Input: Find x in x^3 - 7/6x^2 - 493/18x + 578/9 = 0

Output:
x^3 - 7/6x^2 - 493/18x + 578/9 = 0
(x - -17/3)(x - 17/6)(x - 4) = 0
x - -17/3 = 0
x - 17/6 = 0
x - 4 = 0
x = -17/3
x = 17/6
x = 4


Input: Solve quickly: x^3 + 295/36x^2 - 1/4x - 130/9 = 0

Output:
x^3 + 295/36x^2 - 1/4x - 130/9 = 0
(x - 5/4)(x - -13/9)(x - -8) = 0
x - 5/4 = 0
x - -13/9 = 0
x - -8 = 0
x = 5/4
x = -13/9
x = -8


Input: Find x in x^3 + 1/2x^2 - 27x + 36 = 0

Output:
x^3 + 1/2x^2 - 27x + 36 = 0
(x - -6)(x - 3/2)(x - 4) = 0
x - -6 = 0
x - 3/2 = 0
x - 4 = 0
x = -6
x = 3/2
x = 4


Input: Determine x in 6x + 96 = 0

Output:
6x + 96 = 0
6x = -96
x = -96 / 6
x = -16


Input: Solve the equation x^3 + 11/4x^2 + 43/18x + 2/3 = 0

Output:
x^3 + 11/4x^2 + 43/18x + 2/3 = 0
(x - -2/3)(x - -4/3)(x - -3/4) = 0
x - -2/3 = 0
x - -4/3 = 0
x - -3/4 = 0
x = -2/3
x = -4/3
x = -3/4


Input: Solve the equation 1x - 5/2 = 0

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


Input: Compute the solution of x^3 - 1252/105x^2 + 1581/35x - 1156/21 = 0

Output:
x^3 - 1252/105x^2 + 1581/35x - 1156/21 = 0
(x - 17/3)(x - 17/5)(x - 20/7) = 0
x - 17/3 = 0
x - 17/5 = 0
x - 20/7 = 0
x = 17/3
x = 17/5
x = 20/7


Input: Compute the solution of x^2 + 7/4x - 57/4 = 0

Output:
x^2 + 7/4x - 57/4 = 0
(x - -19/4)(x - 3) = 0
x - -19/4 = 0  or  x - 3 = 0
x = -19/4
x = 3


Input: Find x for 6x + 30 = 0

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


Input: Solve quickly: 5x + 80/7 = 0

Output:
5x + 80/7 = 0
5x = -80/7
x = -80/7 / 5
x = -16/7


Input: Find the solution to x^3 - 65/6x^2 - 27x - 91/6 = 0

Output:
x^3 - 65/6x^2 - 27x - 91/6 = 0
(x - 13)(x - -1)(x - -7/6) = 0
x - 13 = 0
x - -1 = 0
x - -7/6 = 0
x = 13
x = -1
x = -7/6


Input: Determine x in x^3 - 167/15x^2 + 122/5x + 16/3 = 0

Output:
x^3 - 167/15x^2 + 122/5x + 16/3 = 0
(x - 10/3)(x - 8)(x - -1/5) = 0
x - 10/3 = 0
x - 8 = 0
x - -1/5 = 0
x = 10/3
x = 8
x = -1/5


Input: What value of x satisfies 1x + 4/9 = 0

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


Input: Solve quickly: x^2 - 9/8x + 1/8 = 0

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


Input: Solve x^3 + 67/72x^2 + 61/216x + 1/36 = 0

Output:
x^3 + 67/72x^2 + 61/216x + 1/36 = 0
(x - -3/8)(x - -1/3)(x - -2/9) = 0
x - -3/8 = 0
x - -1/3 = 0
x - -2/9 = 0
x = -3/8
x = -1/3
x = -2/9


Input: Find x for x^3 + 7/2x^2 - 9/2x  = 0

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


Input:
Solve the equations:
10x + 4y = -2/7
8x + 7y = 183/14

Output:
10x + 4y = -2/7
8x + 7y = 183/14

Using elimination
8*(10x + 4y = -2/7)
10*(8x + 7y = 183/14)
80x + 32y = -16/7
80x + 70y = 915/7
Subtract equations
-38y = -133
y = -133/-38
y = 7/2

Substitute y
10x + 4(7/2) = -2/7
10x = -100/7
x = -100/7/10
x = -10/7


Input:
Solve the equations:
9x + 6y = 3
7x + 1y = -4/3

Output:
9x + 6y = 3
7x + 1y = -4/3

Using elimination
7*(9x + 6y = 3)
9*(7x + 1y = -4/3)
63x + 42y = 21
63x + 9y = -12
Subtract equations
33y = 33
y = 33/33
y = 1

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


Input: Find x in x^2 - 209/30x + 361/30 = 0

Output:
x^2 - 209/30x + 361/30 = 0
(x - 19/6)(x - 19/5) = 0
x - 19/6 = 0  or  x - 19/5 = 0
x = 19/6
x = 19/5


Input: Find x in x^3 - 267/28x^2 - 1177/28x - 39 = 0

Output:
x^3 - 267/28x^2 - 1177/28x - 39 = 0
(x - -7/4)(x - 13)(x - -12/7) = 0
x - -7/4 = 0
x - 13 = 0
x - -12/7 = 0
x = -7/4
x = 13
x = -12/7


Input: Solve quickly: x^3 + 11/5x^2 - 137/25x + 57/25 = 0

Output:
x^3 + 11/5x^2 - 137/25x + 57/25 = 0
(x - 3/5)(x - 1)(x - -19/5) = 0
x - 3/5 = 0
x - 1 = 0
x - -19/5 = 0
x = 3/5
x = 1
x = -19/5


Input: Solve the equation x^2 - 17/8x - 77/16 = 0

Output:
x^2 - 17/8x - 77/16 = 0
(x - -11/8)(x - 7/2) = 0
x - -11/8 = 0  or  x - 7/2 = 0
x = -11/8
x = 7/2


Input: Determine x in x^2 + 217/10x + 34 = 0

Output:
x^2 + 217/10x + 34 = 0
(x - -20)(x - -17/10) = 0
x - -20 = 0  or  x - -17/10 = 0
x = -20
x = -17/10


Input:
Solve simultaneously:
2x + 8y = -1058/63
3x + 5y = -151/21

Output:
2x + 8y = -1058/63
3x + 5y = -151/21

Using elimination
3*(2x + 8y = -1058/63)
2*(3x + 5y = -151/21)
6x + 24y = -1058/21
6x + 10y = -302/21
Subtract equations
14y = -36
y = -36/14
y = -18/7

Substitute y
2x + 8(-18/7) = -1058/63
2x = 34/9
x = 34/9/2
x = 17/9


Input:
Find x and y such that
2x + 2y = -113/7
2x + 8y = -428/7

Output:
2x + 2y = -113/7
2x + 8y = -428/7

Using elimination
2*(2x + 2y = -113/7)
2*(2x + 8y = -428/7)
4x + 4y = -226/7
4x + 16y = -856/7
Subtract equations
-12y = 90
y = 90/-12
y = -15/2

Substitute y
2x + 2(-15/2) = -113/7
2x = -8/7
x = -8/7/2
x = -4/7


Input: Solve x^2 + 1/20x - 21/40 = 0

Output:
x^2 + 1/20x - 21/40 = 0
(x - 7/10)(x - -3/4) = 0
x - 7/10 = 0  or  x - -3/4 = 0
x = 7/10
x = -3/4


Input: Compute the solution of 10x - 95 = 0

Output:
10x - 95 = 0
10x = 95
x = 95 / 10
x = 19/2


Input:
Solve simultaneously:
3x + 9y = 213/8
5x + 4y = 119/2

Output:
3x + 9y = 213/8
5x + 4y = 119/2

Using elimination
5*(3x + 9y = 213/8)
3*(5x + 4y = 119/2)
15x + 45y = 1065/8
15x + 12y = 357/2
Subtract equations
33y = -363/8
y = -363/8/33
y = -11/8

Substitute y
3x + 9(-11/8) = 213/8
3x = 39
x = 39/3
x = 13


Input: Find the solution to 3x - 6 = 0

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


Input:
Solve the system:
1x + 4y = 31/3
7x + 2y = 113/3

Output:
1x + 4y = 31/3
7x + 2y = 113/3

Using elimination
7*(1x + 4y = 31/3)
1*(7x + 2y = 113/3)
7x + 28y = 217/3
7x + 2y = 113/3
Subtract equations
26y = 104/3
y = 104/3/26
y = 4/3

Substitute y
1x + 4(4/3) = 31/3
1x = 5
x = 5/1
x = 5


Input: Solve x^3 + 37/40x^2 - 29/5x - 221/32 = 0

Output:
x^3 + 37/40x^2 - 29/5x - 221/32 = 0
(x - -17/8)(x - 5/2)(x - -13/10) = 0
x - -17/8 = 0
x - 5/2 = 0
x - -13/10 = 0
x = -17/8
x = 5/2
x = -13/10


Input: Find x in 3x - 2 = 0

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


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

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


Input:
Solve the equations:
10x + 7y = -205/21
6x + 8y = 10/21

Output:
10x + 7y = -205/21
6x + 8y = 10/21

Using elimination
6*(10x + 7y = -205/21)
10*(6x + 8y = 10/21)
60x + 42y = -410/7
60x + 80y = 100/21
Subtract equations
-38y = -190/3
y = -190/3/-38
y = 5/3

Substitute y
10x + 7(5/3) = -205/21
10x = -150/7
x = -150/7/10
x = -15/7


Input: Find the solution to x^2 + 21/10x - 1 = 0

Output:
x^2 + 21/10x - 1 = 0
(x - 2/5)(x - -5/2) = 0
x - 2/5 = 0  or  x - -5/2 = 0
x = 2/5
x = -5/2


Input: Compute the solution of x^3 + 87/20x^2 - 67/40x - 63/4 = 0

Output:
x^3 + 87/20x^2 - 67/40x - 63/4 = 0
(x - -18/5)(x - -5/2)(x - 7/4) = 0
x - -18/5 = 0
x - -5/2 = 0
x - 7/4 = 0
x = -18/5
x = -5/2
x = 7/4


Input:
Solve simultaneously:
2x + 2y = 185/36
3x + 9y = 491/24

Output:
2x + 2y = 185/36
3x + 9y = 491/24

Using elimination
3*(2x + 2y = 185/36)
2*(3x + 9y = 491/24)
6x + 6y = 185/12
6x + 18y = 491/12
Subtract equations
-12y = -51/2
y = -51/2/-12
y = 17/8

Substitute y
2x + 2(17/8) = 185/36
2x = 8/9
x = 8/9/2
x = 4/9


Input: Compute the solution of x^3 + 527/180x^2 + 211/90x + 8/15 = 0

Output:
x^3 + 527/180x^2 + 211/90x + 8/15 = 0
(x - -2/5)(x - -16/9)(x - -3/4) = 0
x - -2/5 = 0
x - -16/9 = 0
x - -3/4 = 0
x = -2/5
x = -16/9
x = -3/4


Input: Find the solution to x^3 + 48/5x^2 + 333/20x + 27/4 = 0

Output:
x^3 + 48/5x^2 + 333/20x + 27/4 = 0
(x - -15/2)(x - -3/5)(x - -3/2) = 0
x - -15/2 = 0
x - -3/5 = 0
x - -3/2 = 0
x = -15/2
x = -3/5
x = -3/2


Input:
Find x and y such that
3x + 3y = -163/24
3x + 7y = -295/24

Output:
3x + 3y = -163/24
3x + 7y = -295/24

Using elimination
3*(3x + 3y = -163/24)
3*(3x + 7y = -295/24)
9x + 9y = -163/8
9x + 21y = -295/8
Subtract equations
-12y = 33/2
y = 33/2/-12
y = -11/8

Substitute y
3x + 3(-11/8) = -163/24
3x = -8/3
x = -8/3/3
x = -8/9


Input: What value of x satisfies x^2 + 31/4x - 45/4 = 0

Output:
x^2 + 31/4x - 45/4 = 0
(x - -9)(x - 5/4) = 0
x - -9 = 0  or  x - 5/4 = 0
x = -9
x = 5/4


Input:
Solve the equations:
3x + 5y = 13/2
8x + 10y = 77/3

Output:
3x + 5y = 13/2
8x + 10y = 77/3

Using elimination
8*(3x + 5y = 13/2)
3*(8x + 10y = 77/3)
24x + 40y = 52
24x + 30y = 77
Subtract equations
10y = -25
y = -25/10
y = -5/2

Substitute y
3x + 5(-5/2) = 13/2
3x = 19
x = 19/3
x = 19/3


Input: Compute the solution of x^3 - 167/360x^2 - 419/360x - 11/90 = 0

Output:
x^3 - 167/360x^2 - 419/360x - 11/90 = 0
(x - -4/5)(x - 11/8)(x - -1/9) = 0
x - -4/5 = 0
x - 11/8 = 0
x - -1/9 = 0
x = -4/5
x = 11/8
x = -1/9


Input:
Solve simultaneously:
10x + 4y = -44/7
9x + 10y = -174/7

Output:
10x + 4y = -44/7
9x + 10y = -174/7

Using elimination
9*(10x + 4y = -44/7)
10*(9x + 10y = -174/7)
90x + 36y = -396/7
90x + 100y = -1740/7
Subtract equations
-64y = 192
y = 192/-64
y = -3

Substitute y
10x + 4(-3) = -44/7
10x = 40/7
x = 40/7/10
x = 4/7


Input: What value of x satisfies 3x - 9/5 = 0

Output:
3x - 9/5 = 0
3x = 9/5
x = 9/5 / 3
x = 3/5


Input: Find x for x^3 - 193/18x^2 + 35/9x + 100/3 = 0

Output:
x^3 - 193/18x^2 + 35/9x + 100/3 = 0
(x - -3/2)(x - 20/9)(x - 10) = 0
x - -3/2 = 0
x - 20/9 = 0
x - 10 = 0
x = -3/2
x = 20/9
x = 10


Input: Find x in 10x + 190 = 0

Output:
10x + 190 = 0
10x = -190
x = -190 / 10
x = -19


Input: Compute the solution of x^2 - 19/5x + 18/5 = 0

Output:
x^2 - 19/5x + 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^2 + 28/3x - 55/3 = 0

Output:
x^2 + 28/3x - 55/3 = 0
(x - -11)(x - 5/3) = 0
x - -11 = 0  or  x - 5/3 = 0
x = -11
x = 5/3


Input: Find x for x^3 + 22/3x^2 + 40/3x  = 0

Output:
x^3 + 22/3x^2 + 40/3x  = 0
(x - -10/3)(x - -4)(x - 0) = 0
x - -10/3 = 0
x - -4 = 0
x - 0 = 0
x = -10/3
x = -4
x = 0


Input: Find x for 3x + 27/5 = 0

Output:
3x + 27/5 = 0
3x = -27/5
x = -27/5 / 3
x = -9/5


Input: Find x in x^2 + 5x + 56/9 = 0

Output:
x^2 + 5x + 56/9 = 0
(x - -8/3)(x - -7/3) = 0
x - -8/3 = 0  or  x - -7/3 = 0
x = -8/3
x = -7/3


Input: Determine x in 3x + 6 = 0

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


Input:
Solve the system:
10x + 3y = -231/2
3x + 4y = -30

Output:
10x + 3y = -231/2
3x + 4y = -30

Using elimination
3*(10x + 3y = -231/2)
10*(3x + 4y = -30)
30x + 9y = -693/2
30x + 40y = -300
Subtract equations
-31y = -93/2
y = -93/2/-31
y = 3/2

Substitute y
10x + 3(3/2) = -231/2
10x = -120
x = -120/10
x = -12


Input: Find x in 6x - 20/3 = 0

Output:
6x - 20/3 = 0
6x = 20/3
x = 20/3 / 6
x = 10/9


Input: Find x in x^2 - 53/2x + 130 = 0

Output:
x^2 - 53/2x + 130 = 0
(x - 20)(x - 13/2) = 0
x - 20 = 0  or  x - 13/2 = 0
x = 20
x = 13/2


