Input:
Solve the equations:
8x + 2y = 50/7
8x + 4y = 36/7

Output:
8x + 2y = 50/7
8x + 4y = 36/7

Using elimination
8*(8x + 2y = 50/7)
8*(8x + 4y = 36/7)
64x + 16y = 400/7
64x + 32y = 288/7
Subtract equations
-16y = 16
y = 16/-16
y = -1

Substitute y
8x + 2(-1) = 50/7
8x = 64/7
x = 64/7/8
x = 8/7


Input: Solve the equation x^2 - 41/6x + 35/3 = 0

Output:
x^2 - 41/6x + 35/3 = 0
(x - 10/3)(x - 7/2) = 0
x - 10/3 = 0  or  x - 7/2 = 0
x = 10/3
x = 7/2


Input: Solve quickly: x^3 + 247/12x^2 + 943/12x + 84 = 0

Output:
x^3 + 247/12x^2 + 943/12x + 84 = 0
(x - -9/4)(x - -16)(x - -7/3) = 0
x - -9/4 = 0
x - -16 = 0
x - -7/3 = 0
x = -9/4
x = -16
x = -7/3


Input: Solve the equation 5x - 7 = 0

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


Input: Determine x in x^3 - 87/40x^2 - 111/20x - 19/8 = 0

Output:
x^3 - 87/40x^2 - 111/20x - 19/8 = 0
(x - 19/5)(x - -1)(x - -5/8) = 0
x - 19/5 = 0
x - -1 = 0
x - -5/8 = 0
x = 19/5
x = -1
x = -5/8


Input: Solve the equation 6x - 7 = 0

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


Input: What value of x satisfies x^2 - 23/24x - 85/16 = 0

Output:
x^2 - 23/24x - 85/16 = 0
(x - -15/8)(x - 17/6) = 0
x - -15/8 = 0  or  x - 17/6 = 0
x = -15/8
x = 17/6


Input: What value of x satisfies x^2 - 8/3x + 7/9 = 0

Output:
x^2 - 8/3x + 7/9 = 0
(x - 7/3)(x - 1/3) = 0
x - 7/3 = 0  or  x - 1/3 = 0
x = 7/3
x = 1/3


Input: Solve 1x + 7/5 = 0

Output:
1x + 7/5 = 0
1x = -7/5
x = -7/5 / 1
x = -7/5


Input: Find x in x^3 - 194/15x^2 - 53/15x + 104/3 = 0

Output:
x^3 - 194/15x^2 - 53/15x + 104/3 = 0
(x - 8/5)(x - -5/3)(x - 13) = 0
x - 8/5 = 0
x - -5/3 = 0
x - 13 = 0
x = 8/5
x = -5/3
x = 13


Input: What value of x satisfies x^2 + 49/8x + 45/8 = 0

Output:
x^2 + 49/8x + 45/8 = 0
(x - -9/8)(x - -5) = 0
x - -9/8 = 0  or  x - -5 = 0
x = -9/8
x = -5


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

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


Input: Solve the equation x^3 - 1/4x^2 - 19/4x - 35/16 = 0

Output:
x^3 - 1/4x^2 - 19/4x - 35/16 = 0
(x - 5/2)(x - -1/2)(x - -7/4) = 0
x - 5/2 = 0
x - -1/2 = 0
x - -7/4 = 0
x = 5/2
x = -1/2
x = -7/4


Input: Find the solution to x^3 + 55/12x^2 + 53/8x + 35/12 = 0

Output:
x^3 + 55/12x^2 + 53/8x + 35/12 = 0
(x - -7/4)(x - -5/6)(x - -2) = 0
x - -7/4 = 0
x - -5/6 = 0
x - -2 = 0
x = -7/4
x = -5/6
x = -2


Input: Solve the equation x^3 - 407/84x^2 + 123/28x - 15/14 = 0

Output:
x^3 - 407/84x^2 + 123/28x - 15/14 = 0
(x - 15/4)(x - 2/3)(x - 3/7) = 0
x - 15/4 = 0
x - 2/3 = 0
x - 3/7 = 0
x = 15/4
x = 2/3
x = 3/7


Input:
Solve the equations:
5x + 5y = 235/6
1x + 7y = 317/6

Output:
5x + 5y = 235/6
1x + 7y = 317/6

Using elimination
1*(5x + 5y = 235/6)
5*(1x + 7y = 317/6)
5x + 5y = 235/6
5x + 35y = 1585/6
Subtract equations
-30y = -225
y = -225/-30
y = 15/2

Substitute y
5x + 5(15/2) = 235/6
5x = 5/3
x = 5/3/5
x = 1/3


Input: Solve the equation 6x + 18/5 = 0

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


Input: Solve x^2 - 163/63x + 20/21 = 0

Output:
x^2 - 163/63x + 20/21 = 0
(x - 15/7)(x - 4/9) = 0
x - 15/7 = 0  or  x - 4/9 = 0
x = 15/7
x = 4/9


Input:
Solve simultaneously:
4x + 1y = 211/42
10x + 1y = 643/42

Output:
4x + 1y = 211/42
10x + 1y = 643/42

Using elimination
10*(4x + 1y = 211/42)
4*(10x + 1y = 643/42)
40x + 10y = 1055/21
40x + 4y = 1286/21
Subtract equations
6y = -11
y = -11/6
y = -11/6

Substitute y
4x + 1(-11/6) = 211/42
4x = 48/7
x = 48/7/4
x = 12/7


Input:
Solve the equations:
2x + 5y = -29/10
6x + 1y = 67/10

Output:
2x + 5y = -29/10
6x + 1y = 67/10

Using elimination
6*(2x + 5y = -29/10)
2*(6x + 1y = 67/10)
12x + 30y = -87/5
12x + 2y = 67/5
Subtract equations
28y = -154/5
y = -154/5/28
y = -11/10

Substitute y
2x + 5(-11/10) = -29/10
2x = 13/5
x = 13/5/2
x = 13/10


Input: Find x for 1x - 9/10 = 0

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


Input: Compute the solution of 1x + 13/5 = 0

Output:
1x + 13/5 = 0
1x = -13/5
x = -13/5 / 1
x = -13/5


Input:
Solve the equations:
9x + 3y = 251/3
5x + 4y = 374/9

Output:
9x + 3y = 251/3
5x + 4y = 374/9

Using elimination
5*(9x + 3y = 251/3)
9*(5x + 4y = 374/9)
45x + 15y = 1255/3
45x + 36y = 374
Subtract equations
-21y = 133/3
y = 133/3/-21
y = -19/9

Substitute y
9x + 3(-19/9) = 251/3
9x = 90
x = 90/9
x = 10


Input:
Solve simultaneously:
3x + 9y = -5/2
7x + 6y = 65/6

Output:
3x + 9y = -5/2
7x + 6y = 65/6

Using elimination
7*(3x + 9y = -5/2)
3*(7x + 6y = 65/6)
21x + 63y = -35/2
21x + 18y = 65/2
Subtract equations
45y = -50
y = -50/45
y = -10/9

Substitute y
3x + 9(-10/9) = -5/2
3x = 15/2
x = 15/2/3
x = 5/2


Input: Find the solution to x^3 - 163/12x^2 + 515/12x - 627/16 = 0

Output:
x^3 - 163/12x^2 + 515/12x - 627/16 = 0
(x - 11/6)(x - 19/2)(x - 9/4) = 0
x - 11/6 = 0
x - 19/2 = 0
x - 9/4 = 0
x = 11/6
x = 19/2
x = 9/4


Input: Compute the solution of 10x - 50/3 = 0

Output:
10x - 50/3 = 0
10x = 50/3
x = 50/3 / 10
x = 5/3


Input: Find x in x^2 + 111/28x + 95/28 = 0

Output:
x^2 + 111/28x + 95/28 = 0
(x - -5/4)(x - -19/7) = 0
x - -5/4 = 0  or  x - -19/7 = 0
x = -5/4
x = -19/7


Input:
Solve the equations:
1x + 7y = -121/10
7x + 4y = 53/10

Output:
1x + 7y = -121/10
7x + 4y = 53/10

Using elimination
7*(1x + 7y = -121/10)
1*(7x + 4y = 53/10)
7x + 49y = -847/10
7x + 4y = 53/10
Subtract equations
45y = -90
y = -90/45
y = -2

Substitute y
1x + 7(-2) = -121/10
1x = 19/10
x = 19/10/1
x = 19/10


Input: Find x for x^2 + 197/36x + 187/36 = 0

Output:
x^2 + 197/36x + 187/36 = 0
(x - -11/9)(x - -17/4) = 0
x - -11/9 = 0  or  x - -17/4 = 0
x = -11/9
x = -17/4


Input: Find the solution to 3x - 27/4 = 0

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


Input:
Solve simultaneously:
10x + 5y = 55
10x + 1y = 35

Output:
10x + 5y = 55
10x + 1y = 35

Using elimination
10*(10x + 5y = 55)
10*(10x + 1y = 35)
100x + 50y = 550
100x + 10y = 350
Subtract equations
40y = 200
y = 200/40
y = 5

Substitute y
10x + 5(5) = 55
10x = 30
x = 30/10
x = 3


Input: Determine x in x^2 - 27/4x + 81/8 = 0

Output:
x^2 - 27/4x + 81/8 = 0
(x - 9/4)(x - 9/2) = 0
x - 9/4 = 0  or  x - 9/2 = 0
x = 9/4
x = 9/2


Input: Solve quickly: x^3 + 23/10x^2 - 202/5x - 546/5 = 0

Output:
x^3 + 23/10x^2 - 202/5x - 546/5 = 0
(x - -6)(x - 13/2)(x - -14/5) = 0
x - -6 = 0
x - 13/2 = 0
x - -14/5 = 0
x = -6
x = 13/2
x = -14/5


Input: Solve x^2 - 181/30x - 19/10 = 0

Output:
x^2 - 181/30x - 19/10 = 0
(x - -3/10)(x - 19/3) = 0
x - -3/10 = 0  or  x - 19/3 = 0
x = -3/10
x = 19/3


Input: Find x in x^2 - 38/5x + 48/5 = 0

Output:
x^2 - 38/5x + 48/5 = 0
(x - 6)(x - 8/5) = 0
x - 6 = 0  or  x - 8/5 = 0
x = 6
x = 8/5


Input: Find x for x^3 + 503/180x^2 - 13/10x - 169/36 = 0

Output:
x^3 + 503/180x^2 - 13/10x - 169/36 = 0
(x - -13/5)(x - 5/4)(x - -13/9) = 0
x - -13/5 = 0
x - 5/4 = 0
x - -13/9 = 0
x = -13/5
x = 5/4
x = -13/9


Input: Find the solution to 5x - 12 = 0

Output:
5x - 12 = 0
5x = 12
x = 12 / 5
x = 12/5


Input:
Find x and y such that
1x + 2y = -22/9
2x + 3y = -17/3

Output:
1x + 2y = -22/9
2x + 3y = -17/3

Using elimination
2*(1x + 2y = -22/9)
1*(2x + 3y = -17/3)
2x + 4y = -44/9
2x + 3y = -17/3
Subtract equations
1y = 7/9
y = 7/9/1
y = 7/9

Substitute y
1x + 2(7/9) = -22/9
1x = -4
x = -4/1
x = -4


Input: Solve quickly: x^2 - 31/7x - 20/7 = 0

Output:
x^2 - 31/7x - 20/7 = 0
(x - -4/7)(x - 5) = 0
x - -4/7 = 0  or  x - 5 = 0
x = -4/7
x = 5


Input:
Find x and y such that
2x + 7y = 27
5x + 9y = 328/7

Output:
2x + 7y = 27
5x + 9y = 328/7

Using elimination
5*(2x + 7y = 27)
2*(5x + 9y = 328/7)
10x + 35y = 135
10x + 18y = 656/7
Subtract equations
17y = 289/7
y = 289/7/17
y = 17/7

