7
6x + 24y = -2196/7
Subtract equations
-19y = 247
y = 247/-19
y = -13

Substitute y
6x + 5(-13) = -467/7
6x = -12/7
x = -12/7/6
x = -2/7


Input: Solve the equation 9x - 171/4 = 0

Output:
9x - 171/4 = 0
9x = 171/4
x = 171/4 / 9
x = 19/4


Input: Compute the solution of x^2 + 5/4x - 33/8 = 0

Output:
x^2 + 5/4x - 33/8 = 0
(x - 3/2)(x - -11/4) = 0
x - 3/2 = 0  or  x - -11/4 = 0
x = 3/2
x = -11/4


Input: Compute the solution of x^3 + 13/3x^2 + 50/81x - 2200/243 = 0

Output:
x^3 + 13/3x^2 + 50/81x - 2200/243 = 0
(x - 11/9)(x - -10/3)(x - -20/9) = 0
x - 11/9 = 0
x - -10/3 = 0
x - -20/9 = 0
x = 11/9
x = -10/3
x = -20/9


Input: Determine x in x^2 - 13/2x - 17 = 0

Output:
x^2 - 13/2x - 17 = 0
(x - 17/2)(x - -2) = 0
x - 17/2 = 0  or  x - -2 = 0
x = 17/2
x = -2


Input: Compute the solution of x^3 + 47/8x^2 + 135/32x - 567/64 = 0

Output:
x^3 + 47/8x^2 + 135/32x - 567/64 = 0
(x - -9/2)(x - 7/8)(x - -9/4) = 0
x - -9/2 = 0
x - 7/8 = 0
x - -9/4 = 0
x = -9/2
x = 7/8
x = -9/4


Input: Find the solution to 9x + 144/5 = 0

Output:
9x + 144/5 = 0
9x = -144/5
x = -144/5 / 9
x = -16/5


Input: Find x in 4x - 7 = 0

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


Input: Solve quickly: x^2 - 5x + 4 = 0

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


Input:
Solve the equations:
2x + 4y = 8/3
1x + 4y = 8/3

Output:
2x + 4y = 8/3
1x + 4y = 8/3

Using elimination
1*(2x + 4y = 8/3)
2*(1x + 4y = 8/3)
2x + 4y = 8/3
2x + 8y = 16/3
Subtract equations
-4y = -8/3
y = -8/3/-4
y = 2/3

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


Input: Find x in x^2 + 3/4x - 7/4 = 0

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


Input: Compute the solution of 8x - 136/9 = 0

Output:
8x - 136/9 = 0
8x = 136/9
x = 136/9 / 8
x = 17/9


Input:
Solve the system:
1x + 9y = -49/20
5x + 2y = -3/2

Output:
1x + 9y = -49/20
5x + 2y = -3/2

Using elimination
5*(1x + 9y = -49/20)
1*(5x + 2y = -3/2)
5x + 45y = -49/4
5x + 2y = -3/2
Subtract equations
43y = -43/4
y = -43/4/43
y = -1/4

Substitute y
1x + 9(-1/4) = -49/20
1x = -1/5
x = -1/5/1
x = -1/5


Input:
Solve the system:
8x + 1y = 13
5x + 1y = 4

Output:
8x + 1y = 13
5x + 1y = 4

Using elimination
5*(8x + 1y = 13)
8*(5x + 1y = 4)
40x + 5y = 65
40x + 8y = 32
Subtract equations
-3y = 33
y = 33/-3
y = -11

Substitute y
8x + 1(-11) = 13
8x = 24
x = 24/8
x = 3


Input:
Find x and y such that
1x + 10y = 19
8x + 5y = 2

Output:
1x + 10y = 19
8x + 5y = 2

Using elimination
8*(1x + 10y = 19)
1*(8x + 5y = 2)
8x + 80y = 152
8x + 5y = 2
Subtract equations
75y = 150
y = 150/75
y = 2

Substitute y
1x + 10(2) = 19
1x = -1
x = -1/1
x = -1


Input: Determine x in x^2 - 31/6x + 3 = 0

Output:
x^2 - 31/6x + 3 = 0
(x - 2/3)(x - 9/2) = 0
x - 2/3 = 0  or  x - 9/2 = 0
x = 2/3
x = 9/2