Input:
Find x and y such that
1x + 9y = 7
4x + 4y = 52/3

Output:
1x + 9y = 7
4x + 4y = 52/3

Using elimination
4*(1x + 9y = 7)
1*(4x + 4y = 52/3)
4x + 36y = 28
4x + 4y = 52/3
Subtract equations
32y = 32/3
y = 32/3/32
y = 1/3

Substitute y
1x + 9(1/3) = 7
1x = 4
x = 4/1
x = 4


Input: What value of x satisfies 9x - 27/5 = 0

Output:
9x - 27/5 = 0
9x = 27/5
x = 27/5 / 9
x = 3/5


Input: Find the solution to x^2  - 121/36 = 0

Output:
x^2  - 121/36 = 0
(x - 11/6)(x - -11/6) = 0
x - 11/6 = 0  or  x - -11/6 = 0
x = 11/6
x = -11/6


Input: What value of x satisfies 10x - 90 = 0

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


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

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


Input: Find x for x^2 + 3/4x - 9/8 = 0

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


Input:
Solve simultaneously:
9x + 5y = 73/4
6x + 1y = 89/10

Output:
9x + 5y = 73/4
6x + 1y = 89/10

Using elimination
6*(9x + 5y = 73/4)
9*(6x + 1y = 89/10)
54x + 30y = 219/2
54x + 9y = 801/10
Subtract equations
21y = 147/5
y = 147/5/21
y = 7/5

Substitute y
9x + 5(7/5) = 73/4
9x = 45/4
x = 45/4/9
x = 5/4


Input: Determine x in x^2 + 11/28x - 6/7 = 0

Output:
x^2 + 11/28x - 6/7 = 0
(x - 3/4)(x - -8/7) = 0
x - 3/4 = 0  or  x - -8/7 = 0
x = 3/4
x = -8/7


Input: Compute the solution of 9x + 27/2 = 0

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


Input: Compute the solution of 9x - 15 = 0

Output:
9x - 15 = 0
9x = 15
x = 15 / 9
x = 5/3


Input: Solve the equation x^2 + 1/8x - 33/16 = 0

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


Input:
Find x and y such that
4x + 4y = 56/3
5x + 1y = 74/3

Output:
4x + 4y = 56/3
5x + 1y = 74/3

Using elimination
5*(4x + 4y = 56/3)
4*(5x + 1y = 74/3)
20x + 20y = 280/3
20x + 4y = 296/3
Subtract equations
16y = -16/3
y = -16/3/16
y = -1/3

Substitute y
4x + 4(-1/3) = 56/3
4x = 20
x = 20/4
x = 5


Input: Determine x in x^2 + 41/8x - 105/8 = 0

Output:
x^2 + 41/8x - 105/8 = 0
(x - 15/8)(x - -7) = 0
x - 15/8 = 0  or  x - -7 = 0
x = 15/8
x = -7


Input:
Solve simultaneously:
9x + 6y = 387/5
9x + 9y = 801/10

Output:
9x + 6y = 387/5
9x + 9y = 801/10

Using elimination
9*(9x + 6y = 387/5)
9*(9x + 9y = 801/10)
81x + 54y = 3483/5
81x + 81y = 7209/10
Subtract equations
-27y = -243/10
y = -243/10/-27
y = 9/10

Substitute y
9x + 6(9/10) = 387/5
9x = 72
x = 72/9
x = 8


Input: Solve quickly: 9x + 72/5 = 0

Output:
9x + 72/5 = 0
9x = -72/5
x = -72/5 / 9
x = -8/5


Input: Find x for x^2 + 22/3x + 19/3 = 0

Output:
x^2 + 22/3x + 19/3 = 0
(x - -1)(x - -19/3) = 0
x - -1 = 0  or  x - -19/3 = 0
x = -1
x = -19/3


Input: Find x in x^2 + 76/45x - 1/5 = 0

Output:
x^2 + 76/45x - 1/5 = 0
(x - -9/5)(x - 1/9) = 0
x - -9/5 = 0  or  x - 1/9 = 0
x = -9/5
x = 1/9


Input: What value of x satisfies x^3 - 21/2x^2 + 67/2x - 30 = 0

Output:
x^3 - 21/2x^2 + 67/2x - 30 = 0
(x - 3/2)(x - 5)(x - 4) = 0
x - 3/2 = 0
x - 5 = 0
x - 4 = 0
x = 3/2
x = 5
x = 4


Input: What value of x satisfies 4x + 38/3 = 0

Output:
4x + 38/3 = 0
4x = -38/3
x = -38/3 / 4
x = -19/6


Input: Solve the equation 10x - 10 = 0

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


Input: Determine x in 9x + 6 = 0

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


Input: Solve quickly: 2x - 19/3 = 0

Output:
2x - 19/3 = 0
2x = 19/3
x = 19/3 / 2
x = 19/6


Input:
Solve the system:
7x + 5y = -313/6
9x + 9y = -123/2

Output:
7x + 5y = -313/6
9x + 9y = -123/2

Using elimination
9*(7x + 5y = -313/6)
7*(9x + 9y = -123/2)
63x + 45y = -939/2
63x + 63y = -861/2
Subtract equations
-18y = -39
y = -39/-18
y = 13/6

Substitute y
7x + 5(13/6) = -313/6
7x = -63
x = -63/7
x = -9


Input: Solve quickly: 5x + 55/7 = 0

Output:
5x + 55/7 = 0
5x = -55/7
x = -55/7 / 5
x = -11/7


Input:
Solve the system:
10x + 6y = 230/3
8x + 9y = 247/3

Output:
10x + 6y = 230/3
8x + 9y = 247/3

Using elimination
8*(10x + 6y = 230/3)
10*(8x + 9y = 247/3)
80x + 48y = 1840/3
80x + 90y = 2470/3
Subtract equations
-42y = -210
y = -210/-42
y = 5

Substitute y
10x + 6(5) = 230/3
10x = 140/3
x = 140/3/10
x = 14/3


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 3x + 57 = 0

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


Input: Determine x in x^2 - 1x - 11/100 = 0

Output:
x^2 - 1x - 11/100 = 0
(x - 11/10)(x - -1/10) = 0
x - 11/10 = 0  or  x - -1/10 = 0
x = 11/10
x = -1/10


Input: Find x in x^3 - 77/6x^2 + 35/2x + 325/3 = 0

Output:
x^3 - 77/6x^2 + 35/2x + 325/3 = 0
(x - 10)(x - 5)(x - -13/6) = 0
x - 10 = 0
x - 5 = 0
x - -13/6 = 0
x = 10
x = 5
x = -13/6


Input: Compute the solution of x^2 - 89/18x + 2 = 0

Output:
x^2 - 89/18x + 2 = 0
(x - 4/9)(x - 9/2) = 0
x - 4/9 = 0  or  x - 9/2 = 0
x = 4/9
x = 9/2


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

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


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

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


Input: Determine x in x^2 + 11/4x - 39/2 = 0

Output:
x^2 + 11/4x - 39/2 = 0
(x - 13/4)(x - -6) = 0
x - 13/4 = 0  or  x - -6 = 0
x = 13/4
x = -6


Input: Find the solution to 7x + 2 = 0

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


Input: Find x in x^3 - 11/42x^2 - 5/2x + 25/21 = 0

Output:
x^3 - 11/42x^2 - 5/2x + 25/21 = 0
(x - 1/2)(x - 10/7)(x - -5/3) = 0
x - 1/2 = 0
x - 10/7 = 0
x - -5/3 = 0
x = 1/2
x = 10/7
x = -5/3


Input: Solve quickly: x^2 - 27/4x + 19/2 = 0

Output:
x^2 - 27/4x + 19/2 = 0
(x - 19/4)(x - 2) = 0
x - 19/4 = 0  or  x - 2 = 0
x = 19/4
x = 2


Input: Find x for x^3 - 47/12x^2 + 19/24x + 11/24 = 0

Output:
x^3 - 47/12x^2 + 19/24x + 11/24 = 0
(x - 11/3)(x - 1/2)(x - -1/4) = 0
x - 11/3 = 0
x - 1/2 = 0
x - -1/4 = 0
x = 11/3
x = 1/2
x = -1/4


Input: Determine x in x^2 - 67/18x + 10/3 = 0

Output:
x^2 - 67/18x + 10/3 = 0
(x - 3/2)(x - 20/9) = 0
x - 3/2 = 0  or  x - 20/9 = 0
x = 3/2
x = 20/9


Input:
Find x and y such that
5x + 4y = 19
10x + 10y = 42

Output:
5x + 4y = 19
10x + 10y = 42

Using elimination
10*(5x + 4y = 19)
5*(10x + 10y = 42)
50x + 40y = 190
50x + 50y = 210
Subtract equations
-10y = -20
y = -20/-10
y = 2

Substitute y
5x + 4(2) = 19
5x = 11
x = 11/5
x = 11/5


Input: Find x in x^3 + 13/2x^2 + 1/2x - 35 = 0

Output:
x^3 + 13/2x^2 + 1/2x - 35 = 0
(x - -5)(x - 2)(x - -7/2) = 0
x - -5 = 0
x - 2 = 0
x - -7/2 = 0
x = -5
x = 2
x = -7/2


Input: Determine x in 10x + 13 = 0

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


Input: Solve quickly: x^3 + 106/15x^2 + 312/25x + 448/75 = 0

Output:
x^3 + 106/15x^2 + 312/25x + 448/75 = 0
(x - -8/5)(x - -14/3)(x - -4/5) = 0
x - -8/5 = 0
x - -14/3 = 0
x - -4/5 = 0
x = -8/5
x = -14/3
x = -4/5


Input: Compute the solution of 3x - 17 = 0

Output:
3x - 17 = 0
3x = 17
x = 17 / 3
x = 17/3


Input: Compute the solution of 1x + 13/6 = 0

Output:
1x + 13/6 = 0
1x = -13/6
x = -13/6 / 1
x = -13/6


Input: Find x in x^3 + 33/14x^2 - 731/350x - 66/35 = 0

Output:
x^3 + 33/14x^2 - 731/350x - 66/35 = 0
(x - -20/7)(x - -3/5)(x - 11/10) = 0
x - -20/7 = 0
x - -3/5 = 0
x - 11/10 = 0
x = -20/7
x = -3/5
x = 11/10


Input: Find x for x^3 - 17/3x^2 - 249x - 247/3 = 0

Output:
x^3 - 17/3x^2 - 249x - 247/3 = 0
(x - -13)(x - 19)(x - -1/3) = 0
x - -13 = 0
x - 19 = 0
x - -1/3 = 0
x = -13
x = 19
x = -1/3


Input:
Solve the equations:
9x + 6y = 126
8x + 7y = 112

Output:
9x + 6y = 126
8x + 7y = 112

Using elimination
8*(9x + 6y = 126)
9*(8x + 7y = 112)
72x + 48y = 1008
72x + 63y = 1008
Subtract equations
-15y = 0
y = 0/-15
y = 0

Substitute y
9x + 6(0) = 126
9x = 126
x = 126/9
x = 14


Input: Find the solution to 3x + 24/5 = 0

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


Input: Find x in 6x - 39 = 0

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


Input:
Find x and y such that
5x + 1y = -14/9
10x + 10y = -340/9

Output:
5x + 1y = -14/9
10x + 10y = -340/9

Using elimination
10*(5x + 1y = -14/9)
5*(10x + 10y = -340/9)
50x + 10y = -140/9
50x + 50y = -1700/9
Subtract equations
-40y = 520/3
y = 520/3/-40
y = -13/3

Substitute y
5x + 1(-13/3) = -14/9
5x = 25/9
x = 25/9/5
x = 5/9


Input:
Solve the equations:
1x + 10y = -22
7x + 9y = -221/5

Output:
1x + 10y = -22
7x + 9y = -221/5

Using elimination
7*(1x + 10y = -22)
1*(7x + 9y = -221/5)
7x + 70y = -154
7x + 9y = -221/5
Subtract equations
61y = -549/5
y = -549/5/61
y = -9/5

Substitute y
1x + 10(-9/5) = -22
1x = -4
x = -4/1
x = -4


Input:
Solve the equations:
3x + 3y = -15/2
9x + 5y = -69/2

Output:
3x + 3y = -15/2
9x + 5y = -69/2

Using elimination
9*(3x + 3y = -15/2)
3*(9x + 5y = -69/2)
27x + 27y = -135/2
27x + 15y = -207/2
Subtract equations
12y = 36
y = 36/12
y = 3

Substitute y
3x + 3(3) = -15/2
3x = -33/2
x = -33/2/3
x = -11/2


Input: Solve the equation x^3 - 7/3x^2 - 20/3x  = 0

Output:
x^3 - 7/3x^2 - 20/3x  = 0
(x - 4)(x - -5/3)(x - 0) = 0
x - 4 = 0
x - -5/3 = 0
x - 0 = 0
x = 4
x = -5/3
x = 0


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 + 19/10x  = 0

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


Input: Solve x^3 + 147/20x^2 - 128/5x + 9 = 0

Output:
x^3 + 147/20x^2 - 128/5x + 9 = 0
(x - 2/5)(x - -10)(x - 9/4) = 0
x - 2/5 = 0
x - -10 = 0
x - 9/4 = 0
x = 2/5
x = -10
x = 9/4


Input:
Solve the system:
2x + 9y = 0
4x + 2y = 0

Output:
2x + 9y = 0
4x + 2y = 0

Using elimination
4*(2x + 9y = 0)
2*(4x + 2y = 0)
8x + 36y = 0
8x + 4y = 0
Subtract equations
32y = 0
y = 0/32
y = 0

Substitute y
2x + 9(0) = 0
2x = 0
x = 0/2
x = 0


Input: Solve the equation x^3 + 8x^2 + 13x + 6 = 0

Output:
x^3 + 8x^2 + 13x + 6 = 0
(x - -1)(x - -6)(x - -1) = 0
x - -1 = 0
x - -6 = 0
x - -1 = 0
x = -1
x = -6
x = -1


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

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


Input: Solve x^2  - 324/49 = 0

Output:
x^2  - 324/49 = 0
(x - -18/7)(x - 18/7) = 0
x - -18/7 = 0  or  x - 18/7 = 0
x = -18/7
x = 18/7


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

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


Input: Find the solution to x^2 + 53/36x - 5/3 = 0

Output:
x^2 + 53/36x - 5/3 = 0
(x - 3/4)(x - -20/9) = 0
x - 3/4 = 0  or  x - -20/9 = 0
x = 3/4
x = -20/9


Input: Determine x in x^2 + 13/3x - 42 = 0

Output:
x^2 + 13/3x - 42 = 0
(x - 14/3)(x - -9) = 0
x - 14/3 = 0  or  x - -9 = 0
x = 14/3
x = -9


Input: Solve the equation x^2 + 13/18x - 7/6 = 0

Output:
x^2 + 13/18x - 7/6 = 0
(x - -3/2)(x - 7/9) = 0
x - -3/2 = 0  or  x - 7/9 = 0
x = -3/2
x = 7/9


Input: Compute the solution of x^3 + 1/3x^2 - 110/3x - 200/3 = 0

Output:
x^3 + 1/3x^2 - 110/3x - 200/3 = 0
(x - -2)(x - 20/3)(x - -5) = 0
x - -2 = 0
x - 20/3 = 0
x - -5 = 0
x = -2
x = 20/3
x = -5


Input: Find x for 4x  = 0

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


Input: Compute the solution of 2x + 6 = 0

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


Input: Solve quickly: x^2 + 1/4x - 95/4 = 0

Output:
x^2 + 1/4x - 95/4 = 0
(x - -5)(x - 19/4) = 0
x - -5 = 0  or  x - 19/4 = 0
x = -5
x = 19/4


Input: Find the solution to x^3 + 53/6x^2 - 71/2x + 30 = 0

Output:
x^3 + 53/6x^2 - 71/2x + 30 = 0
(x - 3/2)(x - 5/3)(x - -12) = 0
x - 3/2 = 0
x - 5/3 = 0
x - -12 = 0
x = 3/2
x = 5/3
x = -12