Substitute y
2x + 7(17/7) = 27
2x = 10
x = 10/2
x = 5


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

Output:
1x - 15/4 = 0
1x = 15/4
x = 15/4 / 1
x = 15/4


Input:
Solve the system:
8x + 2y = -25/3
4x + 9y = -11/2

Output:
8x + 2y = -25/3
4x + 9y = -11/2

Using elimination
4*(8x + 2y = -25/3)
8*(4x + 9y = -11/2)
32x + 8y = -100/3
32x + 72y = -44
Subtract equations
-64y = 32/3
y = 32/3/-64
y = -1/6

Substitute y
8x + 2(-1/6) = -25/3
8x = -8
x = -8/8
x = -1


Input:
Solve the system:
2x + 5y = -22
10x + 1y = -118/5

Output:
2x + 5y = -22
10x + 1y = -118/5

Using elimination
10*(2x + 5y = -22)
2*(10x + 1y = -118/5)
20x + 50y = -220
20x + 2y = -236/5
Subtract equations
48y = -864/5
y = -864/5/48
y = -18/5

Substitute y
2x + 5(-18/5) = -22
2x = -4
x = -4/2
x = -2


Input: What value of x satisfies x^2 + 23/8x + 15/8 = 0

Output:
x^2 + 23/8x + 15/8 = 0
(x - -15/8)(x - -1) = 0
x - -15/8 = 0  or  x - -1 = 0
x = -15/8
x = -1


Input: Solve the equation x^2 - 29/10x - 24/25 = 0

Output:
x^2 - 29/10x - 24/25 = 0
(x - -3/10)(x - 16/5) = 0
x - -3/10 = 0  or  x - 16/5 = 0
x = -3/10
x = 16/5


Input:
Find x and y such that
7x + 2y = -218/15
7x + 4y = -296/15

Output:
7x + 2y = -218/15
7x + 4y = -296/15

Using elimination
7*(7x + 2y = -218/15)
7*(7x + 4y = -296/15)
49x + 14y = -1526/15
49x + 28y = -2072/15
Subtract equations
-14y = 182/5
y = 182/5/-14
y = -13/5

Substitute y
7x + 2(-13/5) = -218/15
7x = -28/3
x = -28/3/7
x = -4/3


Input: What value of x satisfies x^3 - 79/8x^2 + 15x  = 0

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


Input: Compute the solution of 7x + 28/3 = 0

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


Input: Solve the equation x^2 + 83/20x + 117/40 = 0

Output:
x^2 + 83/20x + 117/40 = 0
(x - -9/10)(x - -13/4) = 0
x - -9/10 = 0  or  x - -13/4 = 0
x = -9/10
x = -13/4


Input: Solve quickly: x^3 + 17/12x^2 - 25/4x - 9/2 = 0

Output:
x^3 + 17/12x^2 - 25/4x - 9/2 = 0
(x - -2/3)(x - 9/4)(x - -3) = 0
x - -2/3 = 0
x - 9/4 = 0
x - -3 = 0
x = -2/3
x = 9/4
x = -3


Input: What value of x satisfies x^3 - 1081/72x^2 + 515/36x - 14/9 = 0

Output:
x^3 - 1081/72x^2 + 515/36x - 14/9 = 0
(x - 8/9)(x - 1/8)(x - 14) = 0
x - 8/9 = 0
x - 1/8 = 0
x - 14 = 0
x = 8/9
x = 1/8
x = 14


Input: Solve the equation x^2  - 1/4 = 0

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


Input:
Solve the equations:
9x + 1y = -8
2x + 3y = -491/9

Output:
9x + 1y = -8
2x + 3y = -491/9

Using elimination
2*(9x + 1y = -8)
9*(2x + 3y = -491/9)
18x + 2y = -16
18x + 27y = -491
Subtract equations
-25y = 475
y = 475/-25
y = -19

Substitute y
9x + 1(-19) = -8
9x = 11
x = 11/9
x = 11/9


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

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


Input: Find x for x^2 - 7/18x - 4/9 = 0

Output:
x^2 - 7/18x - 4/9 = 0
(x - 8/9)(x - -1/2) = 0
x - 8/9 = 0  or  x - -1/2 = 0
x = 8/9
x = -1/2


Input: Find x for x^3 + 155/18x^2 - 1453/9x + 136 = 0

Output:
x^3 + 155/18x^2 - 1453/9x + 136 = 0
(x - 17/2)(x - -18)(x - 8/9) = 0
x - 17/2 = 0
x - -18 = 0
x - 8/9 = 0
x = 17/2
x = -18
x = 8/9


Input: Solve x^3 + 7/10x^2 - 11/25x  = 0

Output:
x^3 + 7/10x^2 - 11/25x  = 0
(x - 0)(x - 2/5)(x - -11/10) = 0
x - 0 = 0
x - 2/5 = 0
x - -11/10 = 0
x = 0
x = 2/5
x = -11/10


Input: Find x for x^3 - 35/9x^2 - 379/27x - 247/27 = 0

Output:
x^3 - 35/9x^2 - 379/27x - 247/27 = 0
(x - -13/9)(x - 19/3)(x - -1) = 0
x - -13/9 = 0
x - 19/3 = 0
x - -1 = 0
x = -13/9
x = 19/3
x = -1


Input: Compute the solution of x^3 + 281/30x^2 + 811/30x + 119/5 = 0

Output:
x^3 + 281/30x^2 + 811/30x + 119/5 = 0
(x - -14/3)(x - -17/10)(x - -3) = 0
x - -14/3 = 0
x - -17/10 = 0
x - -3 = 0
x = -14/3
x = -17/10
x = -3


Input: Find x for 10x - 110 = 0

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


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

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


Input: Solve the equation 4x  = 0

Output:
4x  = 0
4x = 0
x = 0 / 4
x = 0


Input: Solve 9x + 27/2 = 0

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


Input: Solve quickly: x^2 + 8x - 180 = 0

Output:
x^2 + 8x - 180 = 0
(x - 10)(x - -18) = 0
x - 10 = 0  or  x - -18 = 0
x = 10
x = -18


Input: Solve 8x - 72 = 0

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


Input: What value of x satisfies x^3 + 249/70x^2 + 1233/490x - 54/49 = 0

Output:
x^3 + 249/70x^2 + 1233/490x - 54/49 = 0
(x - -12/7)(x - -15/7)(x - 3/10) = 0
x - -12/7 = 0
x - -15/7 = 0
x - 3/10 = 0
x = -12/7
x = -15/7
x = 3/10


Input:
Solve the equations:
1x + 4y = -19/7
9x + 5y = -33/28

Output:
1x + 4y = -19/7
9x + 5y = -33/28

Using elimination
9*(1x + 4y = -19/7)
1*(9x + 5y = -33/28)
9x + 36y = -171/7
9x + 5y = -33/28
Subtract equations
31y = -93/4
y = -93/4/31
y = -3/4

Substitute y
1x + 4(-3/4) = -19/7
1x = 2/7
x = 2/7/1
x = 2/7


Input: Find x for x^2 - 43/18x + 17/18 = 0

Output:
x^2 - 43/18x + 17/18 = 0
(x - 17/9)(x - 1/2) = 0
x - 17/9 = 0  or  x - 1/2 = 0
x = 17/9
x = 1/2


Input: Find x for x^2 + 67/24x - 19/16 = 0

Output:
x^2 + 67/24x - 19/16 = 0
(x - 3/8)(x - -19/6) = 0
x - 3/8 = 0  or  x - -19/6 = 0
x = 3/8
x = -19/6


Input:
Solve the equations:
8x + 5y = -255/7
4x + 6y = -250/7

Output:
8x + 5y = -255/7
4x + 6y = -250/7

Using elimination
4*(8x + 5y = -255/7)
8*(4x + 6y = -250/7)
32x + 20y = -1020/7
32x + 48y = -2000/7
Subtract equations
-28y = 140
y = 140/-28
y = -5

Substitute y
8x + 5(-5) = -255/7
8x = -80/7
x = -80/7/8
x = -10/7


Input: Solve x^3 + 69/5x^2 + 27x - 209/5 = 0

Output:
x^3 + 69/5x^2 + 27x - 209/5 = 0
(x - -11)(x - -19/5)(x - 1) = 0
x - -11 = 0
x - -19/5 = 0
x - 1 = 0
x = -11
x = -19/5
x = 1


Input: Compute the solution of 7x - 49/3 = 0

Output:
7x - 49/3 = 0
7x = 49/3
x = 49/3 / 7
x = 7/3


Input: Find x for 9x + 13 = 0

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


Input: Solve 5x + 65/2 = 0

Output:
5x + 65/2 = 0
5x = -65/2
x = -65/2 / 5
x = -13/2


Input:
Solve the equations:
2x + 2y = -3
7x + 4y = -9

Output:
2x + 2y = -3
7x + 4y = -9

Using elimination
7*(2x + 2y = -3)
2*(7x + 4y = -9)
14x + 14y = -21
14x + 8y = -18
Subtract equations
6y = -3
y = -3/6
y = -1/2

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


Input: Find x in x^3 + 16/21x^2 - 5/63x - 2/21 = 0

Output:
x^3 + 16/21x^2 - 5/63x - 2/21 = 0
(x - 1/3)(x - -2/3)(x - -3/7) = 0
x - 1/3 = 0
x - -2/3 = 0
x - -3/7 = 0
x = 1/3
x = -2/3
x = -3/7


Input: Determine x in 6x - 18 = 0

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


Input:
Solve the equations:
10x + 3y = 259/5
10x + 7y = 271/5

Output:
10x + 3y = 259/5
10x + 7y = 271/5

Using elimination
10*(10x + 3y = 259/5)
10*(10x + 7y = 271/5)
100x + 30y = 518
100x + 70y = 542
Subtract equations
-40y = -24
y = -24/-40
y = 3/5

Substitute y
10x + 3(3/5) = 259/5
10x = 50
x = 50/10
x = 5


Input: Find x in 5x + 5 = 0

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


Input: What value of x satisfies x^3 + 18/5x^2 - 273/25x - 98/5 = 0

Output:
x^3 + 18/5x^2 - 273/25x - 98/5 = 0
(x - -5)(x - -7/5)(x - 14/5) = 0
x - -5 = 0
x - -7/5 = 0
x - 14/5 = 0
x = -5
x = -7/5
x = 14/5


Input: Determine x in 4x - 6 = 0

Output:
4x - 6 = 0
4x = 6
x = 6 / 4
x = 3/2


Input:
Solve the equations:
5x + 2y = -32
10x + 2y = -32

Output:
5x + 2y = -32
10x + 2y = -32

Using elimination
10*(5x + 2y = -32)
5*(10x + 2y = -32)
50x + 20y = -320
50x + 10y = -160
Subtract equations
10y = -160
y = -160/10
y = -16

Substitute y
5x + 2(-16) = -32
5x = 0
x = 0/5
x = 0


Input:
Solve the system:
6x + 7y = -125/3
2x + 7y = -65/3

Output:
6x + 7y = -125/3
2x + 7y = -65/3

Using elimination
2*(6x + 7y = -125/3)
6*(2x + 7y = -65/3)
12x + 14y = -250/3
12x + 42y = -130
Subtract equations
-28y = 140/3
y = 140/3/-28
y = -5/3

Substitute y
6x + 7(-5/3) = -125/3
6x = -30
x = -30/6
x = -5


Input: Compute the solution of x^2 + 3/4x - 5/2 = 0

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


Input: Determine x in x^3 + 7/4x^2 + 21/25x + 27/400 = 0

Output:
x^3 + 7/4x^2 + 21/25x + 27/400 = 0
(x - -1/10)(x - -9/10)(x - -3/4) = 0
x - -1/10 = 0
x - -9/10 = 0
x - -3/4 = 0
x = -1/10
x = -9/10
x = -3/4


Input: Find x in x^2 + 31/15x + 14/15 = 0

Output:
x^2 + 31/15x + 14/15 = 0
(x - -2/3)(x - -7/5) = 0
x - -2/3 = 0  or  x - -7/5 = 0
x = -2/3
x = -7/5