Input: Find x in x^2 + 6x + 9 = 0

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


Input: Find the solution to 7x + 42/5 = 0

Output:
7x + 42/5 = 0
7x = -42/5
x = -42/5 / 7
x = -6/5


Input:
Solve the equations:
6x + 1y = -92/7
8x + 1y = -118/7

Output:
6x + 1y = -92/7
8x + 1y = -118/7

Using elimination
8*(6x + 1y = -92/7)
6*(8x + 1y = -118/7)
48x + 8y = -736/7
48x + 6y = -708/7
Subtract equations
2y = -4
y = -4/2
y = -2

Substitute y
6x + 1(-2) = -92/7
6x = -78/7
x = -78/7/6
x = -13/7


Input:
Find x and y such that
8x + 6y = -6
3x + 3y = -27/4

Output:
8x + 6y = -6
3x + 3y = -27/4

Using elimination
3*(8x + 6y = -6)
8*(3x + 3y = -27/4)
24x + 18y = -18
24x + 24y = -54
Subtract equations
-6y = 36
y = 36/-6
y = -6

Substitute y
8x + 6(-6) = -6
8x = 30
x = 30/8
x = 15/4


Input: Determine x in x^3 + 19/6x^2 + 82/75x - 16/25 = 0

Output:
x^3 + 19/6x^2 + 82/75x - 16/25 = 0
(x - -8/3)(x - -4/5)(x - 3/10) = 0
x - -8/3 = 0
x - -4/5 = 0
x - 3/10 = 0
x = -8/3
x = -4/5
x = 3/10


Input: Find x in x^3 - 245/12x^2 + 467/12x + 165/2 = 0

Output:
x^3 - 245/12x^2 + 467/12x + 165/2 = 0
(x - 11/3)(x - 18)(x - -5/4) = 0
x - 11/3 = 0
x - 18 = 0
x - -5/4 = 0
x = 11/3
x = 18
x = -5/4


Input: Find x for 7x - 140/3 = 0

Output:
7x - 140/3 = 0
7x = 140/3
x = 140/3 / 7
x = 20/3


Input: Find x in x^2 + 163/35x + 26/5 = 0

Output:
x^2 + 163/35x + 26/5 = 0
(x - -13/7)(x - -14/5) = 0
x - -13/7 = 0  or  x - -14/5 = 0
x = -13/7
x = -14/5


Input:
Find x and y such that
3x + 9y = -201/4
6x + 2y = -41/2

Output:
3x + 9y = -201/4
6x + 2y = -41/2

Using elimination
6*(3x + 9y = -201/4)
3*(6x + 2y = -41/2)
18x + 54y = -603/2
18x + 6y = -123/2
Subtract equations
48y = -240
y = -240/48
y = -5

Substitute y
3x + 9(-5) = -201/4
3x = -21/4
x = -21/4/3
x = -7/4


Input:
Solve the equations:
3x + 4y = -3/8
1x + 10y = -79/8

Output:
3x + 4y = -3/8
1x + 10y = -79/8

Using elimination
1*(3x + 4y = -3/8)
3*(1x + 10y = -79/8)
3x + 4y = -3/8
3x + 30y = -237/8
Subtract equations
-26y = 117/4
y = 117/4/-26
y = -9/8

Substitute y
3x + 4(-9/8) = -3/8
3x = 33/8
x = 33/8/3
x = 11/8


Input: Solve quickly: 7x - 63/4 = 0

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


Input:
Solve simultaneously:
4x + 7y = 50/9
8x + 6y = -4/3

Output:
4x + 7y = 50/9
8x + 6y = -4/3

Using elimination
8*(4x + 7y = 50/9)
4*(8x + 6y = -4/3)
32x + 56y = 400/9
32x + 24y = -16/3
Subtract equations
32y = 448/9
y = 448/9/32
y = 14/9

Substitute y
4x + 7(14/9) = 50/9
4x = -16/3
x = -16/3/4
x = -4/3


Input:
Solve the equations:
3x + 6y = 51/7
3x + 8y = 75/7

Output:
3x + 6y = 51/7
3x + 8y = 75/7

Using elimination
3*(3x + 6y = 51/7)
3*(3x + 8y = 75/7)
9x + 18y = 153/7
9x + 24y = 225/7
Subtract equations
-6y = -72/7
y = -72/7/-6
y = 12/7

Substitute y
3x + 6(12/7) = 51/7
3x = -3
x = -3/3
x = -1


Input: Determine x in x^3 - 89/15x^2 + 146/15x - 24/5 = 0

Output:
x^3 - 89/15x^2 + 146/15x - 24/5 = 0
(x - 18/5)(x - 4/3)(x - 1) = 0
x - 18/5 = 0
x - 4/3 = 0
x - 1 = 0
x = 18/5
x = 4/3
x = 1