Input: Find the solution to x^2 + 29/90x + 1/45 = 0

Output:
x^2 + 29/90x + 1/45 = 0
(x - -2/9)(x - -1/10) = 0
x - -2/9 = 0  or  x - -1/10 = 0
x = -2/9
x = -1/10


Input: Solve quickly: 2x + 16 = 0

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


Input:
Solve the system:
1x + 7y = -29/10
10x + 3y = -11/5

Output:
1x + 7y = -29/10
10x + 3y = -11/5

Using elimination
10*(1x + 7y = -29/10)
1*(10x + 3y = -11/5)
10x + 70y = -29
10x + 3y = -11/5
Subtract equations
67y = -134/5
y = -134/5/67
y = -2/5

Substitute y
1x + 7(-2/5) = -29/10
1x = -1/10
x = -1/10/1
x = -1/10


Input:
Solve the equations:
9x + 2y = -909/14
10x + 2y = -507/7

Output:
9x + 2y = -909/14
10x + 2y = -507/7

Using elimination
10*(9x + 2y = -909/14)
9*(10x + 2y = -507/7)
90x + 20y = -4545/7
90x + 18y = -4563/7
Subtract equations
2y = 18/7
y = 18/7/2
y = 9/7

Substitute y
9x + 2(9/7) = -909/14
9x = -135/2
x = -135/2/9
x = -15/2


Input: Solve the equation x^2 - 68/45x - 32/15 = 0

Output:
x^2 - 68/45x - 32/15 = 0
(x - -8/9)(x - 12/5) = 0
x - -8/9 = 0  or  x - 12/5 = 0
x = -8/9
x = 12/5


Input: What value of x satisfies x^2 + 30/7x + 27/7 = 0

Output:
x^2 + 30/7x + 27/7 = 0
(x - -9/7)(x - -3) = 0
x - -9/7 = 0  or  x - -3 = 0
x = -9/7
x = -3


Input: Compute the solution of 10x - 100/9 = 0

Output:
10x - 100/9 = 0
10x = 100/9
x = 100/9 / 10
x = 10/9


Input:
Solve simultaneously:
7x + 9y = -841/30
6x + 7y = -231/10

Output:
7x + 9y = -841/30
6x + 7y = -231/10

Using elimination
6*(7x + 9y = -841/30)
7*(6x + 7y = -231/10)
42x + 54y = -841/5
42x + 49y = -1617/10
Subtract equations
5y = -13/2
y = -13/2/5
y = -13/10

Substitute y
7x + 9(-13/10) = -841/30
7x = -49/3
x = -49/3/7
x = -7/3


Input:
Solve the system:
3x + 5y = -23/4
2x + 7y = -41/4

Output:
3x + 5y = -23/4
2x + 7y = -41/4

Using elimination
2*(3x + 5y = -23/4)
3*(2x + 7y = -41/4)
6x + 10y = -23/2
6x + 21y = -123/4
Subtract equations
-11y = 77/4
y = 77/4/-11
y = -7/4

Substitute y
3x + 5(-7/4) = -23/4
3x = 3
x = 3/3
x = 1


Input: Solve quickly: x^2 - 25/6x + 34/9 = 0

Output:
x^2 - 25/6x + 34/9 = 0
(x - 17/6)(x - 4/3) = 0
x - 17/6 = 0  or  x - 4/3 = 0
x = 17/6
x = 4/3


Input: Find the solution to 8x - 16/3 = 0

Output:
8x - 16/3 = 0
8x = 16/3
x = 16/3 / 8
x = 2/3


Input: Determine x in x^2 + 7x - 8 = 0

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


Input: Solve quickly: x^3 - 71/14x^2 + 7x - 33/14 = 0

Output:
x^3 - 71/14x^2 + 7x - 33/14 = 0
(x - 3)(x - 11/7)(x - 1/2) = 0
x - 3 = 0
x - 11/7 = 0
x - 1/2 = 0
x = 3
x = 11/7
x = 1/2


Input:
Solve simultaneously:
9x + 3y = 68/7
8x + 3y = 55/7

Output:
9x + 3y = 68/7
8x + 3y = 55/7

Using elimination
8*(9x + 3y = 68/7)
9*(8x + 3y = 55/7)
72x + 24y = 544/7
72x + 27y = 495/7
Subtract equations
-3y = 7
y = 7/-3
y = -7/3

Substitute y
9x + 3(-7/3) = 68/7
9x = 117/7
x = 117/7/9
x = 13/7


Input:
Solve the system:
1x + 5y = -713/56
4x + 10y = -761/28

Output:
1x + 5y = -713/56
4x + 10y = -761/28

Using elimination
4*(1x + 5y = -713/56)
1*(4x + 10y = -761/28)
4x + 20y = -713/14
4x + 10y = -761/28
Subtract equations
10y = -95/4
y = -95/4/10
y = -19/8

Substitute y
1x + 5(-19/8) = -713/56
1x = -6/7
x = -6/7/1
x = -6/7


Input: What value of x satisfies 10x + 20 = 0

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


Input:
Find x and y such that
6x + 1y = 67/3
4x + 7y = 17

Output:
6x + 1y = 67/3
4x + 7y = 17

Using elimination
4*(6x + 1y = 67/3)
6*(4x + 7y = 17)
24x + 4y = 268/3
24x + 42y = 102
Subtract equations
-38y = -38/3
y = -38/3/-38
y = 1/3

Substitute y
6x + 1(1/3) = 67/3
6x = 22
x = 22/6
x = 11/3


Input: Find the solution to x^3 + 97/35x^2 - 158/35x - 352/35 = 0

Output:
x^3 + 97/35x^2 - 158/35x - 352/35 = 0
(x - -16/5)(x - -11/7)(x - 2) = 0
x - -16/5 = 0
x - -11/7 = 0
x - 2 = 0
x = -16/5
x = -11/7
x = 2


Input:
Solve simultaneously:
7x + 4y = -8/9
1x + 4y = 76/9

Output:
7x + 4y = -8/9
1x + 4y = 76/9

Using elimination
1*(7x + 4y = -8/9)
7*(1x + 4y = 76/9)
7x + 4y = -8/9
7x + 28y = 532/9
Subtract equations
-24y = -60
y = -60/-24
y = 5/2

Substitute y
7x + 4(5/2) = -8/9
7x = -98/9
x = -98/9/7
x = -14/9


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

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

Using elimination
6*(4x + 6y = 1/3)
4*(6x + 10y = 2)
24x + 36y = 2
24x + 40y = 8
Subtract equations
-4y = -6
y = -6/-4
y = 3/2

Substitute y
4x + 6(3/2) = 1/3
4x = -26/3
x = -26/3/4
x = -13/6


Input:
Solve the equations:
9x + 10y = -180
1x + 7y = -325/3

Output:
9x + 10y = -180
1x + 7y = -325/3

Using elimination
1*(9x + 10y = -180)
9*(1x + 7y = -325/3)
9x + 10y = -180
9x + 63y = -975
Subtract equations
-53y = 795
y = 795/-53
y = -15

Substitute y
9x + 10(-15) = -180
9x = -30
x = -30/9
x = -10/3


Input: Solve the equation x^2 + 11/10x - 7/2 = 0

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


Input: Solve the equation x^3 - 53/28x^2 + 6/7x  = 0

Output:
x^3 - 53/28x^2 + 6/7x  = 0
(x - 3/4)(x - 0)(x - 8/7) = 0
x - 3/4 = 0
x - 0 = 0
x - 8/7 = 0
x = 3/4
x = 0
x = 8/7


Input: Determine x in x^2 - 19x  = 0

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


Input: Solve x^2 - 12/5x + 27/20 = 0

Output:
x^2 - 12/5x + 27/20 = 0
(x - 9/10)(x - 3/2) = 0
x - 9/10 = 0  or  x - 3/2 = 0
x = 9/10
x = 3/2


Input:
Solve the system:
1x + 7y = 11/6
7x + 2y = -32/3

Output:
1x + 7y = 11/6
7x + 2y = -32/3

Using elimination
7*(1x + 7y = 11/6)
1*(7x + 2y = -32/3)
7x + 49y = 77/6
7x + 2y = -32/3
Subtract equations
47y = 47/2
y = 47/2/47
y = 1/2

Substitute y
1x + 7(1/2) = 11/6
1x = -5/3
x = -5/3/1
x = -5/3


Input:
Find x and y such that
3x + 7y = -808/45
8x + 9y = -132/5

Output:
3x + 7y = -808/45
8x + 9y = -132/5

Using elimination
8*(3x + 7y = -808/45)
3*(8x + 9y = -132/5)
24x + 56y = -6464/45
24x + 27y = -396/5
Subtract equations
29y = -580/9
y = -580/9/29
y = -20/9

Substitute y
3x + 7(-20/9) = -808/45
3x = -12/5
x = -12/5/3
x = -4/5


Input: Find x for 2x - 10 = 0

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


Input: Compute the solution of x^2 + 18x - 19 = 0

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


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

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


Input: Find x in 10x - 20 = 0

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


Input: Solve 1x - 1/2 = 0

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


Input: Solve the equation 6x - 20 = 0

Output:
6x - 20 = 0
6x = 20
x = 20 / 6
x = 10/3


Input: Compute the solution of 4x + 12 = 0

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


Input: Compute the solution of 3x - 60/7 = 0

Output:
3x - 60/7 = 0
3x = 60/7
x = 60/7 / 3
x = 20/7


Input: Compute the solution of x^2 + 145/21x + 76/21 = 0

Output:
x^2 + 145/21x + 76/21 = 0
(x - -19/3)(x - -4/7) = 0
x - -19/3 = 0  or  x - -4/7 = 0
x = -19/3
x = -4/7


Input: Solve the equation 8x + 64/5 = 0

Output:
8x + 64/5 = 0
8x = -64/5
x = -64/5 / 8
x = -8/5


Input:
Solve simultaneously:
7x + 5y = 10
5x + 3y = 8

Output:
7x + 5y = 10
5x + 3y = 8

Using elimination
5*(7x + 5y = 10)
7*(5x + 3y = 8)
35x + 25y = 50
35x + 21y = 56
Subtract equations
4y = -6
y = -6/4
y = -3/2

Substitute y
7x + 5(-3/2) = 10
7x = 35/2
x = 35/2/7
x = 5/2


Input: Solve x^3 + 107/40x^2 + 173/400x - 133/200 = 0

Output:
x^3 + 107/40x^2 + 173/400x - 133/200 = 0
(x - 2/5)(x - -19/8)(x - -7/10) = 0
x - 2/5 = 0
x - -19/8 = 0
x - -7/10 = 0
x = 2/5
x = -19/8
x = -7/10


Input: Find the solution to x^3 + 199/21x^2 - 92/3x - 32/7 = 0

Output:
x^3 + 199/21x^2 - 92/3x - 32/7 = 0
(x - 8/3)(x - -12)(x - -1/7) = 0
x - 8/3 = 0
x - -12 = 0
x - -1/7 = 0
x = 8/3
x = -12
x = -1/7


Input: Solve x^3 + 169/70x^2 - 187/50x - 1482/175 = 0

Output:
x^3 + 169/70x^2 - 187/50x - 1482/175 = 0
(x - -12/7)(x - 19/10)(x - -13/5) = 0
x - -12/7 = 0
x - 19/10 = 0
x - -13/5 = 0
x = -12/7
x = 19/10
x = -13/5


Input: Solve quickly: x^2 - 1x - 285/16 = 0

Output:
x^2 - 1x - 285/16 = 0
(x - 19/4)(x - -15/4) = 0
x - 19/4 = 0  or  x - -15/4 = 0
x = 19/4
x = -15/4


Input: Solve the equation 3x - 15/4 = 0

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


Input: Compute the solution of 7x - 70/3 = 0

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


Input: Solve quickly: x^3 - 10/63x^2 - 43/63x - 10/63 = 0

Output:
x^3 - 10/63x^2 - 43/63x - 10/63 = 0
(x - -5/9)(x - 1)(x - -2/7) = 0
x - -5/9 = 0
x - 1 = 0
x - -2/7 = 0
x = -5/9
x = 1
x = -2/7


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

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


Input: Determine x in x^2 + 7x + 20/9 = 0

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


Input: Find x in 8x + 12 = 0

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


Input:
Find x and y such that
7x + 5y = 6
3x + 7y = 42/5

Output:
7x + 5y = 6
3x + 7y = 42/5

Using elimination
3*(7x + 5y = 6)
7*(3x + 7y = 42/5)
21x + 15y = 18
21x + 49y = 294/5
Subtract equations
-34y = -204/5
y = -204/5/-34
y = 6/5

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


Input: What value of x satisfies x^3 + 20/3x^2 - 17/3x - 70/3 = 0

Output:
x^3 + 20/3x^2 - 17/3x - 70/3 = 0
(x - -5/3)(x - -7)(x - 2) = 0
x - -5/3 = 0
x - -7 = 0
x - 2 = 0
x = -5/3
x = -7
x = 2


Input: Determine x in 9x - 81/4 = 0

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


Input: Compute the solution of x^3 - 71/21x^2 + 87/28x - 3/7 = 0

Output:
x^3 - 71/21x^2 + 87/28x - 3/7 = 0
(x - 12/7)(x - 3/2)(x - 1/6) = 0
x - 12/7 = 0
x - 3/2 = 0
x - 1/6 = 0
x = 12/7
x = 3/2
x = 1/6


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

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


Input: Find the solution to x^3 - 68/35x^2 + 47/700x + 19/700 = 0

Output:
x^3 - 68/35x^2 + 47/700x + 19/700 = 0
(x - 19/10)(x - 1/7)(x - -1/10) = 0
x - 19/10 = 0
x - 1/7 = 0
x - -1/10 = 0
x = 19/10
x = 1/7
x = -1/10


Input: Solve the equation 10x + 65/3 = 0

Output:
10x + 65/3 = 0
10x = -65/3
x = -65/3 / 10
x = -13/6


Input: Find the solution to x^2 + 7/3x - 8/9 = 0

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


Input:
Solve simultaneously:
5x + 4y = 7
1x + 1y = 1

Output:
5x + 4y = 7
1x + 1y = 1

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

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


Input: Compute the solution of 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:
Solve simultaneously:
4x + 8y = -472/5
8x + 7y = -494/5

Output:
4x + 8y = -472/5
8x + 7y = -494/5

Using elimination
8*(4x + 8y = -472/5)
4*(8x + 7y = -494/5)
32x + 64y = -3776/5
32x + 28y = -1976/5
Subtract equations
36y = -360
y = -360/36
y = -10

Substitute y
4x + 8(-10) = -472/5
4x = -72/5
x = -72/5/4
x = -18/5


Input: What value of x satisfies 6x + 48 = 0

Output:
6x + 48 = 0
6x = -48
x = -48 / 6
x = -8


Input:
Solve simultaneously:
3x + 2y = -4
7x + 1y = -61/3

Output:
3x + 2y = -4
7x + 1y = -61/3

Using elimination
7*(3x + 2y = -4)
3*(7x + 1y = -61/3)
21x + 14y = -28
21x + 3y = -61
Subtract equations
11y = 33
y = 33/11
y = 3

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


Input: Find x in x^2 + 1/6x - 19/2 = 0

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


Input: Solve the equation x^2 - 5x - 126 = 0

Output:
x^2 - 5x - 126 = 0
(x - -9)(x - 14) = 0
x - -9 = 0  or  x - 14 = 0
x = -9
x = 14


Input: Find x in x^2 - 1/18x - 7/3 = 0

Output:
x^2 - 1/18x - 7/3 = 0
(x - 14/9)(x - -3/2) = 0
x - 14/9 = 0  or  x - -3/2 = 0
x = 14/9
x = -3/2


Input:
Solve simultaneously:
4x + 7y = -59/8
7x + 7y = -35/8

Output:
4x + 7y = -59/8
7x + 7y = -35/8

Using elimination
7*(4x + 7y = -59/8)
4*(7x + 7y = -35/8)
28x + 49y = -413/8
28x + 28y = -35/2
Subtract equations
21y = -273/8
y = -273/8/21
y = -13/8