Input: Compute the solution of x^3 + 26/45x^2 - 4009/405x + 722/81 = 0

Output:
x^3 + 26/45x^2 - 4009/405x + 722/81 = 0
(x - 10/9)(x - 19/9)(x - -19/5) = 0
x - 10/9 = 0
x - 19/9 = 0
x - -19/5 = 0
x = 10/9
x = 19/9
x = -19/5


Input: Determine x in 9x + 6 = 0

Output:
9x + 6 = 0
9x = -6
x = -6 / 9
x = -2/3


Input: Solve the equation x^3 - 24/35x^2 - 43/28x + 33/70 = 0

Output:
x^3 - 24/35x^2 - 43/28x + 33/70 = 0
(x - 2/7)(x - -11/10)(x - 3/2) = 0
x - 2/7 = 0
x - -11/10 = 0
x - 3/2 = 0
x = 2/7
x = -11/10
x = 3/2


Input: Find the solution to 3x - 12 = 0

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


Input: Solve the equation x^2 + 61/18x + 17/6 = 0

Output:
x^2 + 61/18x + 17/6 = 0
(x - -17/9)(x - -3/2) = 0
x - -17/9 = 0  or  x - -3/2 = 0
x = -17/9
x = -3/2


Input: What value of x satisfies x^2 - 11/5x + 2/5 = 0

Output:
x^2 - 11/5x + 2/5 = 0
(x - 2)(x - 1/5) = 0
x - 2 = 0  or  x - 1/5 = 0
x = 2
x = 1/5


Input:
Solve the system:
2x + 7y = 41
5x + 2y = 131/4

Output:
2x + 7y = 41
5x + 2y = 131/4

Using elimination
5*(2x + 7y = 41)
2*(5x + 2y = 131/4)
10x + 35y = 205
10x + 4y = 131/2
Subtract equations
31y = 279/2
y = 279/2/31
y = 9/2

Substitute y
2x + 7(9/2) = 41
2x = 19/2
x = 19/2/2
x = 19/4


Input: Solve the equation x^2 + 29/9x - 44/27 = 0

Output:
x^2 + 29/9x - 44/27 = 0
(x - -11/3)(x - 4/9) = 0
x - -11/3 = 0  or  x - 4/9 = 0
x = -11/3
x = 4/9


Input: Solve quickly: x^2 + 27/14x + 5/7 = 0

Output:
x^2 + 27/14x + 5/7 = 0
(x - -1/2)(x - -10/7) = 0
x - -1/2 = 0  or  x - -10/7 = 0
x = -1/2
x = -10/7


Input: Determine x in 4x - 8 = 0

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


Input: Solve x^3 - 107/63x^2 + 106/189x + 16/189 = 0

Output:
x^3 - 107/63x^2 + 106/189x + 16/189 = 0
(x - 8/7)(x - -1/9)(x - 2/3) = 0
x - 8/7 = 0
x - -1/9 = 0
x - 2/3 = 0
x = 8/7
x = -1/9
x = 2/3


Input: Solve x^2 - 1x - 42 = 0

Output:
x^2 - 1x - 42 = 0
(x - -6)(x - 7) = 0
x - -6 = 0  or  x - 7 = 0
x = -6
x = 7


Input: Find x for 9x  = 0

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


Input: Determine x in x^2 + 97/5x - 12 = 0

Output:
x^2 + 97/5x - 12 = 0
(x - -20)(x - 3/5) = 0
x - -20 = 0  or  x - 3/5 = 0
x = -20
x = 3/5


Input: Solve x^2 - 79/45x + 2/3 = 0

Output:
x^2 - 79/45x + 2/3 = 0
(x - 5/9)(x - 6/5) = 0
x - 5/9 = 0  or  x - 6/5 = 0
x = 5/9
x = 6/5


Input:
Find x and y such that
4x + 5y = -1/5
1x + 2y = 11/5

Output:
4x + 5y = -1/5
1x + 2y = 11/5

Using elimination
1*(4x + 5y = -1/5)
4*(1x + 2y = 11/5)
4x + 5y = -1/5
4x + 8y = 44/5
Subtract equations
-3y = -9
y = -9/-3
y = 3

Substitute y
4x + 5(3) = -1/5
4x = -76/5
x = -76/5/4
x = -19/5


Input: Solve the equation 9x - 18 = 0

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


Input: Solve x^3 - 1555/72x^2 + 275/9x + 250/9 = 0

Output:
x^3 - 1555/72x^2 + 275/9x + 250/9 = 0
(x - 20/9)(x - -5/8)(x - 20) = 0
x - 20/9 = 0
x - -5/8 = 0
x - 20 = 0
x = 20/9
x = -5/8
x = 20


Input: Find the solution to x^3 - 113/20x^2 - 133/10x + 539/20 = 0

Output:
x^3 - 113/20x^2 - 133/10x + 539/20 = 0
(x - -11/4)(x - 7/5)(x - 7) = 0
x - -11/4 = 0
x - 7/5 = 0
x - 7 = 0
x = -11/4
x = 7/5
x = 7


Input: Find x in x^2 + 11/8x - 5/4 = 0

Output:
x^2 + 11/8x - 5/4 = 0
(x - 5/8)(x - -2) = 0
x - 5/8 = 0  or  x - -2 = 0
x = 5/8
x = -2


Input:
Solve the system:
1x + 7y = -103/10
1x + 4y = -32/5

Output:
1x + 7y = -103/10
1x + 4y = -32/5

Using elimination
1*(1x + 7y = -103/10)
1*(1x + 4y = -32/5)
1x + 7y = -103/10
1x + 4y = -32/5
Subtract equations
3y = -39/10
y = -39/10/3
y = -13/10

Substitute y
1x + 7(-13/10) = -103/10
1x = -6/5
x = -6/5/1
x = -6/5


Input: Find the solution to x^3 + 17/6x^2 - 99/16x + 65/48 = 0

Output:
x^3 + 17/6x^2 - 99/16x + 65/48 = 0
(x - 5/4)(x - 1/4)(x - -13/3) = 0
x - 5/4 = 0
x - 1/4 = 0
x - -13/3 = 0
x = 5/4
x = 1/4
x = -13/3


Input:
Solve the equations:
10x + 1y = 361/9
4x + 3y = 49/3

Output:
10x + 1y = 361/9
4x + 3y = 49/3

Using elimination
4*(10x + 1y = 361/9)
10*(4x + 3y = 49/3)
40x + 4y = 1444/9
40x + 30y = 490/3
Subtract equations
-26y = -26/9
y = -26/9/-26
y = 1/9

Substitute y
10x + 1(1/9) = 361/9
10x = 40
x = 40/10
x = 4


Input: Find x for x^3 + 39/10x^2 + 19/20x - 63/40 = 0

Output:
x^3 + 39/10x^2 + 19/20x - 63/40 = 0
(x - -7/2)(x - 1/2)(x - -9/10) = 0
x - -7/2 = 0
x - 1/2 = 0
x - -9/10 = 0
x = -7/2
x = 1/2
x = -9/10


Input: Find x for x^3 - 12x^2 + 41x - 42 = 0

Output:
x^3 - 12x^2 + 41x - 42 = 0
(x - 3)(x - 7)(x - 2) = 0
x - 3 = 0
x - 7 = 0
x - 2 = 0
x = 3
x = 7
x = 2


Input: What value of x satisfies x^2 - 13/4x + 21/8 = 0

Output:
x^2 - 13/4x + 21/8 = 0
(x - 3/2)(x - 7/4) = 0
x - 3/2 = 0  or  x - 7/4 = 0
x = 3/2
x = 7/4


Input: Find x in x^3 + 179/36x^2 - 7/36x - 5/18 = 0

Output:
x^3 + 179/36x^2 - 7/36x - 5/18 = 0
(x - -5)(x - -2/9)(x - 1/4) = 0
x - -5 = 0
x - -2/9 = 0
x - 1/4 = 0
x = -5
x = -2/9
x = 1/4


Input:
Solve the system:
10x + 9y = 60
10x + 5y = 36

Output:
10x + 9y = 60
10x + 5y = 36

Using elimination
10*(10x + 9y = 60)
10*(10x + 5y = 36)
100x + 90y = 600
100x + 50y = 360
Subtract equations
40y = 240
y = 240/40
y = 6

Substitute y
10x + 9(6) = 60
10x = 6
x = 6/10
x = 3/5


Input:
Solve the system:
6x + 10y = 62
3x + 6y = 38

Output:
6x + 10y = 62
3x + 6y = 38

Using elimination
3*(6x + 10y = 62)
6*(3x + 6y = 38)
18x + 30y = 186
18x + 36y = 228
Subtract equations
-6y = -42
y = -42/-6
y = 7

Substitute y
6x + 10(7) = 62
6x = -8
x = -8/6
x = -4/3


Input: What value of x satisfies x^2 + 9/2x + 85/18 = 0

Output:
x^2 + 9/2x + 85/18 = 0
(x - -17/6)(x - -5/3) = 0
x - -17/6 = 0  or  x - -5/3 = 0
x = -17/6
x = -5/3


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

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


Input: Solve x^3 + 37/5x^2 + 51/4x - 27/20 = 0

Output:
x^3 + 37/5x^2 + 51/4x - 27/20 = 0
(x - 1/10)(x - -9/2)(x - -3) = 0
x - 1/10 = 0
x - -9/2 = 0
x - -3 = 0
x = 1/10
x = -9/2
x = -3


Input: Find x in 7x + 35/3 = 0

Output:
7x + 35/3 = 0
7x = -35/3
x = -35/3 / 7
x = -5/3


Input: Compute the solution of x^2 - 311/90x + 133/45 = 0

Output:
x^2 - 311/90x + 133/45 = 0
(x - 14/9)(x - 19/10) = 0
x - 14/9 = 0  or  x - 19/10 = 0
x = 14/9
x = 19/10


Input:
Solve simultaneously:
1x + 5y = -71/24
10x + 10y = -35/12

Output:
1x + 5y = -71/24
10x + 10y = -35/12

Using elimination
10*(1x + 5y = -71/24)
1*(10x + 10y = -35/12)
10x + 50y = -355/12
10x + 10y = -35/12
Subtract equations
40y = -80/3
y = -80/3/40
y = -2/3

Substitute y
1x + 5(-2/3) = -71/24
1x = 3/8
x = 3/8/1
x = 3/8


Input: Determine x in x^3 + 155/8x^2 + 451/8x + 38 = 0

Output:
x^3 + 155/8x^2 + 451/8x + 38 = 0
(x - -1)(x - -16)(x - -19/8) = 0
x - -1 = 0
x - -16 = 0
x - -19/8 = 0
x = -1
x = -16
x = -19/8


Input: Find the solution to x^2 + 19/6x  = 0

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


Input: Find x for x^3 - 111/10x^2 - 279/5x - 81/2 = 0

Output:
x^3 - 111/10x^2 - 279/5x - 81/2 = 0
(x - 15)(x - -3)(x - -9/10) = 0
x - 15 = 0
x - -3 = 0
x - -9/10 = 0
x = 15
x = -3
x = -9/10


Input: Find x for x^2 + 4/3x - 32/9 = 0

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


Input: Find x for x^3 - 299/63x^2 - 464/63x - 20/21 = 0

Output:
x^3 - 299/63x^2 - 464/63x - 20/21 = 0
(x - 6)(x - -10/9)(x - -1/7) = 0
x - 6 = 0
x - -10/9 = 0
x - -1/7 = 0
x = 6
x = -10/9
x = -1/7


Input: Solve the equation x^3 + 7/3x^2 - 7/3x - 1 = 0

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


Input: Solve the equation x^2 + 19/30x + 1/10 = 0

Output:
x^2 + 19/30x + 1/10 = 0
(x - -1/3)(x - -3/10) = 0
x - -1/3 = 0  or  x - -3/10 = 0
x = -1/3
x = -3/10