Input: Find the solution to x^2 + 11/9x - 16/3 = 0

Output:
x^2 + 11/9x - 16/3 = 0
(x - 16/9)(x - -3) = 0
x - 16/9 = 0  or  x - -3 = 0
x = 16/9
x = -3


Input: Find x for x^3 - 71/3x^2 + 62x + 680/3 = 0

Output:
x^3 - 71/3x^2 + 62x + 680/3 = 0
(x - -2)(x - 20)(x - 17/3) = 0
x - -2 = 0
x - 20 = 0
x - 17/3 = 0
x = -2
x = 20
x = 17/3


Input: Find the solution to x^3 + 19/2x^2 - 1043/18x + 637/9 = 0

Output:
x^3 + 19/2x^2 - 1043/18x + 637/9 = 0
(x - 7/3)(x - 13/6)(x - -14) = 0
x - 7/3 = 0
x - 13/6 = 0
x - -14 = 0
x = 7/3
x = 13/6
x = -14


Input: Find x in x^3 + 127/5x^2 + 767/5x - 507/5 = 0

Output:
x^3 + 127/5x^2 + 767/5x - 507/5 = 0
(x - -13)(x - 3/5)(x - -13) = 0
x - -13 = 0
x - 3/5 = 0
x - -13 = 0
x = -13
x = 3/5
x = -13


Input: Solve x^3 - 47/12x^2 - 99/4x + 595/6 = 0

Output:
x^3 - 47/12x^2 - 99/4x + 595/6 = 0
(x - 14/3)(x - 17/4)(x - -5) = 0
x - 14/3 = 0
x - 17/4 = 0
x - -5 = 0
x = 14/3
x = 17/4
x = -5


Input: Find x for 2x - 3/5 = 0

Output:
2x - 3/5 = 0
2x = 3/5
x = 3/5 / 2
x = 3/10


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

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


Input:
Solve the system:
4x + 5y = 15/2
9x + 3y = 543/40

Output:
4x + 5y = 15/2
9x + 3y = 543/40

Using elimination
9*(4x + 5y = 15/2)
4*(9x + 3y = 543/40)
36x + 45y = 135/2
36x + 12y = 543/10
Subtract equations
33y = 66/5
y = 66/5/33
y = 2/5

Substitute y
4x + 5(2/5) = 15/2
4x = 11/2
x = 11/2/4
x = 11/8


Input: Solve 5x + 95/8 = 0

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


Input:
Solve the system:
1x + 1y = -157/40
5x + 10y = -269/8

Output:
1x + 1y = -157/40
5x + 10y = -269/8

Using elimination
5*(1x + 1y = -157/40)
1*(5x + 10y = -269/8)
5x + 5y = -157/8
5x + 10y = -269/8
Subtract equations
-5y = 14
y = 14/-5
y = -14/5

Substitute y
1x + 1(-14/5) = -157/40
1x = -9/8
x = -9/8/1
x = -9/8


Input: Solve x^3 - 78/7x^2 + 5/7x + 66/7 = 0

Output:
x^3 - 78/7x^2 + 5/7x + 66/7 = 0
(x - -6/7)(x - 11)(x - 1) = 0
x - -6/7 = 0
x - 11 = 0
x - 1 = 0
x = -6/7
x = 11
x = 1


Input: What value of x satisfies x^2 - 28/15x - 247/60 = 0

Output:
x^2 - 28/15x - 247/60 = 0
(x - -13/10)(x - 19/6) = 0
x - -13/10 = 0  or  x - 19/6 = 0
x = -13/10
x = 19/6


Input: Find the solution to x^3 + 54/5x^2 + 17x + 36/5 = 0

Output:
x^3 + 54/5x^2 + 17x + 36/5 = 0
(x - -4/5)(x - -9)(x - -1) = 0
x - -4/5 = 0
x - -9 = 0
x - -1 = 0
x = -4/5
x = -9
x = -1


Input: Solve quickly: x^2 - 68/35x - 247/35 = 0

Output:
x^2 - 68/35x - 247/35 = 0
(x - -13/7)(x - 19/5) = 0
x - -13/7 = 0  or  x - 19/5 = 0
x = -13/7
x = 19/5