Substitute y
4x + 7(-13/8) = -59/8
4x = 4
x = 4/4
x = 1


Input: Compute the solution of 6x - 114 = 0

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


Input: Solve the equation 9x + 27/5 = 0

Output:
9x + 27/5 = 0
9x = -27/5
x = -27/5 / 9
x = -3/5


Input: Solve the equation 7x - 56 = 0

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


Input: Solve quickly: 4x - 20/3 = 0

Output:
4x - 20/3 = 0
4x = 20/3
x = 20/3 / 4
x = 5/3


Input: Find x in x^2 + 119/24x - 2 = 0

Output:
x^2 + 119/24x - 2 = 0
(x - 3/8)(x - -16/3) = 0
x - 3/8 = 0  or  x - -16/3 = 0
x = 3/8
x = -16/3


Input: Compute the solution of x^3 - 17x^2 - 74x + 1440 = 0

Output:
x^3 - 17x^2 - 74x + 1440 = 0
(x - 16)(x - 10)(x - -9) = 0
x - 16 = 0
x - 10 = 0
x - -9 = 0
x = 16
x = 10
x = -9


Input: Solve quickly: 7x - 49/2 = 0

Output:
7x - 49/2 = 0
7x = 49/2
x = 49/2 / 7
x = 7/2


Input: Compute the solution of x^3 + 562/45x^2 - 33/5x + 26/45 = 0

Output:
x^3 + 562/45x^2 - 33/5x + 26/45 = 0
(x - -13)(x - 1/9)(x - 2/5) = 0
x - -13 = 0
x - 1/9 = 0
x - 2/5 = 0
x = -13
x = 1/9
x = 2/5


Input:
Solve simultaneously:
3x + 2y = 43/4
6x + 3y = 45/2

Output:
3x + 2y = 43/4
6x + 3y = 45/2

Using elimination
6*(3x + 2y = 43/4)
3*(6x + 3y = 45/2)
18x + 12y = 129/2
18x + 9y = 135/2
Subtract equations
3y = -3
y = -3/3
y = -1

Substitute y
3x + 2(-1) = 43/4
3x = 51/4
x = 51/4/3
x = 17/4


Input: Compute the solution of 3x + 19/3 = 0

Output:
3x + 19/3 = 0
3x = -19/3
x = -19/3 / 3
x = -19/9


Input: Solve quickly: x^2 - 43/10x + 39/10 = 0

Output:
x^2 - 43/10x + 39/10 = 0
(x - 3)(x - 13/10) = 0
x - 3 = 0  or  x - 13/10 = 0
x = 3
x = 13/10


Input: Find x in x^2 + 47/72x - 55/24 = 0

Output:
x^2 + 47/72x - 55/24 = 0
(x - -15/8)(x - 11/9) = 0
x - -15/8 = 0  or  x - 11/9 = 0
x = -15/8
x = 11/9


Input: Find x for x^3 - 97/12x^2 + 37/2x - 38/3 = 0

Output:
x^3 - 97/12x^2 + 37/2x - 38/3 = 0
(x - 4/3)(x - 19/4)(x - 2) = 0
x - 4/3 = 0
x - 19/4 = 0
x - 2 = 0
x = 4/3
x = 19/4
x = 2


Input: What value of x satisfies 3x + 6/7 = 0

Output:
3x + 6/7 = 0
3x = -6/7
x = -6/7 / 3
x = -2/7


Input: Solve 1x - 5/4 = 0

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


Input: What value of x satisfies 4x + 44/3 = 0

Output:
4x + 44/3 = 0
4x = -44/3
x = -44/3 / 4
x = -11/3


Input:
Solve the system:
8x + 10y = 36
7x + 8y = 57/2

Output:
8x + 10y = 36
7x + 8y = 57/2

Using elimination
7*(8x + 10y = 36)
8*(7x + 8y = 57/2)
56x + 70y = 252
56x + 64y = 228
Subtract equations
6y = 24
y = 24/6
y = 4

Substitute y
8x + 10(4) = 36
8x = -4
x = -4/8
x = -1/2


Input:
Solve the equations:
3x + 7y = -6
3x + 10y = -6

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

Using elimination
3*(3x + 7y = -6)
3*(3x + 10y = -6)
9x + 21y = -18
9x + 30y = -18
Subtract equations
-9y = 0
y = 0/-9
y = 0

Substitute y
3x + 7(0) = -6
3x = -6
x = -6/3
x = -2


Input: Find the solution to x^2 + 37/6x - 19/18 = 0

Output:
x^2 + 37/6x - 19/18 = 0
(x - 1/6)(x - -19/3) = 0
x - 1/6 = 0  or  x - -19/3 = 0
x = 1/6
x = -19/3


Input: Solve quickly: x^3 + 55/24x^2 - 107/48x - 5/16 = 0

Output:
x^3 + 55/24x^2 - 107/48x - 5/16 = 0
(x - -3)(x - -1/8)(x - 5/6) = 0
x - -3 = 0
x - -1/8 = 0
x - 5/6 = 0
x = -3
x = -1/8
x = 5/6


Input:
Solve simultaneously:
10x + 6y = 529/7
9x + 1y = 367/14

Output:
10x + 6y = 529/7
9x + 1y = 367/14

Using elimination
9*(10x + 6y = 529/7)
10*(9x + 1y = 367/14)
90x + 54y = 4761/7
90x + 10y = 1835/7
Subtract equations
44y = 418
y = 418/44
y = 19/2

Substitute y
10x + 6(19/2) = 529/7
10x = 130/7
x = 130/7/10
x = 13/7


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

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


Input: Find the solution to x^3 + 83/10x^2 - 411/10x + 198/5 = 0

Output:
x^3 + 83/10x^2 - 411/10x + 198/5 = 0
(x - -12)(x - 3/2)(x - 11/5) = 0
x - -12 = 0
x - 3/2 = 0
x - 11/5 = 0
x = -12
x = 3/2
x = 11/5


Input: Solve 10x - 95/3 = 0

Output:
10x - 95/3 = 0
10x = 95/3
x = 95/3 / 10
x = 19/6


Input:
Solve the system:
10x + 1y = -108
4x + 8y = -28

Output:
10x + 1y = -108
4x + 8y = -28

Using elimination
4*(10x + 1y = -108)
10*(4x + 8y = -28)
40x + 4y = -432
40x + 80y = -280
Subtract equations
-76y = -152
y = -152/-76
y = 2

Substitute y
10x + 1(2) = -108
10x = -110
x = -110/10
x = -11


Input: Find the solution to 8x + 24 = 0

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


Input: Find x in x^2 + 141/10x + 7/5 = 0

Output:
x^2 + 141/10x + 7/5 = 0
(x - -1/10)(x - -14) = 0
x - -1/10 = 0  or  x - -14 = 0
x = -1/10
x = -14


Input: Solve x^3 - 344/105x^2 + 368/105x - 128/105 = 0

Output:
x^3 - 344/105x^2 + 368/105x - 128/105 = 0
(x - 8/7)(x - 4/3)(x - 4/5) = 0
x - 8/7 = 0
x - 4/3 = 0
x - 4/5 = 0
x = 8/7
x = 4/3
x = 4/5


Input: What value of x satisfies 1x + 13/5 = 0

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


Input: Determine x in x^3 + 61/35x^2 - 1509/140x + 513/70 = 0

Output:
x^3 + 61/35x^2 - 1509/140x + 513/70 = 0
(x - -9/2)(x - 6/7)(x - 19/10) = 0
x - -9/2 = 0
x - 6/7 = 0
x - 19/10 = 0
x = -9/2
x = 6/7
x = 19/10


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

Output:
x^2 + 14x - 15 = 0
(x - 1)(x - -15) = 0
x - 1 = 0  or  x - -15 = 0
x = 1
x = -15


Input: Compute the solution of x^3 - 305/8x^2 + 793/2x - 680 = 0

Output:
x^3 - 305/8x^2 + 793/2x - 680 = 0
(x - 20)(x - 16)(x - 17/8) = 0
x - 20 = 0
x - 16 = 0
x - 17/8 = 0
x = 20
x = 16
x = 17/8


Input:
Solve simultaneously:
2x + 5y = -4
10x + 3y = 2

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

Using elimination
10*(2x + 5y = -4)
2*(10x + 3y = 2)
20x + 50y = -40
20x + 6y = 4
Subtract equations
44y = -44
y = -44/44
y = -1

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


Input: Compute the solution of x^3 + 73/20x^2 - 229/10x - 323/4 = 0

Output:
x^3 + 73/20x^2 - 229/10x - 323/4 = 0
(x - 19/4)(x - -5)(x - -17/5) = 0
x - 19/4 = 0
x - -5 = 0
x - -17/5 = 0
x = 19/4
x = -5
x = -17/5


Input:
Solve the system:
3x + 10y = 73
2x + 10y = 72

Output:
3x + 10y = 73
2x + 10y = 72

Using elimination
2*(3x + 10y = 73)
3*(2x + 10y = 72)
6x + 20y = 146
6x + 30y = 216
Subtract equations
-10y = -70
y = -70/-10
y = 7

Substitute y
3x + 10(7) = 73
3x = 3
x = 3/3
x = 1


Input: Compute the solution of x^2 + 16x + 63 = 0

Output:
x^2 + 16x + 63 = 0
(x - -9)(x - -7) = 0
x - -9 = 0  or  x - -7 = 0
x = -9
x = -7


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

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


Input: Compute the solution of 6x - 72/5 = 0

Output:
6x - 72/5 = 0
6x = 72/5
x = 72/5 / 6
x = 12/5


Input: Find the solution to x^2 - 19/45x - 14/15 = 0

Output:
x^2 - 19/45x - 14/15 = 0
(x - -7/9)(x - 6/5) = 0
x - -7/9 = 0  or  x - 6/5 = 0
x = -7/9
x = 6/5


Input: Find x in x^2 + 9/5x + 4/5 = 0

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


Input:
Find x and y such that
6x + 10y = -1349/35
6x + 5y = -874/35

Output:
6x + 10y = -1349/35
6x + 5y = -874/35

Using elimination
6*(6x + 10y = -1349/35)
6*(6x + 5y = -874/35)
36x + 60y = -8094/35
36x + 30y = -5244/35
Subtract equations
30y = -570/7
y = -570/7/30
y = -19/7

Substitute y
6x + 10(-19/7) = -1349/35
6x = -57/5
x = -57/5/6
x = -19/10


Input: Determine x in x^2 - 69/10x + 13/5 = 0

Output:
x^2 - 69/10x + 13/5 = 0
(x - 2/5)(x - 13/2) = 0
x - 2/5 = 0  or  x - 13/2 = 0
x = 2/5
x = 13/2


Input: Find the solution to 2x + 36/7 = 0

Output:
2x + 36/7 = 0
2x = -36/7
x = -36/7 / 2
x = -18/7


Input:
Solve the system:
9x + 4y = 114/5
6x + 3y = 73/5

Output:
9x + 4y = 114/5
6x + 3y = 73/5

Using elimination
6*(9x + 4y = 114/5)
9*(6x + 3y = 73/5)
54x + 24y = 684/5
54x + 27y = 657/5
Subtract equations
-3y = 27/5
y = 27/5/-3
y = -9/5

Substitute y
9x + 4(-9/5) = 114/5
9x = 30
x = 30/9
x = 10/3


Input:
Solve simultaneously:
3x + 1y = -25/2
1x + 5y = 1/2

Output:
3x + 1y = -25/2
1x + 5y = 1/2

Using elimination
1*(3x + 1y = -25/2)
3*(1x + 5y = 1/2)
3x + 1y = -25/2
3x + 15y = 3/2
Subtract equations
-14y = -14
y = -14/-14
y = 1

Substitute y
3x + 1(1) = -25/2
3x = -27/2
x = -27/2/3
x = -9/2


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

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


Input:
Solve the system:
7x + 6y = -73/9
4x + 8y = -76/9

Output:
7x + 6y = -73/9
4x + 8y = -76/9

Using elimination
4*(7x + 6y = -73/9)
7*(4x + 8y = -76/9)
28x + 24y = -292/9
28x + 56y = -532/9
Subtract equations
-32y = 80/3
y = 80/3/-32
y = -5/6

Substitute y
7x + 6(-5/6) = -73/9
7x = -28/9
x = -28/9/7
x = -4/9


Input: Solve quickly: x^3 - 31/8x^2 - 59/8x + 35/4 = 0

Output:
x^3 - 31/8x^2 - 59/8x + 35/4 = 0
(x - -2)(x - 5)(x - 7/8) = 0
x - -2 = 0
x - 5 = 0
x - 7/8 = 0
x = -2
x = 5
x = 7/8


Input: Find x in 2x  = 0

Output:
2x  = 0
2x = 0
x = 0 / 2
x = 0


Input: Find x for x^2 - 27/4x + 9/2 = 0

Output:
x^2 - 27/4x + 9/2 = 0
(x - 3/4)(x - 6) = 0
x - 3/4 = 0  or  x - 6 = 0
x = 3/4
x = 6


Input: Find the solution to x^3 - 26/5x^2 + 63/20x  = 0

Output:
x^3 - 26/5x^2 + 63/20x  = 0
(x - 7/10)(x - 0)(x - 9/2) = 0
x - 7/10 = 0
x - 0 = 0
x - 9/2 = 0
x = 7/10
x = 0
x = 9/2


Input: Solve 3x + 57/8 = 0

Output:
3x + 57/8 = 0
3x = -57/8
x = -57/8 / 3
x = -19/8


Input: Compute the solution of x^2 - 13/45x - 14/9 = 0

Output:
x^2 - 13/45x - 14/9 = 0
(x - -10/9)(x - 7/5) = 0
x - -10/9 = 0  or  x - 7/5 = 0
x = -10/9
x = 7/5


Input:
Solve the system:
1x + 4y = 122/5
5x + 3y = 20

Output:
1x + 4y = 122/5
5x + 3y = 20

Using elimination
5*(1x + 4y = 122/5)
1*(5x + 3y = 20)
5x + 20y = 122
5x + 3y = 20
Subtract equations
17y = 102
y = 102/17
y = 6

Substitute y
1x + 4(6) = 122/5
1x = 2/5
x = 2/5/1
x = 2/5


Input: Solve quickly: 5x - 35/8 = 0

Output:
5x - 35/8 = 0
5x = 35/8
x = 35/8 / 5
x = 7/8


Input: Find the solution to x^3 - 1x^2 - 15/4x + 9/2 = 0

Output:
x^3 - 1x^2 - 15/4x + 9/2 = 0
(x - -2)(x - 3/2)(x - 3/2) = 0
x - -2 = 0
x - 3/2 = 0
x - 3/2 = 0
x = -2
x = 3/2
x = 3/2


Input: Find x for x^3 - 127/20x^2 + 9/5x + 9/5 = 0

Output:
x^3 - 127/20x^2 + 9/5x + 9/5 = 0
(x - -2/5)(x - 6)(x - 3/4) = 0
x - -2/5 = 0
x - 6 = 0
x - 3/4 = 0
x = -2/5
x = 6
x = 3/4


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

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


Input: Determine x in 3x - 3 = 0

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


Input:
Solve simultaneously:
8x + 2y = 328/9
6x + 2y = 106/3

Output:
8x + 2y = 328/9
6x + 2y = 106/3

Using elimination
6*(8x + 2y = 328/9)
8*(6x + 2y = 106/3)
48x + 12y = 656/3
48x + 16y = 848/3
Subtract equations
-4y = -64
y = -64/-4
y = 16

Substitute y
8x + 2(16) = 328/9
8x = 40/9
x = 40/9/8
x = 5/9


Input: Find the solution to 9x + 153 = 0

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


Input: Compute the solution of x^3 - 26/9x^2 - 200/27x + 1600/81 = 0

Output:
x^3 - 26/9x^2 - 200/27x + 1600/81 = 0
(x - 20/9)(x - 10/3)(x - -8/3) = 0
x - 20/9 = 0
x - 10/3 = 0
x - -8/3 = 0
x = 20/9
x = 10/3
x = -8/3