Input: Find x in 9x + 10 = 0

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


Input: Determine x in x^3 + 5/7x^2 - 191/448x + 9/224 = 0

Output:
x^3 + 5/7x^2 - 191/448x + 9/224 = 0
(x - 1/8)(x - -9/8)(x - 2/7) = 0
x - 1/8 = 0
x - -9/8 = 0
x - 2/7 = 0
x = 1/8
x = -9/8
x = 2/7


Input: Find x for x^3 - 481/24x^2 - 23/48x + 105/4 = 0

Output:
x^3 - 481/24x^2 - 23/48x + 105/4 = 0
(x - -9/8)(x - 7/6)(x - 20) = 0
x - -9/8 = 0
x - 7/6 = 0
x - 20 = 0
x = -9/8
x = 7/6
x = 20


Input:
Find x and y such that
3x + 5y = 193/21
1x + 3y = 37/7

Output:
3x + 5y = 193/21
1x + 3y = 37/7

Using elimination
1*(3x + 5y = 193/21)
3*(1x + 3y = 37/7)
3x + 5y = 193/21
3x + 9y = 111/7
Subtract equations
-4y = -20/3
y = -20/3/-4
y = 5/3

Substitute y
3x + 5(5/3) = 193/21
3x = 6/7
x = 6/7/3
x = 2/7


Input:
Solve the system:
10x + 2y = -221/6
6x + 8y = -17/6

Output:
10x + 2y = -221/6
6x + 8y = -17/6

Using elimination
6*(10x + 2y = -221/6)
10*(6x + 8y = -17/6)
60x + 12y = -221
60x + 80y = -85/3
Subtract equations
-68y = -578/3
y = -578/3/-68
y = 17/6

Substitute y
10x + 2(17/6) = -221/6
10x = -85/2
x = -85/2/10
x = -17/4


Input:
Solve the system:
8x + 9y = 69
5x + 2y = 25

Output:
8x + 9y = 69
5x + 2y = 25

Using elimination
5*(8x + 9y = 69)
8*(5x + 2y = 25)
40x + 45y = 345
40x + 16y = 200
Subtract equations
29y = 145
y = 145/29
y = 5

Substitute y
8x + 9(5) = 69
8x = 24
x = 24/8
x = 3


Input:
Solve the equations:
6x + 7y = 72
8x + 1y = 46

Output:
6x + 7y = 72
8x + 1y = 46

Using elimination
8*(6x + 7y = 72)
6*(8x + 1y = 46)
48x + 56y = 576
48x + 6y = 276
Subtract equations
50y = 300
y = 300/50
y = 6

Substitute y
6x + 7(6) = 72
6x = 30
x = 30/6
x = 5


Input: Find x for 10x + 5 = 0

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


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

Output:
x^2 - 23/3x + 20/3 = 0
(x - 1)(x - 20/3) = 0
x - 1 = 0  or  x - 20/3 = 0
x = 1
x = 20/3


Input: Solve x^3 - 12/5x^2 - 273/5x + 392/5 = 0

Output:
x^3 - 12/5x^2 - 273/5x + 392/5 = 0
(x - -7)(x - 8)(x - 7/5) = 0
x - -7 = 0
x - 8 = 0
x - 7/5 = 0
x = -7
x = 8
x = 7/5


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

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


Input: Find the solution to 1x - 7/5 = 0

Output:
1x - 7/5 = 0
1x = 7/5
x = 7/5 / 1
x = 7/5


Input:
Solve the equations:
3x + 1y = 11/5
3x + 8y = 256/5

Output:
3x + 1y = 11/5
3x + 8y = 256/5

Using elimination
3*(3x + 1y = 11/5)
3*(3x + 8y = 256/5)
9x + 3y = 33/5
9x + 24y = 768/5
Subtract equations
-21y = -147
y = -147/-21
y = 7

Substitute y
3x + 1(7) = 11/5
3x = -24/5
x = -24/5/3
x = -8/5


Input: What value of x satisfies x^3 + 397/36x^2 - 157/2x + 152/9 = 0

Output:
x^3 + 397/36x^2 - 157/2x + 152/9 = 0
(x - -16)(x - 2/9)(x - 19/4) = 0
x - -16 = 0
x - 2/9 = 0
x - 19/4 = 0
x = -16
x = 2/9
x = 19/4


Input:
Solve simultaneously:
8x + 10y = 68/3
3x + 1y = 14

Output:
8x + 10y = 68/3
3x + 1y = 14

Using elimination
3*(8x + 10y = 68/3)
8*(3x + 1y = 14)
24x + 30y = 68
24x + 8y = 112
Subtract equations
22y = -44
y = -44/22
y = -2

Substitute y
8x + 10(-2) = 68/3
8x = 128/3
x = 128/3/8
x = 16/3


Input:
Solve simultaneously:
5x + 1y = -6
1x + 2y = 0

Output:
5x + 1y = -6
1x + 2y = 0

Using elimination
1*(5x + 1y = -6)
5*(1x + 2y = 0)
5x + 1y = -6
5x + 10y = 0
Subtract equations
-9y = -6
y = -6/-9
y = 2/3

Substitute y
5x + 1(2/3) = -6
5x = -20/3
x = -20/3/5
x = -4/3


Input: Find x in 1x + 2 = 0

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


Input: Find x in x^2 + 2/5x - 57/20 = 0

Output:
x^2 + 2/5x - 57/20 = 0
(x - 3/2)(x - -19/10) = 0
x - 3/2 = 0  or  x - -19/10 = 0
x = 3/2
x = -19/10


Input: Solve the equation x^3 - 17x^2 + 47x + 65 = 0

Output:
x^3 - 17x^2 + 47x + 65 = 0
(x - 13)(x - 5)(x - -1) = 0
x - 13 = 0
x - 5 = 0
x - -1 = 0
x = 13
x = 5
x = -1


Input: Find x for x^2 + 14/9x  = 0

Output:
x^2 + 14/9x  = 0
(x - 0)(x - -14/9) = 0
x - 0 = 0  or  x - -14/9 = 0
x = 0
x = -14/9


Input: Compute the solution of x^2 - 1/30x - 26/15 = 0

Output:
x^2 - 1/30x - 26/15 = 0
(x - 4/3)(x - -13/10) = 0
x - 4/3 = 0  or  x - -13/10 = 0
x = 4/3
x = -13/10


Input:
Solve the system:
4x + 7y = 917/45
6x + 7y = 259/15

Output:
4x + 7y = 917/45
6x + 7y = 259/15

Using elimination
6*(4x + 7y = 917/45)
4*(6x + 7y = 259/15)
24x + 42y = 1834/15
24x + 28y = 1036/15
Subtract equations
14y = 266/5
y = 266/5/14
y = 19/5

Substitute y
4x + 7(19/5) = 917/45
4x = -56/9
x = -56/9/4
x = -14/9


Input: Compute the solution of x^2 + 4/5x - 153/100 = 0

Output:
x^2 + 4/5x - 153/100 = 0
(x - -17/10)(x - 9/10) = 0
x - -17/10 = 0  or  x - 9/10 = 0
x = -17/10
x = 9/10


Input: Find x in 2x - 4 = 0

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


Input: Find x in 1x - 7/9 = 0

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


Input: Find x in x^2 + 1/56x - 1/56 = 0

Output:
x^2 + 1/56x - 1/56 = 0
(x - -1/7)(x - 1/8) = 0
x - -1/7 = 0  or  x - 1/8 = 0
x = -1/7
x = 1/8


Input:
Solve the equations:
9x + 5y = 229/28
3x + 9y = 135/28

Output:
9x + 5y = 229/28
3x + 9y = 135/28

Using elimination
3*(9x + 5y = 229/28)
9*(3x + 9y = 135/28)
27x + 15y = 687/28
27x + 81y = 1215/28
Subtract equations
-66y = -132/7
y = -132/7/-66
y = 2/7

Substitute y
9x + 5(2/7) = 229/28
9x = 27/4
x = 27/4/9
x = 3/4


Input:
Solve the system:
4x + 7y = -58/15
8x + 10y = -28/3

Output:
4x + 7y = -58/15
8x + 10y = -28/3

Using elimination
8*(4x + 7y = -58/15)
4*(8x + 10y = -28/3)
32x + 56y = -464/15
32x + 40y = -112/3
Subtract equations
16y = 32/5
y = 32/5/16
y = 2/5

Substitute y
4x + 7(2/5) = -58/15
4x = -20/3
x = -20/3/4
x = -5/3


Input:
Solve the equations:
4x + 6y = -590/7
3x + 5y = -495/7

Output:
4x + 6y = -590/7
3x + 5y = -495/7

Using elimination
3*(4x + 6y = -590/7)
4*(3x + 5y = -495/7)
12x + 18y = -1770/7
12x + 20y = -1980/7
Subtract equations
-2y = 30
y = 30/-2
y = -15

Substitute y
4x + 6(-15) = -590/7
4x = 40/7
x = 40/7/4
x = 10/7


Input: Find x in x^3 + 3x^2 - 295/4x - 75/2 = 0

Output:
x^3 + 3x^2 - 295/4x - 75/2 = 0
(x - 15/2)(x - -1/2)(x - -10) = 0
x - 15/2 = 0
x - -1/2 = 0
x - -10 = 0
x = 15/2
x = -1/2
x = -10


Input: Find the solution to x^2 - 49/8x - 323/16 = 0

Output:
x^2 - 49/8x - 323/16 = 0
(x - 17/2)(x - -19/8) = 0
x - 17/2 = 0  or  x - -19/8 = 0
x = 17/2
x = -19/8


Input: Compute the solution of x^2 + 1/9x - 8/9 = 0

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


Input: Solve 3x + 45 = 0

Output:
3x + 45 = 0
3x = -45
x = -45 / 3
x = -15


Input:
Solve the system:
8x + 4y = 88/63
2x + 6y = -16/21

Output:
8x + 4y = 88/63
2x + 6y = -16/21

Using elimination
2*(8x + 4y = 88/63)
8*(2x + 6y = -16/21)
16x + 8y = 176/63
16x + 48y = -128/21
Subtract equations
-40y = 80/9
y = 80/9/-40
y = -2/9

Substitute y
8x + 4(-2/9) = 88/63
8x = 16/7
x = 16/7/8
x = 2/7


Input: Compute the solution of x^2 + 169/21x + 304/21 = 0

Output:
x^2 + 169/21x + 304/21 = 0
(x - -16/3)(x - -19/7) = 0
x - -16/3 = 0  or  x - -19/7 = 0
x = -16/3
x = -19/7


Input: Determine x in x^2 - 37/5x - 72/5 = 0

Output:
x^2 - 37/5x - 72/5 = 0
(x - -8/5)(x - 9) = 0
x - -8/5 = 0  or  x - 9 = 0
x = -8/5
x = 9


Input: Solve x^3 + 67/12x^2 - 1097/12x + 65 = 0

Output:
x^3 + 67/12x^2 - 1097/12x + 65 = 0
(x - -13)(x - 3/4)(x - 20/3) = 0
x - -13 = 0
x - 3/4 = 0
x - 20/3 = 0
x = -13
x = 3/4
x = 20/3


Input: Compute the solution of x^2 + 37/3x - 102 = 0

Output:
x^2 + 37/3x - 102 = 0
(x - 17/3)(x - -18) = 0
x - 17/3 = 0  or  x - -18 = 0
x = 17/3
x = -18


Input: Compute the solution of 4x + 4/9 = 0

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


Input: Find the solution to 4x + 4/5 = 0

Output:
4x + 4/5 = 0
4x = -4/5
x = -4/5 / 4
x = -1/5


Input: Find x for 8x + 6 = 0

Output:
8x + 6 = 0
8x = -6
x = -6 / 8
x = -3/4


Input: Determine x in x^2 + 24/5x - 128/5 = 0

Output:
x^2 + 24/5x - 128/5 = 0
(x - 16/5)(x - -8) = 0
x - 16/5 = 0  or  x - -8 = 0
x = 16/5
x = -8