Input:
Find x and y such that
1x + 6y = 347/3
5x + 2y = 139/3

Output:
1x + 6y = 347/3
5x + 2y = 139/3

Using elimination
5*(1x + 6y = 347/3)
1*(5x + 2y = 139/3)
5x + 30y = 1735/3
5x + 2y = 139/3
Subtract equations
28y = 532
y = 532/28
y = 19

Substitute y
1x + 6(19) = 347/3
1x = 5/3
x = 5/3/1
x = 5/3


Input:
Solve the system:
2x + 5y = -111/4
2x + 8y = -30

Output:
2x + 5y = -111/4
2x + 8y = -30

Using elimination
2*(2x + 5y = -111/4)
2*(2x + 8y = -30)
4x + 10y = -111/2
4x + 16y = -60
Subtract equations
-6y = 9/2
y = 9/2/-6
y = -3/4

Substitute y
2x + 5(-3/4) = -111/4
2x = -24
x = -24/2
x = -12


Input: Determine x in x^2 - 3/8x - 11/8 = 0

Output:
x^2 - 3/8x - 11/8 = 0
(x - 11/8)(x - -1) = 0
x - 11/8 = 0  or  x - -1 = 0
x = 11/8
x = -1


Input: Solve 4x + 4/7 = 0

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


Input: Solve quickly: x^3 - 5/6x^2 - 1/2x + 1/3 = 0

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


Input: Find x for x^2 - 179/30x + 17/10 = 0

Output:
x^2 - 179/30x + 17/10 = 0
(x - 17/3)(x - 3/10) = 0
x - 17/3 = 0  or  x - 3/10 = 0
x = 17/3
x = 3/10


Input:
Find x and y such that
4x + 9y = -132/7
2x + 6y = -81/7

Output:
4x + 9y = -132/7
2x + 6y = -81/7

Using elimination
2*(4x + 9y = -132/7)
4*(2x + 6y = -81/7)
8x + 18y = -264/7
8x + 24y = -324/7
Subtract equations
-6y = 60/7
y = 60/7/-6
y = -10/7

Substitute y
4x + 9(-10/7) = -132/7
4x = -6
x = -6/4
x = -3/2


Input: Determine x in 3x - 51/4 = 0

Output:
3x - 51/4 = 0
3x = 51/4
x = 51/4 / 3
x = 17/4


Input:
Solve simultaneously:
10x + 7y = -117/8
7x + 9y = -471/40

Output:
10x + 7y = -117/8
7x + 9y = -471/40

Using elimination
7*(10x + 7y = -117/8)
10*(7x + 9y = -471/40)
70x + 49y = -819/8
70x + 90y = -471/4
Subtract equations
-41y = 123/8
y = 123/8/-41
y = -3/8

Substitute y
10x + 7(-3/8) = -117/8
10x = -12
x = -12/10
x = -6/5


Input: Solve the equation x^2 + 23/28x - 15/28 = 0

Output:
x^2 + 23/28x - 15/28 = 0
(x - 3/7)(x - -5/4) = 0
x - 3/7 = 0  or  x - -5/4 = 0
x = 3/7
x = -5/4


Input: Solve quickly: 5x + 13/2 = 0

Output:
5x + 13/2 = 0
5x = -13/2
x = -13/2 / 5
x = -13/10


Input: Find x for 2x - 26 = 0

Output:
2x - 26 = 0
2x = 26
x = 26 / 2
x = 13


Input: Solve quickly: x^3 - 1/2x^2 - 14x  = 0

Output:
x^3 - 1/2x^2 - 14x  = 0
(x - 0)(x - -7/2)(x - 4) = 0
x - 0 = 0
x - -7/2 = 0
x - 4 = 0
x = 0
x = -7/2
x = 4


Input: Solve the equation x^3 + 20/3x^2 - 869/12x + 1547/12 = 0

Output:
x^3 + 20/3x^2 - 869/12x + 1547/12 = 0
(x - 17/6)(x - 7/2)(x - -13) = 0
x - 17/6 = 0
x - 7/2 = 0
x - -13 = 0
x = 17/6
x = 7/2
x = -13


Input: Solve the equation x^2 + 51/7x + 2 = 0

Output:
x^2 + 51/7x + 2 = 0
(x - -7)(x - -2/7) = 0
x - -7 = 0  or  x - -2/7 = 0
x = -7
x = -2/7