Input: Solve 5x - 65/3 = 0

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


Input: Compute the solution of 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: Solve the equation 5x + 10 = 0

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


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

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


Input: Find x for 4x  = 0

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


Input: Solve the equation 3x + 24 = 0

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


Input:
Solve simultaneously:
8x + 4y = -184/5
6x + 8y = -288/5

Output:
8x + 4y = -184/5
6x + 8y = -288/5

Using elimination
6*(8x + 4y = -184/5)
8*(6x + 8y = -288/5)
48x + 24y = -1104/5
48x + 64y = -2304/5
Subtract equations
-40y = 240
y = 240/-40
y = -6

Substitute y
8x + 4(-6) = -184/5
8x = -64/5
x = -64/5/8
x = -8/5


Input: Find x for x^3 - 7/5x^2 - 32/5x + 52/5 = 0

Output:
x^3 - 7/5x^2 - 32/5x + 52/5 = 0
(x - 2)(x - 2)(x - -13/5) = 0
x - 2 = 0
x - 2 = 0
x - -13/5 = 0
x = 2
x = 2
x = -13/5


Input: Find the solution to x^2 - 12/7x - 27/7 = 0

Output:
x^2 - 12/7x - 27/7 = 0
(x - 3)(x - -9/7) = 0
x - 3 = 0  or  x - -9/7 = 0
x = 3
x = -9/7


Input: What value of x satisfies x^2 - 19/2x + 45/2 = 0

Output:
x^2 - 19/2x + 45/2 = 0
(x - 9/2)(x - 5) = 0
x - 9/2 = 0  or  x - 5 = 0
x = 9/2
x = 5


Input:
Solve the system:
9x + 4y = 349/7
8x + 4y = 928/21

Output:
9x + 4y = 349/7
8x + 4y = 928/21

Using elimination
8*(9x + 4y = 349/7)
9*(8x + 4y = 928/21)
72x + 32y = 2792/7
72x + 36y = 2784/7
Subtract equations
-4y = 8/7
y = 8/7/-4
y = -2/7

Substitute y
9x + 4(-2/7) = 349/7
9x = 51
x = 51/9
x = 17/3


Input: Find the solution to x^2 + 37/8x + 39/8 = 0

Output:
x^2 + 37/8x + 39/8 = 0
(x - -13/8)(x - -3) = 0
x - -13/8 = 0  or  x - -3 = 0
x = -13/8
x = -3


Input:
Solve the equations:
10x + 1y = -55/3
9x + 1y = -49/3

Output:
10x + 1y = -55/3
9x + 1y = -49/3

Using elimination
9*(10x + 1y = -55/3)
10*(9x + 1y = -49/3)
90x + 9y = -165
90x + 10y = -490/3
Subtract equations
-1y = -5/3
y = -5/3/-1
y = 5/3

Substitute y
10x + 1(5/3) = -55/3
10x = -20
x = -20/10
x = -2


Input: Find x in 7x - 63/5 = 0

Output:
7x - 63/5 = 0
7x = 63/5
x = 63/5 / 7
x = 9/5


Input:
Solve the equations:
6x + 4y = 145/6
6x + 10y = 241/6

Output:
6x + 4y = 145/6
6x + 10y = 241/6

Using elimination
6*(6x + 4y = 145/6)
6*(6x + 10y = 241/6)
36x + 24y = 145
36x + 60y = 241
Subtract equations
-36y = -96
y = -96/-36
y = 8/3

Substitute y
6x + 4(8/3) = 145/6
6x = 27/2
x = 27/2/6
x = 9/4


Input:
Solve the system:
7x + 2y = -341/30
6x + 3y = -83/5

Output:
7x + 2y = -341/30
6x + 3y = -83/5

Using elimination
6*(7x + 2y = -341/30)
7*(6x + 3y = -83/5)
42x + 12y = -341/5
42x + 21y = -581/5
Subtract equations
-9y = 48
y = 48/-9
y = -16/3

Substitute y
7x + 2(-16/3) = -341/30
7x = -7/10
x = -7/10/7
x = -1/10


Input: Solve x^2 - 7/10x - 17/10 = 0

Output:
x^2 - 7/10x - 17/10 = 0
(x - -1)(x - 17/10) = 0
x - -1 = 0  or  x - 17/10 = 0
x = -1
x = 17/10


Input: What value of x satisfies 6x + 24 = 0

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


Input: Find x for 9x + 9 = 0

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


Input:
Solve simultaneously:
3x + 7y = 25
10x + 6y = 14

Output:
3x + 7y = 25
10x + 6y = 14

Using elimination
10*(3x + 7y = 25)
3*(10x + 6y = 14)
30x + 70y = 250
30x + 18y = 42
Subtract equations
52y = 208
y = 208/52
y = 4

Substitute y
3x + 7(4) = 25
3x = -3
x = -3/3
x = -1


Input: Compute the solution of x^3 - 92/35x^2 + 361/175x - 12/25 = 0

Output:
x^3 - 92/35x^2 + 361/175x - 12/25 = 0
(x - 3/7)(x - 7/5)(x - 4/5) = 0
x - 3/7 = 0
x - 7/5 = 0
x - 4/5 = 0
x = 3/7
x = 7/5
x = 4/5


Input:
Solve the system:
5x + 10y = -305/12
10x + 8y = -113/6

Output:
5x + 10y = -305/12
10x + 8y = -113/6

Using elimination
10*(5x + 10y = -305/12)
5*(10x + 8y = -113/6)
50x + 100y = -1525/6
50x + 40y = -565/6
Subtract equations
60y = -160
y = -160/60
y = -8/3

Substitute y
5x + 10(-8/3) = -305/12
5x = 5/4
x = 5/4/5
x = 1/4


Input:
Solve the system:
4x + 4y = -8/3
7x + 8y = -15/2

Output:
4x + 4y = -8/3
7x + 8y = -15/2

Using elimination
7*(4x + 4y = -8/3)
4*(7x + 8y = -15/2)
28x + 28y = -56/3
28x + 32y = -30
Subtract equations
-4y = 34/3
y = 34/3/-4
y = -17/6

Substitute y
4x + 4(-17/6) = -8/3
4x = 26/3
x = 26/3/4
x = 13/6


Input: What value of x satisfies x^2 + 8/9x - 19/3 = 0

Output:
x^2 + 8/9x - 19/3 = 0
(x - -3)(x - 19/9) = 0
x - -3 = 0  or  x - 19/9 = 0
x = -3
x = 19/9


Input: Solve quickly: 10x - 65/3 = 0

Output:
10x - 65/3 = 0
10x = 65/3
x = 65/3 / 10
x = 13/6


Input: Solve quickly: 9x + 7 = 0

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


Input:
Solve simultaneously:
1x + 2y = -13/3
8x + 8y = -76/3

Output:
1x + 2y = -13/3
8x + 8y = -76/3

Using elimination
8*(1x + 2y = -13/3)
1*(8x + 8y = -76/3)
8x + 16y = -104/3
8x + 8y = -76/3
Subtract equations
8y = -28/3
y = -28/3/8
y = -7/6

Substitute y
1x + 2(-7/6) = -13/3
1x = -2
x = -2/1
x = -2


Input:
Solve the equations:
10x + 8y = -137/6
7x + 1y = -17/12

Output:
10x + 8y = -137/6
7x + 1y = -17/12

Using elimination
7*(10x + 8y = -137/6)
10*(7x + 1y = -17/12)
70x + 56y = -959/6
70x + 10y = -85/6
Subtract equations
46y = -437/3
y = -437/3/46
y = -19/6

Substitute y
10x + 8(-19/6) = -137/6
10x = 5/2
x = 5/2/10
x = 1/4


Input: What value of x satisfies x^3 + 7/3x^2 - 91/3x - 95/3 = 0

Output:
x^3 + 7/3x^2 - 91/3x - 95/3 = 0
(x - -1)(x - -19/3)(x - 5) = 0
x - -1 = 0
x - -19/3 = 0
x - 5 = 0
x = -1
x = -19/3
x = 5


Input: Compute the solution of 9x - 117/5 = 0

Output:
9x - 117/5 = 0
9x = 117/5
x = 117/5 / 9
x = 13/5


Input: Find the solution to x^2 - 19/2x + 45/2 = 0

Output:
x^2 - 19/2x + 45/2 = 0
(x - 9/2)(x - 5) = 0
x - 9/2 = 0  or  x - 5 = 0
x = 9/2
x = 5


Input: Find x in x^3 + 29/6x^2 - 11/16x - 455/24 = 0

Output:
x^3 + 29/6x^2 - 11/16x - 455/24 = 0
(x - -13/4)(x - -10/3)(x - 7/4) = 0
x - -13/4 = 0
x - -10/3 = 0
x - 7/4 = 0
x = -13/4
x = -10/3
x = 7/4


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

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


Input: Find x in x^3 - 1/3x^2 - 25/12x + 1 = 0

Output:
x^3 - 1/3x^2 - 25/12x + 1 = 0
(x - 4/3)(x - 1/2)(x - -3/2) = 0
x - 4/3 = 0
x - 1/2 = 0
x - -3/2 = 0
x = 4/3
x = 1/2
x = -3/2


Input:
Find x and y such that
4x + 4y = -26
4x + 10y = -59

Output:
4x + 4y = -26
4x + 10y = -59

Using elimination
4*(4x + 4y = -26)
4*(4x + 10y = -59)
16x + 16y = -104
16x + 40y = -236
Subtract equations
-24y = 132
y = 132/-24
y = -11/2

Substitute y
4x + 4(-11/2) = -26
4x = -4
x = -4/4
x = -1


Input: Solve 3x + 10 = 0

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


Input:
Solve the equations:
9x + 2y = 51
8x + 9y = 67

Output:
9x + 2y = 51
8x + 9y = 67

Using elimination
8*(9x + 2y = 51)
9*(8x + 9y = 67)
72x + 16y = 408
72x + 81y = 603
Subtract equations
-65y = -195
y = -195/-65
y = 3

Substitute y
9x + 2(3) = 51
9x = 45
x = 45/9
x = 5


Input: Solve 2x + 17/2 = 0

Output:
2x + 17/2 = 0
2x = -17/2
x = -17/2 / 2
x = -17/4


Input: Solve quickly: x^2 + 26/15x - 96/5 = 0

Output:
x^2 + 26/15x - 96/5 = 0
(x - 18/5)(x - -16/3) = 0
x - 18/5 = 0  or  x - -16/3 = 0
x = 18/5
x = -16/3


Input: Find x for x^3 + 10/3x^2 - 397/75x - 104/25 = 0

Output:
x^3 + 10/3x^2 - 397/75x - 104/25 = 0
(x - -3/5)(x - 8/5)(x - -13/3) = 0
x - -3/5 = 0
x - 8/5 = 0
x - -13/3 = 0
x = -3/5
x = 8/5
x = -13/3


Input: Compute the solution of x^2 + 10/3x - 16 = 0

Output:
x^2 + 10/3x - 16 = 0
(x - -6)(x - 8/3) = 0
x - -6 = 0  or  x - 8/3 = 0
x = -6
x = 8/3


Input: Find x for x^2 - 139/28x + 171/28 = 0

Output:
x^2 - 139/28x + 171/28 = 0
(x - 19/7)(x - 9/4) = 0
x - 19/7 = 0  or  x - 9/4 = 0
x = 19/7
x = 9/4


Input:
Solve simultaneously:
8x + 7y = 475/8
8x + 2y = 205/4

Output:
8x + 7y = 475/8
8x + 2y = 205/4

Using elimination
8*(8x + 7y = 475/8)
8*(8x + 2y = 205/4)
64x + 56y = 475
64x + 16y = 410
Subtract equations
40y = 65
y = 65/40
y = 13/8

Substitute y
8x + 7(13/8) = 475/8
8x = 48
x = 48/8
x = 6


Input:
Solve the equations:
5x + 8y = -3/2
8x + 5y = -75/2

Output:
5x + 8y = -3/2
8x + 5y = -75/2

Using elimination
8*(5x + 8y = -3/2)
5*(8x + 5y = -75/2)
40x + 64y = -12
40x + 25y = -375/2
Subtract equations
39y = 351/2
y = 351/2/39
y = 9/2

Substitute y
5x + 8(9/2) = -3/2
5x = -75/2
x = -75/2/5
x = -15/2


Input: Solve quickly: 1x - 8/9 = 0

Output:
1x - 8/9 = 0
1x = 8/9
x = 8/9 / 1
x = 8/9


Input:
Solve the system:
3x + 1y = 43/4
8x + 4y = 89/3

Output:
3x + 1y = 43/4
8x + 4y = 89/3

Using elimination
8*(3x + 1y = 43/4)
3*(8x + 4y = 89/3)
24x + 8y = 86
24x + 12y = 89
Subtract equations
-4y = -3
y = -3/-4
y = 3/4

Substitute y
3x + 1(3/4) = 43/4
3x = 10
x = 10/3
x = 10/3


Input: Solve the equation 10x - 55 = 0

Output:
10x - 55 = 0
10x = 55
x = 55 / 10
x = 11/2


Input: Compute the solution of x^2 + 19/21x - 170/21 = 0

Output:
x^2 + 19/21x - 170/21 = 0
(x - 17/7)(x - -10/3) = 0
x - 17/7 = 0  or  x - -10/3 = 0
x = 17/7
x = -10/3


Input: Determine x in x^3 - 1943/504x^2 + 229/56x - 221/252 = 0

Output:
x^3 - 1943/504x^2 + 229/56x - 221/252 = 0
(x - 2/7)(x - 17/8)(x - 13/9) = 0
x - 2/7 = 0
x - 17/8 = 0
x - 13/9 = 0
x = 2/7
x = 17/8
x = 13/9


Input: What value of x satisfies 4x + 80/3 = 0

Output:
4x + 80/3 = 0
4x = -80/3
x = -80/3 / 4
x = -20/3


Input: What value of x satisfies x^3 + 159/140x^2 - 139/280x - 33/56 = 0

Output:
x^3 + 159/140x^2 - 139/280x - 33/56 = 0
(x - -11/10)(x - -3/4)(x - 5/7) = 0
x - -11/10 = 0
x - -3/4 = 0
x - 5/7 = 0
x = -11/10
x = -3/4
x = 5/7


Input: Solve 1x - 13/4 = 0

Output:
1x - 13/4 = 0
1x = 13/4
x = 13/4 / 1
x = 13/4


Input:
Solve the system:
6x + 6y = -42
9x + 6y = -129/2

Output:
6x + 6y = -42
9x + 6y = -129/2

Using elimination
9*(6x + 6y = -42)
6*(9x + 6y = -129/2)
54x + 54y = -378
54x + 36y = -387
Subtract equations
18y = 9
y = 9/18
y = 1/2

Substitute y
6x + 6(1/2) = -42
6x = -45
x = -45/6
x = -15/2


Input: Find x in x^3 + 139/10x^2 + 107/2x + 252/5 = 0

Output:
x^3 + 139/10x^2 + 107/2x + 252/5 = 0
(x - -9/2)(x - -7/5)(x - -8) = 0
x - -9/2 = 0
x - -7/5 = 0
x - -8 = 0
x = -9/2
x = -7/5
x = -8


Input:
Find x and y such that
4x + 3y = 129/5
7x + 8y = 699/10

Output:
4x + 3y = 129/5
7x + 8y = 699/10

Using elimination
7*(4x + 3y = 129/5)
4*(7x + 8y = 699/10)
28x + 21y = 903/5
28x + 32y = 1398/5
Subtract equations
-11y = -99
y = -99/-11
y = 9

Substitute y
4x + 3(9) = 129/5
4x = -6/5
x = -6/5/4
x = -3/10


Input: Find the solution to x^3 - 115/72x^2 - 383/216x - 19/108 = 0

Output:
x^3 - 115/72x^2 - 383/216x - 19/108 = 0
(x - 19/8)(x - -1/9)(x - -2/3) = 0
x - 19/8 = 0
x - -1/9 = 0
x - -2/3 = 0
x = 19/8
x = -1/9
x = -2/3