Input:
Solve the system:
7x + 4y = -211/10
1x + 1y = -97/40

Output:
7x + 4y = -211/10
1x + 1y = -97/40

Using elimination
1*(7x + 4y = -211/10)
7*(1x + 1y = -97/40)
7x + 4y = -211/10
7x + 7y = -679/40
Subtract equations
-3y = -33/8
y = -33/8/-3
y = 11/8

Substitute y
7x + 4(11/8) = -211/10
7x = -133/5
x = -133/5/7
x = -19/5


Input: Compute the solution of 4x + 3 = 0

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


Input:
Solve the system:
1x + 7y = -23
10x + 10y = -110

Output:
1x + 7y = -23
10x + 10y = -110

Using elimination
10*(1x + 7y = -23)
1*(10x + 10y = -110)
10x + 70y = -230
10x + 10y = -110
Subtract equations
60y = -120
y = -120/60
y = -2

Substitute y
1x + 7(-2) = -23
1x = -9
x = -9/1
x = -9


Input: What value of x satisfies 9x - 42 = 0

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


Input:
Solve the system:
10x + 8y = -28/3
3x + 3y = -8/3

Output:
10x + 8y = -28/3
3x + 3y = -8/3

Using elimination
3*(10x + 8y = -28/3)
10*(3x + 3y = -8/3)
30x + 24y = -28
30x + 30y = -80/3
Subtract equations
-6y = -4/3
y = -4/3/-6
y = 2/9

Substitute y
10x + 8(2/9) = -28/3
10x = -100/9
x = -100/9/10
x = -10/9


Input: Compute the solution of 6x - 84 = 0

Output:
6x - 84 = 0
6x = 84
x = 84 / 6
x = 14


Input: Find x for x^3 + 133/12x^2 - 679/12x + 65/2 = 0

Output:
x^3 + 133/12x^2 - 679/12x + 65/2 = 0
(x - -15)(x - 13/4)(x - 2/3) = 0
x - -15 = 0
x - 13/4 = 0
x - 2/3 = 0
x = -15
x = 13/4
x = 2/3


Input: Find x in x^2 - 111/10x + 76/5 = 0

Output:
x^2 - 111/10x + 76/5 = 0
(x - 19/2)(x - 8/5) = 0
x - 19/2 = 0  or  x - 8/5 = 0
x = 19/2
x = 8/5


Input: Find x in 8x - 12 = 0

Output:
8x - 12 = 0
8x = 12
x = 12 / 8
x = 3/2


Input:
Solve simultaneously:
4x + 2y = -152/3
4x + 9y = -551/3

Output:
4x + 2y = -152/3
4x + 9y = -551/3

Using elimination
4*(4x + 2y = -152/3)
4*(4x + 9y = -551/3)
16x + 8y = -608/3
16x + 36y = -2204/3
Subtract equations
-28y = 532
y = 532/-28
y = -19

Substitute y
4x + 2(-19) = -152/3
4x = -38/3
x = -38/3/4
x = -19/6


Input: What value of x satisfies 6x + 108/5 = 0

Output:
6x + 108/5 = 0
6x = -108/5
x = -108/5 / 6
x = -18/5


Input: Solve the equation 9x + 117 = 0

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


Input: Solve the equation 4x  = 0

Output:
4x  = 0
4x = 0
x = 0 / 4
x = 0


Input:
Find x and y such that
10x + 8y = 199/3
5x + 1y = 151/6

Output:
10x + 8y = 199/3
5x + 1y = 151/6

Using elimination
5*(10x + 8y = 199/3)
10*(5x + 1y = 151/6)
50x + 40y = 995/3
50x + 10y = 755/3
Subtract equations
30y = 80
y = 80/30
y = 8/3

Substitute y
10x + 8(8/3) = 199/3
10x = 45
x = 45/10
x = 9/2


Input:
Solve simultaneously:
1x + 10y = 1/2
10x + 8y = 117/5

Output:
1x + 10y = 1/2
10x + 8y = 117/5

Using elimination
10*(1x + 10y = 1/2)
1*(10x + 8y = 117/5)
10x + 100y = 5
10x + 8y = 117/5
Subtract equations
92y = -92/5
y = -92/5/92
y = -1/5

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


Input: Find x for x^2 + 24x + 108 = 0

Output:
x^2 + 24x + 108 = 0
(x - -6)(x - -18) = 0
x - -6 = 0  or  x - -18 = 0
x = -6
x = -18


Input: Solve x^3 + 15/8x^2 - 27/8x  = 0

Output:
x^3 + 15/8x^2 - 27/8x  = 0
(x - 9/8)(x - -3)(x - 0) = 0
x - 9/8 = 0
x - -3 = 0
x - 0 = 0
x = 9/8
x = -3
x = 0


Input:
Solve the equations:
9x + 5y = 23
5x + 4y = 59/5

Output:
9x + 5y = 23
5x + 4y = 59/5

Using elimination
5*(9x + 5y = 23)
9*(5x + 4y = 59/5)
45x + 25y = 115
45x + 36y = 531/5
Subtract equations
-11y = 44/5
y = 44/5/-11
y = -4/5

Substitute y
9x + 5(-4/5) = 23
9x = 27
x = 27/9
x = 3


Input:
Solve the system:
5x + 3y = 17
10x + 7y = 71/2

Output:
5x + 3y = 17
10x + 7y = 71/2

Using elimination
10*(5x + 3y = 17)
5*(10x + 7y = 71/2)
50x + 30y = 170
50x + 35y = 355/2
Subtract equations
-5y = -15/2
y = -15/2/-5
y = 3/2

Substitute y
5x + 3(3/2) = 17
5x = 25/2
x = 25/2/5
x = 5/2


Input: Solve the equation 7x + 21/8 = 0

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


Input: What value of x satisfies x^2 + 21x + 38 = 0

Output:
x^2 + 21x + 38 = 0
(x - -19)(x - -2) = 0
x - -19 = 0  or  x - -2 = 0
x = -19
x = -2


Input: What value of x satisfies x^3 - 77/72x^2 - 17/6x + 35/18 = 0

Output:
x^3 - 77/72x^2 - 17/6x + 35/18 = 0
(x - -14/9)(x - 2)(x - 5/8) = 0
x - -14/9 = 0
x - 2 = 0
x - 5/8 = 0
x = -14/9
x = 2
x = 5/8


Input: Solve the equation 4x - 64/3 = 0

Output:
4x - 64/3 = 0
4x = 64/3
x = 64/3 / 4
x = 16/3


Input: Find x in x^2 + 6x + 8 = 0

Output:
x^2 + 6x + 8 = 0
(x - -2)(x - -4) = 0
x - -2 = 0  or  x - -4 = 0
x = -2
x = -4


Input: Solve x^2 + 97/30x - 1/3 = 0

Output:
x^2 + 97/30x - 1/3 = 0
(x - 1/10)(x - -10/3) = 0
x - 1/10 = 0  or  x - -10/3 = 0
x = 1/10
x = -10/3


Input:
Find x and y such that
1x + 8y = 51/2
3x + 2y = -1/2

Output:
1x + 8y = 51/2
3x + 2y = -1/2

Using elimination
3*(1x + 8y = 51/2)
1*(3x + 2y = -1/2)
3x + 24y = 153/2
3x + 2y = -1/2
Subtract equations
22y = 77
y = 77/22
y = 7/2

Substitute y
1x + 8(7/2) = 51/2
1x = -5/2
x = -5/2/1
x = -5/2


Input: Compute the solution of x^3 - 31/6x^2 - 29/2x + 35/3 = 0

Output:
x^3 - 31/6x^2 - 29/2x + 35/3 = 0
(x - 2/3)(x - -5/2)(x - 7) = 0
x - 2/3 = 0
x - -5/2 = 0
x - 7 = 0
x = 2/3
x = -5/2
x = 7


Input: Solve quickly: 1x - 5/6 = 0

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


Input: Solve x^3 + 43/10x^2 - 11/5x - 68/5 = 0

Output:
x^3 + 43/10x^2 - 11/5x - 68/5 = 0
(x - 17/10)(x - -4)(x - -2) = 0
x - 17/10 = 0
x - -4 = 0
x - -2 = 0
x = 17/10
x = -4
x = -2


Input: Find x in x^2 + 37/10x - 99/10 = 0

Output:
x^2 + 37/10x - 99/10 = 0
(x - -11/2)(x - 9/5) = 0
x - -11/2 = 0  or  x - 9/5 = 0
x = -11/2
x = 9/5


Input: Find x in x^2 - 16/5x - 9 = 0

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


Input: Find x in x^3 - 25/4x^2 - 23x - 63/4 = 0

Output:
x^3 - 25/4x^2 - 23x - 63/4 = 0
(x - 9)(x - -1)(x - -7/4) = 0
x - 9 = 0
x - -1 = 0
x - -7/4 = 0
x = 9
x = -1
x = -7/4


Input: Find the solution to x^2 + 124/15x + 84/5 = 0

Output:
x^2 + 124/15x + 84/5 = 0
(x - -14/3)(x - -18/5) = 0
x - -14/3 = 0  or  x - -18/5 = 0
x = -14/3
x = -18/5


Input: Solve the equation x^3 + 419/72x^2 + 797/72x + 247/36 = 0

Output:
x^3 + 419/72x^2 + 797/72x + 247/36 = 0
(x - -13/9)(x - -2)(x - -19/8) = 0
x - -13/9 = 0
x - -2 = 0
x - -19/8 = 0
x = -13/9
x = -2
x = -19/8


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

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


Input: Determine x in x^2 + 16/9x - 4/9 = 0

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


Input: Find the solution to 7x - 28/9 = 0

Output:
7x - 28/9 = 0
7x = 28/9
x = 28/9 / 7
x = 4/9


Input: Find x in 4x - 64/3 = 0

Output:
4x - 64/3 = 0
4x = 64/3
x = 64/3 / 4
x = 16/3


Input:
Find x and y such that
2x + 4y = -80/3
8x + 8y = -256/3

Output:
2x + 4y = -80/3
8x + 8y = -256/3

Using elimination
8*(2x + 4y = -80/3)
2*(8x + 8y = -256/3)
16x + 32y = -640/3
16x + 16y = -512/3
Subtract equations
16y = -128/3
y = -128/3/16
y = -8/3

Substitute y
2x + 4(-8/3) = -80/3
2x = -16
x = -16/2
x = -8


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

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


Input: Find x for 7x - 14 = 0

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


Input:
Find x and y such that
8x + 7y = -115/4
5x + 3y = -65/4

Output:
8x + 7y = -115/4
5x + 3y = -65/4

Using elimination
5*(8x + 7y = -115/4)
8*(5x + 3y = -65/4)
40x + 35y = -575/4
40x + 24y = -130
Subtract equations
11y = -55/4
y = -55/4/11
y = -5/4

Substitute y
8x + 7(-5/4) = -115/4
8x = -20
x = -20/8
x = -5/2


Input: Determine x in x^3 + 53/6x^2 + 29/12x - 85/24 = 0

Output:
x^3 + 53/6x^2 + 29/12x - 85/24 = 0
(x - -17/2)(x - -5/6)(x - 1/2) = 0
x - -17/2 = 0
x - -5/6 = 0
x - 1/2 = 0
x = -17/2
x = -5/6
x = 1/2


Input: Solve quickly: 4x - 4/9 = 0

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


Input: Compute the solution of 3x - 48 = 0

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


Input: Solve the equation x^2 + 27/10x + 11/10 = 0

Output:
x^2 + 27/10x + 11/10 = 0
(x - -1/2)(x - -11/5) = 0
x - -1/2 = 0  or  x - -11/5 = 0
x = -1/2
x = -11/5


Input: Solve quickly: 8x + 16 = 0

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


Input: Solve the equation 4x + 8/9 = 0

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


Input: Solve the equation 9x - 81/4 = 0

Output:
9x - 81/4 = 0
9x = 81/4
x = 81/4 / 9
x = 9/4


Input: Solve quickly: x^3 + 227/56x^2 - 1627/112x + 143/16 = 0

Output:
x^3 + 227/56x^2 - 1627/112x + 143/16 = 0
(x - -13/2)(x - 11/7)(x - 7/8) = 0
x - -13/2 = 0
x - 11/7 = 0
x - 7/8 = 0
x = -13/2
x = 11/7
x = 7/8