Input: Determine x in 5x + 40 = 0

Output:
5x + 40 = 0
5x = -40
x = -40 / 5
x = -8


Input:
Solve the system:
10x + 5y = 55/4
6x + 10y = 69/2

Output:
10x + 5y = 55/4
6x + 10y = 69/2

Using elimination
6*(10x + 5y = 55/4)
10*(6x + 10y = 69/2)
60x + 30y = 165/2
60x + 100y = 345
Subtract equations
-70y = -525/2
y = -525/2/-70
y = 15/4

Substitute y
10x + 5(15/4) = 55/4
10x = -5
x = -5/10
x = -1/2


Input: Find x for x^3 + 17/14x^2 - 33/7x + 27/14 = 0

Output:
x^3 + 17/14x^2 - 33/7x + 27/14 = 0
(x - 9/7)(x - -3)(x - 1/2) = 0
x - 9/7 = 0
x - -3 = 0
x - 1/2 = 0
x = 9/7
x = -3
x = 1/2


Input: Find the solution to 9x + 54/5 = 0

Output:
9x + 54/5 = 0
9x = -54/5
x = -54/5 / 9
x = -6/5


Input: Find the solution to x^2 - 17x - 18 = 0

Output:
x^2 - 17x - 18 = 0
(x - 18)(x - -1) = 0
x - 18 = 0  or  x - -1 = 0
x = 18
x = -1


Input: What value of x satisfies x^2 - 29/7x + 4/7 = 0

Output:
x^2 - 29/7x + 4/7 = 0
(x - 1/7)(x - 4) = 0
x - 1/7 = 0  or  x - 4 = 0
x = 1/7
x = 4


Input: Determine x in x^2 - 32/9x + 64/27 = 0

Output:
x^2 - 32/9x + 64/27 = 0
(x - 8/9)(x - 8/3) = 0
x - 8/9 = 0  or  x - 8/3 = 0
x = 8/9
x = 8/3


Input: Find x for 1x + 4/7 = 0

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


Input: Find x for x^2 - 161/45x + 98/45 = 0

Output:
x^2 - 161/45x + 98/45 = 0
(x - 7/9)(x - 14/5) = 0
x - 7/9 = 0  or  x - 14/5 = 0
x = 7/9
x = 14/5


Input: Find x in 8x + 48 = 0

Output:
8x + 48 = 0
8x = -48
x = -48 / 8
x = -6


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

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


Input: What value of x satisfies x^2 - 107/7x + 30/7 = 0

Output:
x^2 - 107/7x + 30/7 = 0
(x - 2/7)(x - 15) = 0
x - 2/7 = 0  or  x - 15 = 0
x = 2/7
x = 15


Input: Solve quickly: x^3 + 97/4x^2 + 595/4x + 150 = 0

Output:
x^3 + 97/4x^2 + 595/4x + 150 = 0
(x - -5/4)(x - -15)(x - -8) = 0
x - -5/4 = 0
x - -15 = 0
x - -8 = 0
x = -5/4
x = -15
x = -8


Input:
Solve simultaneously:
9x + 9y = -477/5
8x + 1y = -298/5

Output:
9x + 9y = -477/5
8x + 1y = -298/5

Using elimination
8*(9x + 9y = -477/5)
9*(8x + 1y = -298/5)
72x + 72y = -3816/5
72x + 9y = -2682/5
Subtract equations
63y = -1134/5
y = -1134/5/63
y = -18/5

Substitute y
9x + 9(-18/5) = -477/5
9x = -63
x = -63/9
x = -7


Input: Find x in x^3 + 268/35x^2 - 19/7x + 8/35 = 0

Output:
x^3 + 268/35x^2 - 19/7x + 8/35 = 0
(x - 1/5)(x - 1/7)(x - -8) = 0
x - 1/5 = 0
x - 1/7 = 0
x - -8 = 0
x = 1/5
x = 1/7
x = -8


Input: Find x for 6x + 8 = 0

Output:
6x + 8 = 0
6x = -8
x = -8 / 6
x = -4/3


Input: What value of x satisfies x^3 + 11/2x^2 + 433/50x + 104/25 = 0

Output:
x^3 + 11/2x^2 + 433/50x + 104/25 = 0
(x - -13/10)(x - -1)(x - -16/5) = 0
x - -13/10 = 0
x - -1 = 0
x - -16/5 = 0
x = -13/10
x = -1
x = -16/5


Input: What value of x satisfies x^2 + 4/5x - 28/5 = 0

Output:
x^2 + 4/5x - 28/5 = 0
(x - -14/5)(x - 2) = 0
x - -14/5 = 0  or  x - 2 = 0
x = -14/5
x = 2