Input: Solve 8x + 7 = 0

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


Input: Find x in x^2 + 111/56x + 27/28 = 0

Output:
x^2 + 111/56x + 27/28 = 0
(x - -6/7)(x - -9/8) = 0
x - -6/7 = 0  or  x - -9/8 = 0
x = -6/7
x = -9/8


Input: Solve the equation 5x + 65/4 = 0

Output:
5x + 65/4 = 0
5x = -65/4
x = -65/4 / 5
x = -13/4


Input: Find the solution to x^2 - 2/3x - 8/3 = 0

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


Input:
Solve the equations:
6x + 10y = 8/3
8x + 4y = 104/3

Output:
6x + 10y = 8/3
8x + 4y = 104/3

Using elimination
8*(6x + 10y = 8/3)
6*(8x + 4y = 104/3)
48x + 80y = 64/3
48x + 24y = 208
Subtract equations
56y = -560/3
y = -560/3/56
y = -10/3

Substitute y
6x + 10(-10/3) = 8/3
6x = 36
x = 36/6
x = 6


Input: Find the solution to x^3 - 17/5x^2 - 193/25x - 7/5 = 0

Output:
x^3 - 17/5x^2 - 193/25x - 7/5 = 0
(x - -7/5)(x - -1/5)(x - 5) = 0
x - -7/5 = 0
x - -1/5 = 0
x - 5 = 0
x = -7/5
x = -1/5
x = 5


Input: Solve the equation x^3 - 151/24x^2 + 683/96x + 95/96 = 0

Output:
x^3 - 151/24x^2 + 683/96x + 95/96 = 0
(x - 5/3)(x - -1/8)(x - 19/4) = 0
x - 5/3 = 0
x - -1/8 = 0
x - 19/4 = 0
x = 5/3
x = -1/8
x = 19/4


Input: Compute the solution of x^2 - 19/6x + 13/6 = 0

Output:
x^2 - 19/6x + 13/6 = 0
(x - 1)(x - 13/6) = 0
x - 1 = 0  or  x - 13/6 = 0
x = 1
x = 13/6


Input: Determine x in 6x - 12/5 = 0

Output:
6x - 12/5 = 0
6x = 12/5
x = 12/5 / 6
x = 2/5


Input: Compute the solution of x^2 + 23/4x + 45/8 = 0

Output:
x^2 + 23/4x + 45/8 = 0
(x - -5/4)(x - -9/2) = 0
x - -5/4 = 0  or  x - -9/2 = 0
x = -5/4
x = -9/2


Input: Solve quickly: x^2 + 7/6x - 10/3 = 0

Output:
x^2 + 7/6x - 10/3 = 0
(x - -5/2)(x - 4/3) = 0
x - -5/2 = 0  or  x - 4/3 = 0
x = -5/2
x = 4/3


Input: Solve quickly: 6x + 22 = 0

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


Input:
Find x and y such that
2x + 1y = -8/5
3x + 7y = 43/5

Output:
2x + 1y = -8/5
3x + 7y = 43/5

Using elimination
3*(2x + 1y = -8/5)
2*(3x + 7y = 43/5)
6x + 3y = -24/5
6x + 14y = 86/5
Subtract equations
-11y = -22
y = -22/-11
y = 2

Substitute y
2x + 1(2) = -8/5
2x = -18/5
x = -18/5/2
x = -9/5


Input:
Find x and y such that
4x + 10y = 788/45
1x + 1y = 122/45

Output:
4x + 10y = 788/45
1x + 1y = 122/45

Using elimination
1*(4x + 10y = 788/45)
4*(1x + 1y = 122/45)
4x + 10y = 788/45
4x + 4y = 488/45
Subtract equations
6y = 20/3
y = 20/3/6
y = 10/9

Substitute y
4x + 10(10/9) = 788/45
4x = 32/5
x = 32/5/4
x = 8/5


Input: Solve quickly: 10x - 160 = 0

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


Input: Determine x in x^3 + 91/5x^2 + 14/5x - 72/5 = 0

Output:
x^3 + 91/5x^2 + 14/5x - 72/5 = 0
(x - -1)(x - -18)(x - 4/5) = 0
x - -1 = 0
x - -18 = 0
x - 4/5 = 0
x = -1
x = -18
x = 4/5


Input:
Solve the equations:
9x + 3y = 1/2
7x + 3y = 5/2

Output:
9x + 3y = 1/2
7x + 3y = 5/2

Using elimination
7*(9x + 3y = 1/2)
9*(7x + 3y = 5/2)
63x + 21y = 7/2
63x + 27y = 45/2
Subtract equations
-6y = -19
y = -19/-6
y = 19/6

Substitute y
9x + 3(19/6) = 1/2
9x = -9
x = -9/9
x = -1


Input: Determine x in 2x - 15/4 = 0

Output:
2x - 15/4 = 0
2x = 15/4
x = 15/4 / 2
x = 15/8


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

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


Input: Find the solution to 3x + 1/2 = 0

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


Input: Solve quickly: x^2 - 7/18x - 104/27 = 0

Output:
x^2 - 7/18x - 104/27 = 0
(x - 13/6)(x - -16/9) = 0
x - 13/6 = 0  or  x - -16/9 = 0
x = 13/6
x = -16/9


Input:
Solve the equations:
5x + 9y = 42
4x + 4y = 296/9

Output:
5x + 9y = 42
4x + 4y = 296/9

Using elimination
4*(5x + 9y = 42)
5*(4x + 4y = 296/9)
20x + 36y = 168
20x + 20y = 1480/9
Subtract equations
16y = 32/9
y = 32/9/16
y = 2/9

Substitute y
5x + 9(2/9) = 42
5x = 40
x = 40/5
x = 8


Input: Solve quickly: x^3 - 20/3x^2   = 0

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


Input: Compute the solution of x^2 + 5/2x - 25/2 = 0

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


Input: Solve 10x - 100 = 0

Output:
10x - 100 = 0
10x = 100
x = 100 / 10
x = 10


Input:
Solve simultaneously:
1x + 1y = -31/12
1x + 9y = 41/12

Output:
1x + 1y = -31/12
1x + 9y = 41/12

Using elimination
1*(1x + 1y = -31/12)
1*(1x + 9y = 41/12)
1x + 1y = -31/12
1x + 9y = 41/12
Subtract equations
-8y = -6
y = -6/-8
y = 3/4

Substitute y
1x + 1(3/4) = -31/12
1x = -10/3
x = -10/3/1
x = -10/3


Input:
Find x and y such that
6x + 5y = 43/4
2x + 4y = 3

Output:
6x + 5y = 43/4
2x + 4y = 3

Using elimination
2*(6x + 5y = 43/4)
6*(2x + 4y = 3)
12x + 10y = 43/2
12x + 24y = 18
Subtract equations
-14y = 7/2
y = 7/2/-14
y = -1/4

Substitute y
6x + 5(-1/4) = 43/4
6x = 12
x = 12/6
x = 2


Input: Solve quickly: x^3 - 17/7x^2 - 460/63x + 100/7 = 0

Output:
x^3 - 17/7x^2 - 460/63x + 100/7 = 0
(x - 10/3)(x - -18/7)(x - 5/3) = 0
x - 10/3 = 0
x - -18/7 = 0
x - 5/3 = 0
x = 10/3
x = -18/7
x = 5/3


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

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


Input:
Find x and y such that
7x + 5y = 40/3
5x + 7y = 80/3

Output:
7x + 5y = 40/3
5x + 7y = 80/3

Using elimination
5*(7x + 5y = 40/3)
7*(5x + 7y = 80/3)
35x + 25y = 200/3
35x + 49y = 560/3
Subtract equations
-24y = -120
y = -120/-24
y = 5

Substitute y
7x + 5(5) = 40/3
7x = -35/3
x = -35/3/7
x = -5/3


Input: What value of x satisfies x^2 + 61/5x - 52/5 = 0

Output:
x^2 + 61/5x - 52/5 = 0
(x - -13)(x - 4/5) = 0
x - -13 = 0  or  x - 4/5 = 0
x = -13
x = 4/5


Input:
Solve the equations:
4x + 9y = 26
10x + 10y = 460/9

Output:
4x + 9y = 26
10x + 10y = 460/9

Using elimination
10*(4x + 9y = 26)
4*(10x + 10y = 460/9)
40x + 90y = 260
40x + 40y = 1840/9
Subtract equations
50y = 500/9
y = 500/9/50
y = 10/9

Substitute y
4x + 9(10/9) = 26
4x = 16
x = 16/4
x = 4


Input:
Find x and y such that
9x + 4y = 13/10
7x + 1y = 241/40

Output:
9x + 4y = 13/10
7x + 1y = 241/40

Using elimination
7*(9x + 4y = 13/10)
9*(7x + 1y = 241/40)
63x + 28y = 91/10
63x + 9y = 2169/40
Subtract equations
19y = -361/8
y = -361/8/19
y = -19/8

Substitute y
9x + 4(-19/8) = 13/10
9x = 54/5
x = 54/5/9
x = 6/5


Input: Find x for x^2 + 82/5x - 51/5 = 0

Output:
x^2 + 82/5x - 51/5 = 0
(x - -17)(x - 3/5) = 0
x - -17 = 0  or  x - 3/5 = 0
x = -17
x = 3/5


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

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


Input: Find x for x^3 - 62/63x^2 - 655/189x + 100/63 = 0

Output:
x^3 - 62/63x^2 - 655/189x + 100/63 = 0
(x - 20/9)(x - 3/7)(x - -5/3) = 0
x - 20/9 = 0
x - 3/7 = 0
x - -5/3 = 0
x = 20/9
x = 3/7
x = -5/3


Input: Solve quickly: x^2 - 103/8x + 21/2 = 0

Output:
x^2 - 103/8x + 21/2 = 0
(x - 12)(x - 7/8) = 0
x - 12 = 0  or  x - 7/8 = 0
x = 12
x = 7/8


Input: Solve quickly: x^2 - 58/3x + 19/3 = 0

Output:
x^2 - 58/3x + 19/3 = 0
(x - 1/3)(x - 19) = 0
x - 1/3 = 0  or  x - 19 = 0
x = 1/3
x = 19


Input: Find x for x^3 - 281/120x^2 - 1283/240x + 143/80 = 0

Output:
x^3 - 281/120x^2 - 1283/240x + 143/80 = 0
(x - 11/3)(x - 3/10)(x - -13/8) = 0
x - 11/3 = 0
x - 3/10 = 0
x - -13/8 = 0
x = 11/3
x = 3/10
x = -13/8


Input: Find x for x^2 + 167/45x + 2/5 = 0

Output:
x^2 + 167/45x + 2/5 = 0
(x - -18/5)(x - -1/9) = 0
x - -18/5 = 0  or  x - -1/9 = 0
x = -18/5
x = -1/9


Input: Solve the equation x^2 - 5x - 39/4 = 0

Output:
x^2 - 5x - 39/4 = 0
(x - -3/2)(x - 13/2) = 0
x - -3/2 = 0  or  x - 13/2 = 0
x = -3/2
x = 13/2


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

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


Input: What value of x satisfies 6x  = 0

Output:
6x  = 0
6x = 0
x = 0 / 6
x = 0


Input: Determine x in x^2 + 2/5x - 3/25 = 0

Output:
x^2 + 2/5x - 3/25 = 0
(x - 1/5)(x - -3/5) = 0
x - 1/5 = 0  or  x - -3/5 = 0
x = 1/5
x = -3/5


Input: Solve x^3 + 382/63x^2 + 760/189x + 128/189 = 0

Output:
x^3 + 382/63x^2 + 760/189x + 128/189 = 0
(x - -4/9)(x - -2/7)(x - -16/3) = 0
x - -4/9 = 0
x - -2/7 = 0
x - -16/3 = 0
x = -4/9
x = -2/7
x = -16/3


Input: Compute the solution of 3x - 33/4 = 0

Output:
3x - 33/4 = 0
3x = 33/4
x = 33/4 / 3
x = 11/4


Input:
Solve the equations:
10x + 6y = -39
6x + 8y = -46/3

Output:
10x + 6y = -39
6x + 8y = -46/3

Using elimination
6*(10x + 6y = -39)
10*(6x + 8y = -46/3)
60x + 36y = -234
60x + 80y = -460/3
Subtract equations
-44y = -242/3
y = -242/3/-44
y = 11/6

Substitute y
10x + 6(11/6) = -39
10x = -50
x = -50/10
x = -5


Input: Solve the equation 9x - 45/4 = 0

Output:
9x - 45/4 = 0
9x = 45/4
x = 45/4 / 9
x = 5/4


Input:
Find x and y such that
10x + 10y = -210
4x + 10y = -102

Output:
10x + 10y = -210
4x + 10y = -102

Using elimination
4*(10x + 10y = -210)
10*(4x + 10y = -102)
40x + 40y = -840
40x + 100y = -1020
Subtract equations
-60y = 180
y = 180/-60
y = -3

Substitute y
10x + 10(-3) = -210
10x = -180
x = -180/10
x = -18


Input: What value of x satisfies 9x + 45 = 0

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


Input: Determine x in 10x - 130/9 = 0

Output:
10x - 130/9 = 0
10x = 130/9
x = 130/9 / 10
x = 13/9


Input: Find x for x^2 + 5x - 75/4 = 0

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


Input:
Solve the equations:
9x + 1y = 27/4
4x + 10y = 46

Output:
9x + 1y = 27/4
4x + 10y = 46

Using elimination
4*(9x + 1y = 27/4)
9*(4x + 10y = 46)
36x + 4y = 27
36x + 90y = 414
Subtract equations
-86y = -387
y = -387/-86
y = 9/2

Substitute y
9x + 1(9/2) = 27/4
9x = 9/4
x = 9/4/9
x = 1/4


Input: Solve x^3 - 18/7x^2 - 40/7x  = 0

Output:
x^3 - 18/7x^2 - 40/7x  = 0
(x - 4)(x - -10/7)(x - 0) = 0
x - 4 = 0
x - -10/7 = 0
x - 0 = 0
x = 4
x = -10/7
x = 0


Input:
Solve the equations:
2x + 9y = 242/35
9x + 2y = -66/35

Output:
2x + 9y = 242/35
9x + 2y = -66/35

Using elimination
9*(2x + 9y = 242/35)
2*(9x + 2y = -66/35)
18x + 81y = 2178/35
18x + 4y = -132/35
Subtract equations
77y = 66
y = 66/77
y = 6/7

Substitute y
2x + 9(6/7) = 242/35
2x = -4/5
x = -4/5/2
x = -2/5


Input: Find x in x^3 - 41/6x^2 - 374/9x - 847/18 = 0

Output:
x^3 - 41/6x^2 - 374/9x - 847/18 = 0
(x - -7/3)(x - 11)(x - -11/6) = 0
x - -7/3 = 0
x - 11 = 0
x - -11/6 = 0
x = -7/3
x = 11
x = -11/6


Input: Find the solution to 4x - 36 = 0

Output:
4x - 36 = 0
4x = 36
x = 36 / 4
x = 9


Input:
Solve the equations:
3x + 7y = -14/5
5x + 3y = 112/15

Output:
3x + 7y = -14/5
5x + 3y = 112/15

Using elimination
5*(3x + 7y = -14/5)
3*(5x + 3y = 112/15)
15x + 35y = -14
15x + 9y = 112/5
Subtract equations
26y = -182/5
y = -182/5/26
y = -7/5

Substitute y
3x + 7(-7/5) = -14/5
3x = 7
x = 7/3
x = 7/3


Input: Find the solution to 1x + 11/3 = 0

Output:
1x + 11/3 = 0
1x = -11/3
x = -11/3 / 1
x = -11/3


Input:
Solve the system:
3x + 9y = -28/3
10x + 3y = -91/9

Output:
3x + 9y = -28/3
10x + 3y = -91/9

Using elimination
10*(3x + 9y = -28/3)
3*(10x + 3y = -91/9)
30x + 90y = -280/3
30x + 9y = -91/3
Subtract equations
81y = -63
y = -63/81
y = -7/9