Input: Find the solution to x^3 - 143/36x^2 + 167/36x - 5/3 = 0

Output:
x^3 - 143/36x^2 + 167/36x - 5/3 = 0
(x - 1)(x - 20/9)(x - 3/4) = 0
x - 1 = 0
x - 20/9 = 0
x - 3/4 = 0
x = 1
x = 20/9
x = 3/4


Input:
Solve the equations:
1x + 10y = -163/9
2x + 7y = -131/9

Output:
1x + 10y = -163/9
2x + 7y = -131/9

Using elimination
2*(1x + 10y = -163/9)
1*(2x + 7y = -131/9)
2x + 20y = -326/9
2x + 7y = -131/9
Subtract equations
13y = -65/3
y = -65/3/13
y = -5/3

Substitute y
1x + 10(-5/3) = -163/9
1x = -13/9
x = -13/9/1
x = -13/9


Input: What value of x satisfies x^2 - 5x + 6 = 0

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


Input: Solve x^3 - 18x^2 - 19x  = 0

Output:
x^3 - 18x^2 - 19x  = 0
(x - 0)(x - 19)(x - -1) = 0
x - 0 = 0
x - 19 = 0
x - -1 = 0
x = 0
x = 19
x = -1


Input:
Solve simultaneously:
4x + 4y = 4
8x + 10y = 34/3

Output:
4x + 4y = 4
8x + 10y = 34/3

Using elimination
8*(4x + 4y = 4)
4*(8x + 10y = 34/3)
32x + 32y = 32
32x + 40y = 136/3
Subtract equations
-8y = -40/3
y = -40/3/-8
y = 5/3

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


Input:
Find x and y such that
6x + 2y = -102/35
4x + 6y = 282/35

Output:
6x + 2y = -102/35
4x + 6y = 282/35

Using elimination
4*(6x + 2y = -102/35)
6*(4x + 6y = 282/35)
24x + 8y = -408/35
24x + 36y = 1692/35
Subtract equations
-28y = -60
y = -60/-28
y = 15/7

Substitute y
6x + 2(15/7) = -102/35
6x = -36/5
x = -36/5/6
x = -6/5


Input:
Solve the equations:
1x + 4y = -38/3
7x + 9y = -19

Output:
1x + 4y = -38/3
7x + 9y = -19

Using elimination
7*(1x + 4y = -38/3)
1*(7x + 9y = -19)
7x + 28y = -266/3
7x + 9y = -19
Subtract equations
19y = -209/3
y = -209/3/19
y = -11/3

Substitute y
1x + 4(-11/3) = -38/3
1x = 2
x = 2/1
x = 2


Input: Solve x^3 - 2x^2 - 16x + 32 = 0

Output:
x^3 - 2x^2 - 16x + 32 = 0
(x - 4)(x - 2)(x - -4) = 0
x - 4 = 0
x - 2 = 0
x - -4 = 0
x = 4
x = 2
x = -4


Input: Determine x in x^3 + 217/40x^2 - 309/40x - 513/20 = 0

Output:
x^3 + 217/40x^2 - 309/40x - 513/20 = 0
(x - 19/8)(x - -9/5)(x - -6) = 0
x - 19/8 = 0
x - -9/5 = 0
x - -6 = 0
x = 19/8
x = -9/5
x = -6


Input: Compute the solution of x^3 - 9/4x^2 + 3/2x - 1/4 = 0

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


Input: What value of x satisfies 7x - 119/10 = 0

Output:
7x - 119/10 = 0
7x = 119/10
x = 119/10 / 7
x = 17/10


Input: Find x for x^2 - 43/30x - 4/15 = 0

Output:
x^2 - 43/30x - 4/15 = 0
(x - -1/6)(x - 8/5) = 0
x - -1/6 = 0  or  x - 8/5 = 0
x = -1/6
x = 8/5


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

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


Input:
Find x and y such that
6x + 9y = 207/5
3x + 7y = 86/5

Output:
6x + 9y = 207/5
3x + 7y = 86/5

Using elimination
3*(6x + 9y = 207/5)
6*(3x + 7y = 86/5)
18x + 27y = 621/5
18x + 42y = 516/5
Subtract equations
-15y = 21
y = 21/-15
y = -7/5

Substitute y
6x + 9(-7/5) = 207/5
6x = 54
x = 54/6
x = 9


Input: What value of x satisfies x^3 + 121/20x^2 + 5x - 5/4 = 0

Output:
x^3 + 121/20x^2 + 5x - 5/4 = 0
(x - -5/4)(x - 1/5)(x - -5) = 0
x - -5/4 = 0
x - 1/5 = 0
x - -5 = 0
x = -5/4
x = 1/5
x = -5


Input: Find x for 10x - 20 = 0

Output:
10x - 20 = 0
10x = 20
x = 20 / 10
x = 2


Input: Find x for 7x + 119/9 = 0

Output:
7x + 119/9 = 0
7x = -119/9
x = -119/9 / 7
x = -17/9


Input: Find x for x^3 - 233/20x^2 - 2163/40x + 459/8 = 0

Output:
x^3 - 233/20x^2 - 2163/40x + 459/8 = 0
(x - 15)(x - 9/10)(x - -17/4) = 0
x - 15 = 0
x - 9/10 = 0
x - -17/4 = 0
x = 15
x = 9/10
x = -17/4


Input: Compute the solution of 8x + 19 = 0

Output:
8x + 19 = 0
8x = -19
x = -19 / 8
x = -19/8


Input: Find the solution to x^3 - 37/14x^2 - 27/7x + 117/14 = 0

Output:
x^3 - 37/14x^2 - 27/7x + 117/14 = 0
(x - 3/2)(x - 3)(x - -13/7) = 0
x - 3/2 = 0
x - 3 = 0
x - -13/7 = 0
x = 3/2
x = 3
x = -13/7


Input: Solve the equation 8x - 112/3 = 0

Output:
8x - 112/3 = 0
8x = 112/3
x = 112/3 / 8
x = 14/3


Input:
Solve the system:
6x + 10y = -19/4
1x + 5y = -3/8

Output:
6x + 10y = -19/4
1x + 5y = -3/8

Using elimination
1*(6x + 10y = -19/4)
6*(1x + 5y = -3/8)
6x + 10y = -19/4
6x + 30y = -9/4
Subtract equations
-20y = -5/2
y = -5/2/-20
y = 1/8

Substitute y
6x + 10(1/8) = -19/4
6x = -6
x = -6/6
x = -1


Input: Find x in x^3 + 10/9x^2 - 101/27x + 88/81 = 0

Output:
x^3 + 10/9x^2 - 101/27x + 88/81 = 0
(x - 1/3)(x - -8/3)(x - 11/9) = 0
x - 1/3 = 0
x - -8/3 = 0
x - 11/9 = 0
x = 1/3
x = -8/3
x = 11/9


Input: Solve x^2 - 98/9x + 80/9 = 0

Output:
x^2 - 98/9x + 80/9 = 0
(x - 10)(x - 8/9) = 0
x - 10 = 0  or  x - 8/9 = 0
x = 10
x = 8/9


Input:
Solve simultaneously:
6x + 2y = 97
9x + 4y = 149

Output:
6x + 2y = 97
9x + 4y = 149

Using elimination
9*(6x + 2y = 97)
6*(9x + 4y = 149)
54x + 18y = 873
54x + 24y = 894
Subtract equations
-6y = -21
y = -21/-6
y = 7/2

Substitute y
6x + 2(7/2) = 97
6x = 90
x = 90/6
x = 15


Input: Compute the solution of x^2 - 104/5x + 252/5 = 0

Output:
x^2 - 104/5x + 252/5 = 0
(x - 14/5)(x - 18) = 0
x - 14/5 = 0  or  x - 18 = 0
x = 14/5
x = 18


Input: Find the solution to x^2 + 45/14x - 81/14 = 0

Output:
x^2 + 45/14x - 81/14 = 0
(x - 9/7)(x - -9/2) = 0
x - 9/7 = 0  or  x - -9/2 = 0
x = 9/7
x = -9/2


Input: Find x for 4x - 32 = 0

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


Input: Solve x^2 - 63/40x - 11/8 = 0

Output:
x^2 - 63/40x - 11/8 = 0
(x - 11/5)(x - -5/8) = 0
x - 11/5 = 0  or  x - -5/8 = 0
x = 11/5
x = -5/8


Input: What value of x satisfies 5x - 35/9 = 0

Output:
5x - 35/9 = 0
5x = 35/9
x = 35/9 / 5
x = 7/9


Input:
Find x and y such that
6x + 3y = -69/2
9x + 1y = -51/2

Output:
6x + 3y = -69/2
9x + 1y = -51/2

Using elimination
9*(6x + 3y = -69/2)
6*(9x + 1y = -51/2)
54x + 27y = -621/2
54x + 6y = -153
Subtract equations
21y = -315/2
y = -315/2/21
y = -15/2

Substitute y
6x + 3(-15/2) = -69/2
6x = -12
x = -12/6
x = -2


Input: Find the solution to x^3 - 143/24x^2 + 31/3x - 35/8 = 0

Output:
x^3 - 143/24x^2 + 31/3x - 35/8 = 0
(x - 7/3)(x - 3)(x - 5/8) = 0
x - 7/3 = 0
x - 3 = 0
x - 5/8 = 0
x = 7/3
x = 3
x = 5/8


Input: What value of x satisfies 6x + 32/3 = 0

Output:
6x + 32/3 = 0
6x = -32/3
x = -32/3 / 6
x = -16/9


Input:
Solve the equations:
7x + 4y = -101/10
7x + 8y = -237/10

Output:
7x + 4y = -101/10
7x + 8y = -237/10

Using elimination
7*(7x + 4y = -101/10)
7*(7x + 8y = -237/10)
49x + 28y = -707/10
49x + 56y = -1659/10
Subtract equations
-28y = 476/5
y = 476/5/-28
y = -17/5

Substitute y
7x + 4(-17/5) = -101/10
7x = 7/2
x = 7/2/7
x = 1/2


Input: Find x in x^3 - 13/15x^2 - 674/15x - 1456/15 = 0

Output:
x^3 - 13/15x^2 - 674/15x - 1456/15 = 0
(x - 8)(x - -14/5)(x - -13/3) = 0
x - 8 = 0
x - -14/5 = 0
x - -13/3 = 0
x = 8
x = -14/5
x = -13/3


Input:
Solve simultaneously:
1x + 6y = 187/15
1x + 10y = 71/3

Output:
1x + 6y = 187/15
1x + 10y = 71/3

Using elimination
1*(1x + 6y = 187/15)
1*(1x + 10y = 71/3)
1x + 6y = 187/15
1x + 10y = 71/3
Subtract equations
-4y = -56/5
y = -56/5/-4
y = 14/5

Substitute y
1x + 6(14/5) = 187/15
1x = -13/3
x = -13/3/1
x = -13/3


Input: Find the solution to x^2 + 18/7x - 85/7 = 0

Output:
x^2 + 18/7x - 85/7 = 0
(x - -5)(x - 17/7) = 0
x - -5 = 0  or  x - 17/7 = 0
x = -5
x = 17/7


Input: Find x for 5x + 55/2 = 0

Output:
5x + 55/2 = 0
5x = -55/2
x = -55/2 / 5
x = -11/2


Input: Solve the equation 5x + 80/3 = 0

Output:
5x + 80/3 = 0
5x = -80/3
x = -80/3 / 5
x = -16/3


Input: Determine x in x^3 + 669/40x^2 + 2489/40x + 663/10 = 0

Output:
x^3 + 669/40x^2 + 2489/40x + 663/10 = 0
(x - -17/8)(x - -13/5)(x - -12) = 0
x - -17/8 = 0
x - -13/5 = 0
x - -12 = 0
x = -17/8
x = -13/5
x = -12


Input: Solve 6x - 114/7 = 0

Output:
6x - 114/7 = 0
6x = 114/7
x = 114/7 / 6
x = 19/7


Input:
Solve the equations:
9x + 7y = 58/5
3x + 8y = 127/5

Output:
9x + 7y = 58/5
3x + 8y = 127/5

Using elimination
3*(9x + 7y = 58/5)
9*(3x + 8y = 127/5)
27x + 21y = 174/5
27x + 72y = 1143/5
Subtract equations
-51y = -969/5
y = -969/5/-51
y = 19/5

Substitute y
9x + 7(19/5) = 58/5
9x = -15
x = -15/9
x = -5/3


Input: Compute the solution of x^2 - 19/5x - 4/5 = 0

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


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

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


Input: Solve x^3 + 116/15x^2 + 239/15x + 26/5 = 0

Output:
x^3 + 116/15x^2 + 239/15x + 26/5 = 0
(x - -13/3)(x - -2/5)(x - -3) = 0
x - -13/3 = 0
x - -2/5 = 0
x - -3 = 0
x = -13/3
x = -2/5
x = -3


Input: Solve quickly: x^2 - 12/5x - 9/5 = 0

Output:
x^2 - 12/5x - 9/5 = 0
(x - 3)(x - -3/5) = 0
x - 3 = 0  or  x - -3/5 = 0
x = 3
x = -3/5


Input: Find x for x^3 - 101/6x^2 + 43x + 760/3 = 0

Output:
x^3 - 101/6x^2 + 43x + 760/3 = 0
(x - 19/2)(x - -8/3)(x - 10) = 0
x - 19/2 = 0
x - -8/3 = 0
x - 10 = 0
x = 19/2
x = -8/3
x = 10


Input: Solve quickly: x^3 + 5/3x^2 - 17x - 39 = 0

Output:
x^3 + 5/3x^2 - 17x - 39 = 0
(x - -3)(x - -3)(x - 13/3) = 0
x - -3 = 0
x - -3 = 0
x - 13/3 = 0
x = -3
x = -3
x = 13/3


Input: Compute the solution of 5x + 75/7 = 0

Output:
5x + 75/7 = 0
5x = -75/7
x = -75/7 / 5
x = -15/7


Input:
Solve the system:
6x + 1y = -20
5x + 4y = -23

Output:
6x + 1y = -20
5x + 4y = -23

Using elimination
5*(6x + 1y = -20)
6*(5x + 4y = -23)
30x + 5y = -100
30x + 24y = -138
Subtract equations
-19y = 38
y = 38/-19
y = -2

Substitute y
6x + 1(-2) = -20
6x = -18
x = -18/6
x = -3


Input:
Solve the system:
8x + 5y = 200/3
8x + 3y = 64

Output:
8x + 5y = 200/3
8x + 3y = 64

Using elimination
8*(8x + 5y = 200/3)
8*(8x + 3y = 64)
64x + 40y = 1600/3
64x + 24y = 512
Subtract equations
16y = 64/3
y = 64/3/16
y = 4/3

Substitute y
8x + 5(4/3) = 200/3
8x = 60
x = 60/8
x = 15/2


Input: Find x for x^3 - 143/70x^2 - 491/50x + 418/35 = 0

Output:
x^3 - 143/70x^2 - 491/50x + 418/35 = 0
(x - -20/7)(x - 19/5)(x - 11/10) = 0
x - -20/7 = 0
x - 19/5 = 0
x - 11/10 = 0
x = -20/7
x = 19/5
x = 11/10


Input: Find x in x^3 - 14/3x^2 - 139/4x - 153/4 = 0

Output:
x^3 - 14/3x^2 - 139/4x - 153/4 = 0
(x - 9)(x - -17/6)(x - -3/2) = 0
x - 9 = 0
x - -17/6 = 0
x - -3/2 = 0
x = 9
x = -17/6
x = -3/2


Input: Determine x in 5x - 65/3 = 0

Output:
5x - 65/3 = 0
5x = 65/3
x = 65/3 / 5
x = 13/3


Input:
Solve simultaneously:
1x + 7y = -122/35
6x + 7y = 3/35

Output:
1x + 7y = -122/35
6x + 7y = 3/35

Using elimination
6*(1x + 7y = -122/35)
1*(6x + 7y = 3/35)
6x + 42y = -732/35
6x + 7y = 3/35
Subtract equations
35y = -21
y = -21/35
y = -3/5

Substitute y
1x + 7(-3/5) = -122/35
1x = 5/7
x = 5/7/1
x = 5/7


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

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


Input:
Find x and y such that
4x + 9y = -33/10
1x + 6y = 81/20

Output:
4x + 9y = -33/10
1x + 6y = 81/20

Using elimination
1*(4x + 9y = -33/10)
4*(1x + 6y = 81/20)
4x + 9y = -33/10
4x + 24y = 81/5
Subtract equations
-15y = -39/2
y = -39/2/-15
y = 13/10

Substitute y
4x + 9(13/10) = -33/10
4x = -15
x = -15/4
x = -15/4


Input: Compute the solution of x^2 + 131/56x + 15/14 = 0

Output:
x^2 + 131/56x + 15/14 = 0
(x - -12/7)(x - -5/8) = 0
x - -12/7 = 0  or  x - -5/8 = 0
x = -12/7
x = -5/8


Input:
Solve the equations:
10x + 8y = -208/35
8x + 3y = -71/70

Output:
10x + 8y = -208/35
8x + 3y = -71/70

Using elimination
8*(10x + 8y = -208/35)
10*(8x + 3y = -71/70)
80x + 64y = -1664/35
80x + 30y = -71/7
Subtract equations
34y = -187/5
y = -187/5/34
y = -11/10

Substitute y
10x + 8(-11/10) = -208/35
10x = 20/7
x = 20/7/10
x = 2/7


Input:
Solve the equations:
9x + 8y = 37
6x + 9y = 21

Output:
9x + 8y = 37
6x + 9y = 21

Using elimination
6*(9x + 8y = 37)
9*(6x + 9y = 21)
54x + 48y = 222
54x + 81y = 189
Subtract equations
-33y = 33
y = 33/-33
y = -1

Substitute y
9x + 8(-1) = 37
9x = 45
x = 45/9
x = 5


Input:
Find x and y such that
1x + 10y = -289/7
4x + 6y = -204/7

Output:
1x + 10y = -289/7
4x + 6y = -204/7

Using elimination
4*(1x + 10y = -289/7)
1*(4x + 6y = -204/7)
4x + 40y = -1156/7
4x + 6y = -204/7
Subtract equations
34y = -136
y = -136/34
y = -4

Substitute y
1x + 10(-4) = -289/7
1x = -9/7
x = -9/7/1
x = -9/7


Input:
Solve the system:
2x + 5y = -20/9
2x + 10y = -20/9

Output:
2x + 5y = -20/9
2x + 10y = -20/9

Using elimination
2*(2x + 5y = -20/9)
2*(2x + 10y = -20/9)
4x + 10y = -40/9
4x + 20y = -40/9
Subtract equations
-10y = 0
y = 0/-10
y = 0

Substitute y
2x + 5(0) = -20/9
2x = -20/9
x = -20/9/2
x = -10/9


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

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


Input:
Solve the equations:
8x + 4y = 176/45
8x + 10y = -154/45

Output:
8x + 4y = 176/45
8x + 10y = -154/45

Using elimination
8*(8x + 4y = 176/45)
8*(8x + 10y = -154/45)
64x + 32y = 1408/45
64x + 80y = -1232/45
Subtract equations
-48y = 176/3
y = 176/3/-48
y = -11/9

Substitute y
8x + 4(-11/9) = 176/45
8x = 44/5
x = 44/5/8
x = 11/10


Input: Find x for 10x - 20/9 = 0

Output:
10x - 20/9 = 0
10x = 20/9
x = 20/9 / 10
x = 2/9


Input: Solve the equation x^3 - 46/3x^2 + 17x + 520/3 = 0

Output:
x^3 - 46/3x^2 + 17x + 520/3 = 0
(x - -8/3)(x - 13)(x - 5) = 0
x - -8/3 = 0
x - 13 = 0
x - 5 = 0
x = -8/3
x = 13
x = 5


Input: Solve the equation x^3 + 297/20x^2 - 51/20x - 2023/10 = 0

Output:
x^3 + 297/20x^2 - 51/20x - 2023/10 = 0
(x - 17/5)(x - -14)(x - -17/4) = 0
x - 17/5 = 0
x - -14 = 0
x - -17/4 = 0
x = 17/5
x = -14
x = -17/4


Input: What value of x satisfies x^3 - 814/45x^2 + 17x + 1156/45 = 0

Output:
x^3 - 814/45x^2 + 17x + 1156/45 = 0
(x - 17/9)(x - -4/5)(x - 17) = 0
x - 17/9 = 0
x - -4/5 = 0
x - 17 = 0
x = 17/9
x = -4/5
x = 17


Input: Solve quickly: x^2 + 57/14x + 55/14 = 0

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


Input:
Solve simultaneously:
6x + 5y = 74/3
10x + 8y = 122/3

Output:
6x + 5y = 74/3
10x + 8y = 122/3

Using elimination
10*(6x + 5y = 74/3)
6*(10x + 8y = 122/3)
60x + 50y = 740/3
60x + 48y = 244
Subtract equations
2y = 8/3
y = 8/3/2
y = 4/3

Substitute y
6x + 5(4/3) = 74/3
6x = 18
x = 18/6
x = 3


Input:
Solve simultaneously:
8x + 10y = 54
2x + 3y = 16

Output:
8x + 10y = 54
2x + 3y = 16

Using elimination
2*(8x + 10y = 54)
8*(2x + 3y = 16)
16x + 20y = 108
16x + 24y = 128
Subtract equations
-4y = -20
y = -20/-4
y = 5

Substitute y
8x + 10(5) = 54
8x = 4
x = 4/8
x = 1/2


Input: Find x for x^3 - 181/12x^2 - 311/6x - 12 = 0

Output:
x^3 - 181/12x^2 - 311/6x - 12 = 0
(x - -8/3)(x - -1/4)(x - 18) = 0
x - -8/3 = 0
x - -1/4 = 0
x - 18 = 0
x = -8/3
x = -1/4
x = 18


Input:
Find x and y such that
7x + 5y = -319/10
10x + 8y = -49

Output:
7x + 5y = -319/10
10x + 8y = -49

Using elimination
10*(7x + 5y = -319/10)
7*(10x + 8y = -49)
70x + 50y = -319
70x + 56y = -343
Subtract equations
-6y = 24
y = 24/-6
y = -4

Substitute y
7x + 5(-4) = -319/10
7x = -119/10
x = -119/10/7
x = -17/10


Input: Determine x in 5x + 75/8 = 0

Output:
5x + 75/8 = 0
5x = -75/8
x = -75/8 / 5
x = -15/8


Input:
Solve simultaneously:
4x + 1y = -57/4
7x + 8y = -39

Output:
4x + 1y = -57/4
7x + 8y = -39

Using elimination
7*(4x + 1y = -57/4)
4*(7x + 8y = -39)
28x + 7y = -399/4
28x + 32y = -156
Subtract equations
-25y = 225/4
y = 225/4/-25
y = -9/4

Substitute y
4x + 1(-9/4) = -57/4
4x = -12
x = -12/4
x = -3


Input: Solve quickly: x^3 + 65/8x^2 - 171/4x + 45 = 0

Output:
x^3 + 65/8x^2 - 171/4x + 45 = 0
(x - -12)(x - 2)(x - 15/8) = 0
x - -12 = 0
x - 2 = 0
x - 15/8 = 0
x = -12
x = 2
x = 15/8


Input: Find x in x^3 + 61/10x^2 - 1/5x - 57/2 = 0

Output:
x^3 + 61/10x^2 - 1/5x - 57/2 = 0
(x - -5)(x - 19/10)(x - -3) = 0
x - -5 = 0
x - 19/10 = 0
x - -3 = 0
x = -5
x = 19/10
x = -3