Substitute y
3x + 9(-7/9) = -28/3
3x = -7/3
x = -7/3/3
x = -7/9


Input:
Solve the system:
1x + 8y = 70/3
5x + 2y = -11/3

Output:
1x + 8y = 70/3
5x + 2y = -11/3

Using elimination
5*(1x + 8y = 70/3)
1*(5x + 2y = -11/3)
5x + 40y = 350/3
5x + 2y = -11/3
Subtract equations
38y = 361/3
y = 361/3/38
y = 19/6

Substitute y
1x + 8(19/6) = 70/3
1x = -2
x = -2/1
x = -2


Input: What value of x satisfies x^2 + 77/6x + 85/3 = 0

Output:
x^2 + 77/6x + 85/3 = 0
(x - -10)(x - -17/6) = 0
x - -10 = 0  or  x - -17/6 = 0
x = -10
x = -17/6


Input:
Find x and y such that
6x + 9y = -12
9x + 1y = 13/9

Output:
6x + 9y = -12
9x + 1y = 13/9

Using elimination
9*(6x + 9y = -12)
6*(9x + 1y = 13/9)
54x + 81y = -108
54x + 6y = 26/3
Subtract equations
75y = -350/3
y = -350/3/75
y = -14/9

Substitute y
6x + 9(-14/9) = -12
6x = 2
x = 2/6
x = 1/3


Input:
Solve the equations:
10x + 5y = 245/18
9x + 4y = 455/36

Output:
10x + 5y = 245/18
9x + 4y = 455/36

Using elimination
9*(10x + 5y = 245/18)
10*(9x + 4y = 455/36)
90x + 45y = 245/2
90x + 40y = 2275/18
Subtract equations
5y = -35/9
y = -35/9/5
y = -7/9

Substitute y
10x + 5(-7/9) = 245/18
10x = 35/2
x = 35/2/10
x = 7/4


Input:
Solve the system:
5x + 5y = -37/9
8x + 4y = -436/45

Output:
5x + 5y = -37/9
8x + 4y = -436/45

Using elimination
8*(5x + 5y = -37/9)
5*(8x + 4y = -436/45)
40x + 40y = -296/9
40x + 20y = -436/9
Subtract equations
20y = 140/9
y = 140/9/20
y = 7/9

Substitute y
5x + 5(7/9) = -37/9
5x = -8
x = -8/5
x = -8/5


Input: Determine x in x^2 - 8/9x - 17/9 = 0

Output:
x^2 - 8/9x - 17/9 = 0
(x - 17/9)(x - -1) = 0
x - 17/9 = 0  or  x - -1 = 0
x = 17/9
x = -1


Input: Find x for x^3 + 3/4x^2 - 64/9x - 16/3 = 0

Output:
x^3 + 3/4x^2 - 64/9x - 16/3 = 0
(x - 8/3)(x - -8/3)(x - -3/4) = 0
x - 8/3 = 0
x - -8/3 = 0
x - -3/4 = 0
x = 8/3
x = -8/3
x = -3/4


Input: Solve quickly: x^2 - 13/15x + 2/15 = 0

Output:
x^2 - 13/15x + 2/15 = 0
(x - 1/5)(x - 2/3) = 0
x - 1/5 = 0  or  x - 2/3 = 0
x = 1/5
x = 2/3


Input: What value of x satisfies 8x - 80 = 0

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


Input:
Solve simultaneously:
5x + 7y = 227/3
7x + 4y = 196/3

Output:
5x + 7y = 227/3
7x + 4y = 196/3

Using elimination
7*(5x + 7y = 227/3)
5*(7x + 4y = 196/3)
35x + 49y = 1589/3
35x + 20y = 980/3
Subtract equations
29y = 203
y = 203/29
y = 7

Substitute y
5x + 7(7) = 227/3
5x = 80/3
x = 80/3/5
x = 16/3


Input: Solve quickly: x^3 - 127/21x^2 + 220/21x - 100/21 = 0

Output:
x^3 - 127/21x^2 + 220/21x - 100/21 = 0
(x - 5/7)(x - 2)(x - 10/3) = 0
x - 5/7 = 0
x - 2 = 0
x - 10/3 = 0
x = 5/7
x = 2
x = 10/3


Input:
Solve the equations:
1x + 3y = 3
10x + 7y = 44/3

Output:
1x + 3y = 3
10x + 7y = 44/3

Using elimination
10*(1x + 3y = 3)
1*(10x + 7y = 44/3)
10x + 30y = 30
10x + 7y = 44/3
Subtract equations
23y = 46/3
y = 46/3/23
y = 2/3

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


Input:
Solve the system:
7x + 7y = -490/9
5x + 7y = -458/9

Output:
7x + 7y = -490/9
5x + 7y = -458/9

Using elimination
5*(7x + 7y = -490/9)
7*(5x + 7y = -458/9)
35x + 35y = -2450/9
35x + 49y = -3206/9
Subtract equations
-14y = 84
y = 84/-14
y = -6

Substitute y
7x + 7(-6) = -490/9
7x = -112/9
x = -112/9/7
x = -16/9


Input: Find the solution to 8x - 36 = 0

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


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

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


Input: Find the solution to x^3 - 111/10x^2 + 81/2x - 243/5 = 0

Output:
x^3 - 111/10x^2 + 81/2x - 243/5 = 0
(x - 9/2)(x - 18/5)(x - 3) = 0
x - 9/2 = 0
x - 18/5 = 0
x - 3 = 0
x = 9/2
x = 18/5
x = 3


Input:
Find x and y such that
2x + 8y = -34
3x + 10y = -45

Output:
2x + 8y = -34
3x + 10y = -45

Using elimination
3*(2x + 8y = -34)
2*(3x + 10y = -45)
6x + 24y = -102
6x + 20y = -90
Subtract equations
4y = -12
y = -12/4
y = -3

Substitute y
2x + 8(-3) = -34
2x = -10
x = -10/2
x = -5


Input: Find x for x^3 + 19/10x^2 - 76/5x + 3/2 = 0

Output:
x^3 + 19/10x^2 - 76/5x + 3/2 = 0
(x - 1/10)(x - -5)(x - 3) = 0
x - 1/10 = 0
x - -5 = 0
x - 3 = 0
x = 1/10
x = -5
x = 3


Input: Find the solution to x^2 + 91/9x + 10 = 0

Output:
x^2 + 91/9x + 10 = 0
(x - -10/9)(x - -9) = 0
x - -10/9 = 0  or  x - -9 = 0
x = -10/9
x = -9


Input: Compute the solution of x^2 + 46/9x - 280/27 = 0

Output:
x^2 + 46/9x - 280/27 = 0
(x - -20/3)(x - 14/9) = 0
x - -20/3 = 0  or  x - 14/9 = 0
x = -20/3
x = 14/9


Input:
Solve the system:
2x + 9y = -194/9
7x + 4y = -184/9

Output:
2x + 9y = -194/9
7x + 4y = -184/9

Using elimination
7*(2x + 9y = -194/9)
2*(7x + 4y = -184/9)
14x + 63y = -1358/9
14x + 8y = -368/9
Subtract equations
55y = -110
y = -110/55
y = -2

Substitute y
2x + 9(-2) = -194/9
2x = -32/9
x = -32/9/2
x = -16/9


Input: Solve the equation 4x + 12 = 0

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


Input:
Solve the system:
9x + 10y = -248/7
1x + 1y = -29/7

Output:
9x + 10y = -248/7
1x + 1y = -29/7

Using elimination
1*(9x + 10y = -248/7)
9*(1x + 1y = -29/7)
9x + 10y = -248/7
9x + 9y = -261/7
Subtract equations
1y = 13/7
y = 13/7/1
y = 13/7

Substitute y
9x + 10(13/7) = -248/7
9x = -54
x = -54/9
x = -6


Input:
Solve the equations:
5x + 10y = 137/7
1x + 6y = 397/35

Output:
5x + 10y = 137/7
1x + 6y = 397/35

Using elimination
1*(5x + 10y = 137/7)
5*(1x + 6y = 397/35)
5x + 10y = 137/7
5x + 30y = 397/7
Subtract equations
-20y = -260/7
y = -260/7/-20
y = 13/7

Substitute y
5x + 10(13/7) = 137/7
5x = 1
x = 1/5
x = 1/5


Input: Find x for x^3 - 185/14x^2 - 163/14x + 9 = 0

Output:
x^3 - 185/14x^2 - 163/14x + 9 = 0
(x - 1/2)(x - 14)(x - -9/7) = 0
x - 1/2 = 0
x - 14 = 0
x - -9/7 = 0
x = 1/2
x = 14
x = -9/7


Input: Find x for 1x - 3/2 = 0

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


Input: Find x in x^2 - 5x - 24 = 0

Output:
x^2 - 5x - 24 = 0
(x - -3)(x - 8) = 0
x - -3 = 0  or  x - 8 = 0
x = -3
x = 8


Input:
Solve the equations:
2x + 1y = 58/21
9x + 5y = 78/7

Output:
2x + 1y = 58/21
9x + 5y = 78/7

Using elimination
9*(2x + 1y = 58/21)
2*(9x + 5y = 78/7)
18x + 9y = 174/7
18x + 10y = 156/7
Subtract equations
-1y = 18/7
y = 18/7/-1
y = -18/7

Substitute y
2x + 1(-18/7) = 58/21
2x = 16/3
x = 16/3/2
x = 8/3


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

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


Input:
Solve simultaneously:
5x + 7y = 179/5
2x + 9y = 53/5

Output:
5x + 7y = 179/5
2x + 9y = 53/5

Using elimination
2*(5x + 7y = 179/5)
5*(2x + 9y = 53/5)
10x + 14y = 358/5
10x + 45y = 53
Subtract equations
-31y = 93/5
y = 93/5/-31
y = -3/5

Substitute y
5x + 7(-3/5) = 179/5
5x = 40
x = 40/5
x = 8


Input:
Solve the equations:
10x + 5y = -165/2
10x + 9y = -233/2

Output:
10x + 5y = -165/2
10x + 9y = -233/2

Using elimination
10*(10x + 5y = -165/2)
10*(10x + 9y = -233/2)
100x + 50y = -825
100x + 90y = -1165
Subtract equations
-40y = 340
y = 340/-40
y = -17/2

Substitute y
10x + 5(-17/2) = -165/2
10x = -40
x = -40/10
x = -4


Input: Find x for x^2 - 17/6x + 5/3 = 0

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


Input: Solve quickly: x^3 - 139/30x^2 + 139/30x - 1 = 0

Output:
x^3 - 139/30x^2 + 139/30x - 1 = 0
(x - 10/3)(x - 1)(x - 3/10) = 0
x - 10/3 = 0
x - 1 = 0
x - 3/10 = 0
x = 10/3
x = 1
x = 3/10


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

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


Input: Solve x^2 - 8x + 95/9 = 0

Output:
x^2 - 8x + 95/9 = 0
(x - 19/3)(x - 5/3) = 0
x - 19/3 = 0  or  x - 5/3 = 0
x = 19/3
x = 5/3


Input: Find the solution to x^3 + 7x^2 - 105x + 225 = 0

Output:
x^3 + 7x^2 - 105x + 225 = 0
(x - 5)(x - 3)(x - -15) = 0
x - 5 = 0
x - 3 = 0
x - -15 = 0
x = 5
x = 3
x = -15


Input: Solve x^2 + 13/6x - 5/2 = 0

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


Input:
Solve the system:
5x + 4y = 71/28
5x + 7y = 29/4

Output:
5x + 4y = 71/28
5x + 7y = 29/4

Using elimination
5*(5x + 4y = 71/28)
5*(5x + 7y = 29/4)
25x + 20y = 355/28
25x + 35y = 145/4
Subtract equations
-15y = -165/7
y = -165/7/-15
y = 11/7

Substitute y
5x + 4(11/7) = 71/28
5x = -15/4
x = -15/4/5
x = -3/4


Input:
Find x and y such that
3x + 6y = 53/21
2x + 7y = 64/63

Output:
3x + 6y = 53/21
2x + 7y = 64/63

Using elimination
2*(3x + 6y = 53/21)
3*(2x + 7y = 64/63)
6x + 12y = 106/21
6x + 21y = 64/21
Subtract equations
-9y = 2
y = 2/-9
y = -2/9

Substitute y
3x + 6(-2/9) = 53/21
3x = 27/7
x = 27/7/3
x = 9/7


Input: What value of x satisfies x^3 - 409/70x^2 + 153/14x - 45/7 = 0

Output:
x^3 - 409/70x^2 + 153/14x - 45/7 = 0
(x - 5/2)(x - 15/7)(x - 6/5) = 0
x - 5/2 = 0
x - 15/7 = 0
x - 6/5 = 0
x = 5/2
x = 15/7
x = 6/5


Input:
Solve the system:
9x + 4y = -59/14
3x + 4y = 39/14

Output:
9x + 4y = -59/14
3x + 4y = 39/14

Using elimination
3*(9x + 4y = -59/14)
9*(3x + 4y = 39/14)
27x + 12y = -177/14
27x + 36y = 351/14
Subtract equations
-24y = -264/7
y = -264/7/-24
y = 11/7

Substitute y
9x + 4(11/7) = -59/14
9x = -21/2
x = -21/2/9
x = -7/6


Input: Solve the equation x^3 - 5/2x^2 - 9/2x + 9 = 0

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


Input: Determine x in 3x + 6 = 0

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


Input: Find x in x^2 + 3x + 2 = 0

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


Input:
Solve simultaneously:
8x + 5y = -76
4x + 2y = -34

Output:
8x + 5y = -76
4x + 2y = -34

Using elimination
4*(8x + 5y = -76)
8*(4x + 2y = -34)
32x + 20y = -304
32x + 16y = -272
Subtract equations
4y = -32
y = -32/4
y = -8

Substitute y
8x + 5(-8) = -76
8x = -36
x = -36/8
x = -9/2


Input: Determine x in x^3 + 8/3x^2 - 157/12x - 85/12 = 0

Output:
x^3 + 8/3x^2 - 157/12x - 85/12 = 0
(x - -5)(x - -1/2)(x - 17/6) = 0
x - -5 = 0
x - -1/2 = 0
x - 17/6 = 0
x = -5
x = -1/2
x = 17/6


Input: Compute the solution of x^3 - 11/3x^2 - 32/9x + 140/9 = 0

Output:
x^3 - 11/3x^2 - 32/9x + 140/9 = 0
(x - 7/3)(x - -2)(x - 10/3) = 0
x - 7/3 = 0
x - -2 = 0
x - 10/3 = 0
x = 7/3
x = -2
x = 10/3


Input: Solve the equation x^3 + 92/21x^2 - 65/7x + 18/7 = 0

Output:
x^3 + 92/21x^2 - 65/7x + 18/7 = 0
(x - -6)(x - 9/7)(x - 1/3) = 0
x - -6 = 0
x - 9/7 = 0
x - 1/3 = 0
x = -6
x = 9/7
x = 1/3


Input: Find x in 1x + 2/7 = 0

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


Input: What value of x satisfies x^3 - 209/28x^2 - 367/28x + 494/7 = 0

Output:
x^3 - 209/28x^2 - 367/28x + 494/7 = 0
(x - -13/4)(x - 8)(x - 19/7) = 0
x - -13/4 = 0
x - 8 = 0
x - 19/7 = 0
x = -13/4
x = 8
x = 19/7


Input: Find x for x^3 - 191/45x^2 + 17/15x + 19/9 = 0

Output:
x^3 - 191/45x^2 + 17/15x + 19/9 = 0
(x - 1)(x - -5/9)(x - 19/5) = 0
x - 1 = 0
x - -5/9 = 0
x - 19/5 = 0
x = 1
x = -5/9
x = 19/5


Input:
Solve the equations:
1x + 2y = 3/14
9x + 6y = 387/14

Output:
1x + 2y = 3/14
9x + 6y = 387/14

Using elimination
9*(1x + 2y = 3/14)
1*(9x + 6y = 387/14)
9x + 18y = 27/14
9x + 6y = 387/14
Subtract equations
12y = -180/7
y = -180/7/12
y = -15/7