Input: Find x in x^2 - 39/28x + 5/28 = 0

Output:
x^2 - 39/28x + 5/28 = 0
(x - 1/7)(x - 5/4) = 0
x - 1/7 = 0  or  x - 5/4 = 0
x = 1/7
x = 5/4


Input: Solve x^3 - 133/24x^2 + 6583/648x - 665/108 = 0

Output:
x^3 - 133/24x^2 + 6583/648x - 665/108 = 0
(x - 15/8)(x - 19/9)(x - 14/9) = 0
x - 15/8 = 0
x - 19/9 = 0
x - 14/9 = 0
x = 15/8
x = 19/9
x = 14/9


Input: Find the solution to 7x + 1 = 0

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


Input: Compute the solution of 4x + 38 = 0

Output:
4x + 38 = 0
4x = -38
x = -38 / 4
x = -19/2


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

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


Input: What value of x satisfies x^3 + 682/105x^2 + 397/35x + 374/105 = 0

Output:
x^3 + 682/105x^2 + 397/35x + 374/105 = 0
(x - -11/3)(x - -17/7)(x - -2/5) = 0
x - -11/3 = 0
x - -17/7 = 0
x - -2/5 = 0
x = -11/3
x = -17/7
x = -2/5


Input: What value of x satisfies x^2 + 41/14x + 15/14 = 0

Output:
x^2 + 41/14x + 15/14 = 0
(x - -3/7)(x - -5/2) = 0
x - -3/7 = 0  or  x - -5/2 = 0
x = -3/7
x = -5/2


Input:
Solve the system:
4x + 5y = -15/2
5x + 1y = -69/4

Output:
4x + 5y = -15/2
5x + 1y = -69/4

Using elimination
5*(4x + 5y = -15/2)
4*(5x + 1y = -69/4)
20x + 25y = -75/2
20x + 4y = -69
Subtract equations
21y = 63/2
y = 63/2/21
y = 3/2

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


Input: Find the solution to x^3 + 109/18x^2 - 457/18x + 10 = 0

Output:
x^3 + 109/18x^2 - 457/18x + 10 = 0
(x - 5/2)(x - 4/9)(x - -9) = 0
x - 5/2 = 0
x - 4/9 = 0
x - -9 = 0
x = 5/2
x = 4/9
x = -9


Input: Find x for 5x + 10 = 0

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


Input: What value of x satisfies 10x + 2 = 0

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


Input: Solve quickly: x^2 - 1/3x - 80/3 = 0

Output:
x^2 - 1/3x - 80/3 = 0
(x - 16/3)(x - -5) = 0
x - 16/3 = 0  or  x - -5 = 0
x = 16/3
x = -5


Input: Find x in 3x + 27/4 = 0

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


Input: Find x for x^3 + 29/12x^2 - 55/4x - 91/6 = 0

Output:
x^3 + 29/12x^2 - 55/4x - 91/6 = 0
(x - 13/4)(x - -14/3)(x - -1) = 0
x - 13/4 = 0
x - -14/3 = 0
x - -1 = 0
x = 13/4
x = -14/3
x = -1


Input: Find x in x^3 + 55/3x^2 + 637/12x - 845/4 = 0

Output:
x^3 + 55/3x^2 + 637/12x - 845/4 = 0
(x - -13)(x - -15/2)(x - 13/6) = 0
x - -13 = 0
x - -15/2 = 0
x - 13/6 = 0
x = -13
x = -15/2
x = 13/6


Input: Find x in x^3 + 69/8x^2 + 727/32x + 1197/64 = 0

Output:
x^3 + 69/8x^2 + 727/32x + 1197/64 = 0
(x - -19/8)(x - -7/4)(x - -9/2) = 0
x - -19/8 = 0
x - -7/4 = 0
x - -9/2 = 0
x = -19/8
x = -7/4
x = -9/2


Input: Solve quickly: x^3 + 91/72x^2 - 161/288x + 13/288 = 0

Output:
x^3 + 91/72x^2 - 161/288x + 13/288 = 0
(x - -13/8)(x - 1/4)(x - 1/9) = 0
x - -13/8 = 0
x - 1/4 = 0
x - 1/9 = 0
x = -13/8
x = 1/4
x = 1/9


Input:
Find x and y such that
7x + 5y = 32
10x + 4y = 254/7

Output:
7x + 5y = 32
10x + 4y = 254/7

Using elimination
10*(7x + 5y = 32)
7*(10x + 4y = 254/7)
70x + 50y = 320
70x + 28y = 254
Subtract equations
22y = 66
y = 66/22
y = 3

Substitute y
7x + 5(3) = 32
7x = 17
x = 17/7
x = 17/7


Input: Find x in x^2 - 183/70x + 19/14 = 0

Output:
x^2 - 183/70x + 19/14 = 0
(x - 5/7)(x - 19/10) = 0
x - 5/7 = 0  or  x - 19/10 = 0
x = 5/7
x = 19/10


Input: Find x in x^3 - 38/3x^2 - 409/12x - 55/4 = 0

Output:
x^3 - 38/3x^2 - 409/12x - 55/4 = 0
(x - 15)(x - -11/6)(x - -1/2) = 0
x - 15 = 0
x - -11/6 = 0
x - -1/2 = 0
x = 15
x = -11/6
x = -1/2


Input: Determine x in 9x + 45 = 0

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


Input:
Solve the system:
3x + 8y = -749/40
4x + 4y = -103/10

Output:
3x + 8y = -749/40
4x + 4y = -103/10

Using elimination
4*(3x + 8y = -749/40)
3*(4x + 4y = -103/10)
12x + 32y = -749/10
12x + 12y = -309/10
Subtract equations
20y = -44
y = -44/20
y = -11/5

Substitute y
3x + 8(-11/5) = -749/40
3x = -9/8
x = -9/8/3
x = -3/8


Input: Find x for x^2 - 25/18x - 133/18 = 0

Output:
x^2 - 25/18x - 133/18 = 0
(x - -19/9)(x - 7/2) = 0
x - -19/9 = 0  or  x - 7/2 = 0
x = -19/9
x = 7/2


Input:
Solve simultaneously:
8x + 4y = 10/3
8x + 8y = 32/3

Output:
8x + 4y = 10/3
8x + 8y = 32/3

Using elimination
8*(8x + 4y = 10/3)
8*(8x + 8y = 32/3)
64x + 32y = 80/3
64x + 64y = 256/3
Subtract equations
-32y = -176/3
y = -176/3/-32
y = 11/6

Substitute y
8x + 4(11/6) = 10/3
8x = -4
x = -4/8
x = -1/2


Input: What value of x satisfies x^3 + 10/63x^2 - 17/189x - 2/189 = 0

Output:
x^3 + 10/63x^2 - 17/189x - 2/189 = 0
(x - -1/3)(x - -1/9)(x - 2/7) = 0
x - -1/3 = 0
x - -1/9 = 0
x - 2/7 = 0
x = -1/3
x = -1/9
x = 2/7


Input: Find x for x^3 - 152/21x^2 + 31/3x + 30/7 = 0

Output:
x^3 - 152/21x^2 + 31/3x + 30/7 = 0
(x - 5)(x - -1/3)(x - 18/7) = 0
x - 5 = 0
x - -1/3 = 0
x - 18/7 = 0
x = 5
x = -1/3
x = 18/7


Input:
Find x and y such that
7x + 4y = -74/5
6x + 3y = -867/70

Output:
7x + 4y = -74/5
6x + 3y = -867/70

Using elimination
6*(7x + 4y = -74/5)
7*(6x + 3y = -867/70)
42x + 24y = -444/5
42x + 21y = -867/10
Subtract equations
3y = -21/10
y = -21/10/3
y = -7/10

Substitute y
7x + 4(-7/10) = -74/5
7x = -12
x = -12/7
x = -12/7


Input:
Solve simultaneously:
7x + 4y = -129/5
8x + 3y = -138/5

Output:
7x + 4y = -129/5
8x + 3y = -138/5

Using elimination
8*(7x + 4y = -129/5)
7*(8x + 3y = -138/5)
56x + 32y = -1032/5
56x + 21y = -966/5
Subtract equations
11y = -66/5
y = -66/5/11
y = -6/5

Substitute y
7x + 4(-6/5) = -129/5
7x = -21
x = -21/7
x = -3


Input: Determine x in x^3 - 227/72x^2 + 515/288x + 7/6 = 0

Output:
x^3 - 227/72x^2 + 515/288x + 7/6 = 0
(x - 7/4)(x - -3/8)(x - 16/9) = 0
x - 7/4 = 0
x - -3/8 = 0
x - 16/9 = 0
x = 7/4
x = -3/8
x = 16/9


Input: Find the solution to 1x - 14/9 = 0

Output:
1x - 14/9 = 0
1x = 14/9
x = 14/9 / 1
x = 14/9


Input: Determine x in x^3 - 129/8x^2 - 599/8x - 105/2 = 0

Output:
x^3 - 129/8x^2 - 599/8x - 105/2 = 0
(x - -7/8)(x - -3)(x - 20) = 0
x - -7/8 = 0
x - -3 = 0
x - 20 = 0
x = -7/8
x = -3
x = 20


Input:
Find x and y such that
1x + 8y = -50
3x + 5y = -53/2

Output:
1x + 8y = -50
3x + 5y = -53/2

Using elimination
3*(1x + 8y = -50)
1*(3x + 5y = -53/2)
3x + 24y = -150
3x + 5y = -53/2
Subtract equations
19y = -247/2
y = -247/2/19
y = -13/2

Substitute y
1x + 8(-13/2) = -50
1x = 2
x = 2/1
x = 2


Input: Solve x^3 + 61/14x^2 + 25/14x - 50/7 = 0

Output:
x^3 + 61/14x^2 + 25/14x - 50/7 = 0
(x - 1)(x - -20/7)(x - -5/2) = 0
x - 1 = 0
x - -20/7 = 0
x - -5/2 = 0
x = 1
x = -20/7
x = -5/2


Input: Find x in 9x + 21 = 0

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


Input:
Solve the system:
9x + 6y = -5
5x + 6y = -61/9

Output:
9x + 6y = -5
5x + 6y = -61/9

Using elimination
5*(9x + 6y = -5)
9*(5x + 6y = -61/9)
45x + 30y = -25
45x + 54y = -61
Subtract equations
-24y = 36
y = 36/-24
y = -3/2

Substitute y
9x + 6(-3/2) = -5
9x = 4
x = 4/9
x = 4/9


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

Output:
x^2 - 21/10x + 11/10 = 0
(x - 11/10)(x - 1) = 0
x - 11/10 = 0  or  x - 1 = 0
x = 11/10
x = 1


Input: Find x in 10x + 160 = 0

Output:
10x + 160 = 0
10x = -160
x = -160 / 10
x = -16


Input: Solve the equation x^3 + 115/42x^2 - 401/42x - 51/7 = 0

Output:
x^3 + 115/42x^2 - 401/42x - 51/7 = 0
(x - 17/7)(x - -9/2)(x - -2/3) = 0
x - 17/7 = 0
x - -9/2 = 0
x - -2/3 = 0
x = 17/7
x = -9/2
x = -2/3


Input: Determine x in x^3 - 176/21x^2 + 1459/63x - 190/9 = 0

Output:
x^3 - 176/21x^2 + 1459/63x - 190/9 = 0
(x - 7/3)(x - 10/3)(x - 19/7) = 0
x - 7/3 = 0
x - 10/3 = 0
x - 19/7 = 0
x = 7/3
x = 10/3
x = 19/7


Input:
Find x and y such that
4x + 4y = 20
1x + 3y = 7

Output:
4x + 4y = 20
1x + 3y = 7

Using elimination
1*(4x + 4y = 20)
4*(1x + 3y = 7)
4x + 4y = 20
4x + 12y = 28
Subtract equations
-8y = -8
y = -8/-8
y = 1

Substitute y
4x + 4(1) = 20
4x = 16
x = 16/4
x = 4