Substitute y
1x + 2(-15/7) = 3/14
1x = 9/2
x = 9/2/1
x = 9/2


Input: Determine x in x^2 - 35/8x + 19/4 = 0

Output:
x^2 - 35/8x + 19/4 = 0
(x - 19/8)(x - 2) = 0
x - 19/8 = 0  or  x - 2 = 0
x = 19/8
x = 2


Input: Determine x in x^3 - 13x^2 + 47x - 35 = 0

Output:
x^3 - 13x^2 + 47x - 35 = 0
(x - 5)(x - 1)(x - 7) = 0
x - 5 = 0
x - 1 = 0
x - 7 = 0
x = 5
x = 1
x = 7


Input: What value of x satisfies x^2 - 171/10x - 81/5 = 0

Output:
x^2 - 171/10x - 81/5 = 0
(x - -9/10)(x - 18) = 0
x - -9/10 = 0  or  x - 18 = 0
x = -9/10
x = 18


Input: What value of x satisfies 7x - 63 = 0

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


Input: Find x in 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 simultaneously:
8x + 10y = -434/15
4x + 9y = -79/5

Output:
8x + 10y = -434/15
4x + 9y = -79/5

Using elimination
4*(8x + 10y = -434/15)
8*(4x + 9y = -79/5)
32x + 40y = -1736/15
32x + 72y = -632/5
Subtract equations
-32y = 32/3
y = 32/3/-32
y = -1/3

Substitute y
8x + 10(-1/3) = -434/15
8x = -128/5
x = -128/5/8
x = -16/5


Input:
Find x and y such that
2x + 10y = -539/20
9x + 6y = -573/20

Output:
2x + 10y = -539/20
9x + 6y = -573/20

Using elimination
9*(2x + 10y = -539/20)
2*(9x + 6y = -573/20)
18x + 90y = -4851/20
18x + 12y = -573/10
Subtract equations
78y = -741/4
y = -741/4/78
y = -19/8

Substitute y
2x + 10(-19/8) = -539/20
2x = -16/5
x = -16/5/2
x = -8/5


Input: Determine x in x^3 + 1/2x^2 - 31/9x - 28/9 = 0

Output:
x^3 + 1/2x^2 - 31/9x - 28/9 = 0
(x - -7/6)(x - 2)(x - -4/3) = 0
x - -7/6 = 0
x - 2 = 0
x - -4/3 = 0
x = -7/6
x = 2
x = -4/3


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

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


Input: Determine x in 9x - 60 = 0

Output:
9x - 60 = 0
9x = 60
x = 60 / 9
x = 20/3


Input: Solve quickly: x^2 + 23/3x + 20/3 = 0

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


Input: Compute the solution of 8x + 4 = 0

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


Input:
Solve simultaneously:
4x + 2y = -113/18
6x + 5y = -167/12

Output:
4x + 2y = -113/18
6x + 5y = -167/12

Using elimination
6*(4x + 2y = -113/18)
4*(6x + 5y = -167/12)
24x + 12y = -113/3
24x + 20y = -167/3
Subtract equations
-8y = 18
y = 18/-8
y = -9/4

Substitute y
4x + 2(-9/4) = -113/18
4x = -16/9
x = -16/9/4
x = -4/9


Input: Compute the solution of x^2 - 23/10x - 34/5 = 0

Output:
x^2 - 23/10x - 34/5 = 0
(x - 4)(x - -17/10) = 0
x - 4 = 0  or  x - -17/10 = 0
x = 4
x = -17/10


Input: What value of x satisfies 2x - 12 = 0

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


Input: Solve the equation 1x + 5 = 0

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


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

Output:
5x - 5/9 = 0
5x = 5/9
x = 5/9 / 5
x = 1/9


Input:
Solve the equations:
3x + 7y = -457/15
3x + 4y = -304/15

Output:
3x + 7y = -457/15
3x + 4y = -304/15

Using elimination
3*(3x + 7y = -457/15)
3*(3x + 4y = -304/15)
9x + 21y = -457/5
9x + 12y = -304/5
Subtract equations
9y = -153/5
y = -153/5/9
y = -17/5

Substitute y
3x + 7(-17/5) = -457/15
3x = -20/3
x = -20/3/3
x = -20/9


Input: Find the solution to x^2 + 51/10x + 289/50 = 0

Output:
x^2 + 51/10x + 289/50 = 0
(x - -17/10)(x - -17/5) = 0
x - -17/10 = 0  or  x - -17/5 = 0
x = -17/10
x = -17/5


Input:
Solve simultaneously:
8x + 6y = -130/21
7x + 1y = -101/21

Output:
8x + 6y = -130/21
7x + 1y = -101/21

Using elimination
7*(8x + 6y = -130/21)
8*(7x + 1y = -101/21)
56x + 42y = -130/3
56x + 8y = -808/21
Subtract equations
34y = -34/7
y = -34/7/34
y = -1/7

Substitute y
8x + 6(-1/7) = -130/21
8x = -16/3
x = -16/3/8
x = -2/3


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

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


Input: Determine x in x^3 - 91/90x^2 - 341/45x - 119/30 = 0

Output:
x^3 - 91/90x^2 - 341/45x - 119/30 = 0
(x - 7/2)(x - -3/5)(x - -17/9) = 0
x - 7/2 = 0
x - -3/5 = 0
x - -17/9 = 0
x = 7/2
x = -3/5
x = -17/9


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

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


Input: Find x for x^3 - 5x^2 - 107/4x - 51/2 = 0

Output:
x^3 - 5x^2 - 107/4x - 51/2 = 0
(x - -2)(x - -3/2)(x - 17/2) = 0
x - -2 = 0
x - -3/2 = 0
x - 17/2 = 0
x = -2
x = -3/2
x = 17/2


Input: Compute the solution of x^2 + 22/5x + 21/5 = 0

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


Input: Find the solution to x^2 - 11/9x + 8/27 = 0

Output:
x^2 - 11/9x + 8/27 = 0
(x - 8/9)(x - 1/3) = 0
x - 8/9 = 0  or  x - 1/3 = 0
x = 8/9
x = 1/3


Input: Determine x in 10x - 45 = 0

Output:
10x - 45 = 0
10x = 45
x = 45 / 10
x = 9/2


Input: Find x for x^3 - 4/3x^2 - 25/3x + 14 = 0

Output:
x^3 - 4/3x^2 - 25/3x + 14 = 0
(x - 7/3)(x - 2)(x - -3) = 0
x - 7/3 = 0
x - 2 = 0
x - -3 = 0
x = 7/3
x = 2
x = -3


Input: Compute the solution of x^3 - 61/15x^2 + 29/15x + 17/15 = 0

Output:
x^3 - 61/15x^2 + 29/15x + 17/15 = 0
(x - 17/5)(x - -1/3)(x - 1) = 0
x - 17/5 = 0
x - -1/3 = 0
x - 1 = 0
x = 17/5
x = -1/3
x = 1


Input: Solve the equation x^3 + 325/72x^2 + 493/144x - 7/16 = 0

Output:
x^3 + 325/72x^2 + 493/144x - 7/16 = 0
(x - -9/8)(x - -7/2)(x - 1/9) = 0
x - -9/8 = 0
x - -7/2 = 0
x - 1/9 = 0
x = -9/8
x = -7/2
x = 1/9


Input: Solve x^3 + 49/18x^2 - 7/54x - 20/27 = 0

Output:
x^3 + 49/18x^2 - 7/54x - 20/27 = 0
(x - 1/2)(x - -5/9)(x - -8/3) = 0
x - 1/2 = 0
x - -5/9 = 0
x - -8/3 = 0
x = 1/2
x = -5/9
x = -8/3


Input: Find the solution to x^3 - 35/4x^2 + 137/8x - 15/4 = 0

Output:
x^3 - 35/4x^2 + 137/8x - 15/4 = 0
(x - 5/2)(x - 6)(x - 1/4) = 0
x - 5/2 = 0
x - 6 = 0
x - 1/4 = 0
x = 5/2
x = 6
x = 1/4


Input: Solve the equation x^3 - 47/4x^2 - 195/8x + 513/2 = 0

Output:
x^3 - 47/4x^2 - 195/8x + 513/2 = 0
(x - 12)(x - 9/2)(x - -19/4) = 0
x - 12 = 0
x - 9/2 = 0
x - -19/4 = 0
x = 12
x = 9/2
x = -19/4


Input: Find x in x^3 - 51/20x^2 - 27/5x + 243/20 = 0

Output:
x^3 - 51/20x^2 - 27/5x + 243/20 = 0
(x - 9/5)(x - -9/4)(x - 3) = 0
x - 9/5 = 0
x - -9/4 = 0
x - 3 = 0
x = 9/5
x = -9/4
x = 3


Input: Solve x^3 + 11/5x^2 - 16/5x - 36/5 = 0

Output:
x^3 + 11/5x^2 - 16/5x - 36/5 = 0
(x - -2)(x - -2)(x - 9/5) = 0
x - -2 = 0
x - -2 = 0
x - 9/5 = 0
x = -2
x = -2
x = 9/5


Input:
Solve simultaneously:
7x + 4y = -1139/36
5x + 7y = -1145/36

Output:
7x + 4y = -1139/36
5x + 7y = -1145/36

Using elimination
5*(7x + 4y = -1139/36)
7*(5x + 7y = -1145/36)
35x + 20y = -5695/36
35x + 49y = -8015/36
Subtract equations
-29y = 580/9
y = 580/9/-29
y = -20/9

Substitute y
7x + 4(-20/9) = -1139/36
7x = -91/4
x = -91/4/7
x = -13/4


Input: Find x for x^3 - 41/5x^2 + 8/5x  = 0

Output:
x^3 - 41/5x^2 + 8/5x  = 0
(x - 1/5)(x - 8)(x - 0) = 0
x - 1/5 = 0
x - 8 = 0
x - 0 = 0
x = 1/5
x = 8
x = 0


Input: Find x in 7x  = 0

Output:
7x  = 0
7x = 0
x = 0 / 7
x = 0


Input: Compute the solution of x^2 - 128/7x - 240/7 = 0

Output:
x^2 - 128/7x - 240/7 = 0
(x - -12/7)(x - 20) = 0
x - -12/7 = 0  or  x - 20 = 0
x = -12/7
x = 20


Input: Find x in x^3 + 29/7x^2 + 38/7x + 16/7 = 0

Output:
x^3 + 29/7x^2 + 38/7x + 16/7 = 0
(x - -8/7)(x - -2)(x - -1) = 0
x - -8/7 = 0
x - -2 = 0
x - -1 = 0
x = -8/7
x = -2
x = -1


Input: Find x in x^2 - 47/12x - 17/12 = 0

Output:
x^2 - 47/12x - 17/12 = 0
(x - 17/4)(x - -1/3) = 0
x - 17/4 = 0  or  x - -1/3 = 0
x = 17/4
x = -1/3


Input: Determine x in 2x - 26/3 = 0

Output:
2x - 26/3 = 0
2x = 26/3
x = 26/3 / 2
x = 13/3


Input: Determine x in x^3 - 11/3x^2 - 58x - 160/3 = 0

Output:
x^3 - 11/3x^2 - 58x - 160/3 = 0
(x - -16/3)(x - -1)(x - 10) = 0
x - -16/3 = 0
x - -1 = 0
x - 10 = 0
x = -16/3
x = -1
x = 10


Input:
Solve simultaneously:
2x + 9y = 69
7x + 1y = 28

Output:
2x + 9y = 69
7x + 1y = 28

Using elimination
7*(2x + 9y = 69)
2*(7x + 1y = 28)
14x + 63y = 483
14x + 2y = 56
Subtract equations
61y = 427
y = 427/61
y = 7

Substitute y
2x + 9(7) = 69
2x = 6
x = 6/2
x = 3


Input: Find x in 4x + 64/7 = 0

Output:
4x + 64/7 = 0
4x = -64/7
x = -64/7 / 4
x = -16/7


Input: Solve x^3 - 117/20x^2 + 13/8x + 33/20 = 0

Output:
x^3 - 117/20x^2 + 13/8x + 33/20 = 0
(x - 11/2)(x - 3/4)(x - -2/5) = 0
x - 11/2 = 0
x - 3/4 = 0
x - -2/5 = 0
x = 11/2
x = 3/4
x = -2/5


Input: Solve quickly: 2x + 2/3 = 0

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


Input:
Find x and y such that
3x + 4y = -17
8x + 10y = -259/6

Output:
3x + 4y = -17
8x + 10y = -259/6

Using elimination
8*(3x + 4y = -17)
3*(8x + 10y = -259/6)
24x + 32y = -136
24x + 30y = -259/2
Subtract equations
2y = -13/2
y = -13/2/2
y = -13/4

Substitute y
3x + 4(-13/4) = -17
3x = -4
x = -4/3
x = -4/3


Input: Find x for x^3 - 29/30x^2 - 13/6x + 6/5 = 0

Output:
x^3 - 29/30x^2 - 13/6x + 6/5 = 0
(x - 1/2)(x - -4/3)(x - 9/5) = 0
x - 1/2 = 0
x - -4/3 = 0
x - 9/5 = 0
x = 1/2
x = -4/3
x = 9/5


Input: Determine x in 6x + 108/5 = 0

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


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: Compute the solution of x^2 - 13x + 12 = 0

Output:
x^2 - 13x + 12 = 0
(x - 1)(x - 12) = 0
x - 1 = 0  or  x - 12 = 0
x = 1
x = 12


Input:
Find x and y such that
4x + 9y = 50
3x + 5y = 88/3

Output:
4x + 9y = 50
3x + 5y = 88/3

Using elimination
3*(4x + 9y = 50)
4*(3x + 5y = 88/3)
12x + 27y = 150
12x + 20y = 352/3
Subtract equations
7y = 98/3
y = 98/3/7
y = 14/3

Substitute y
4x + 9(14/3) = 50
4x = 8
x = 8/4
x = 2


Input: Solve quickly: x^2 + 18/35x - 81/35 = 0

Output:
x^2 + 18/35x - 81/35 = 0
(x - -9/5)(x - 9/7) = 0
x - -9/5 = 0  or  x - 9/7 = 0
x = -9/5
x = 9/7


Input: Find the solution to 6x - 5 = 0

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


Input: Find x in x^3 - 31/60x^2 - 93/20x + 14/3 = 0

Output:
x^3 - 31/60x^2 - 93/20x + 14/3 = 0
(x - -7/3)(x - 5/4)(x - 8/5) = 0
x - -7/3 = 0
x - 5/4 = 0
x - 8/5 = 0
x = -7/3
x = 5/4
x = 8/5


Input:
Solve the equations:
1x + 9y = 56/5
6x + 5y = -21

Output:
1x + 9y = 56/5
6x + 5y = -21

Using elimination
6*(1x + 9y = 56/5)
1*(6x + 5y = -21)
6x + 54y = 336/5
6x + 5y = -21
Subtract equations
49y = 441/5
y = 441/5/49
y = 9/5

Substitute y
1x + 9(9/5) = 56/5
1x = -5
x = -5/1
x = -5


Input: Solve 6x - 18 = 0

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


Input: Determine x in x^3 - 365/18x^2 + 628/27x + 1045/54 = 0

Output:
x^3 - 365/18x^2 + 628/27x + 1045/54 = 0
(x - 11/6)(x - 19)(x - -5/9) = 0
x - 11/6 = 0
x - 19 = 0
x - -5/9 = 0
x = 11/6
x = 19
x = -5/9


Input: Compute the solution of x^2 + 61/3x + 42 = 0

Output:
x^2 + 61/3x + 42 = 0
(x - -7/3)(x - -18) = 0
x - -7/3 = 0  or  x - -18 = 0
x = -7/3
x = -18


Input: Find x in 2x + 32 = 0

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


Input: Determine x in x^2 - 19/7x  = 0

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


Input:
Solve the system:
2x + 6y = 15/2
8x + 10y = 16

Output:
2x + 6y = 15/2
8x + 10y = 16

Using elimination
8*(2x + 6y = 15/2)
2*(8x + 10y = 16)
16x + 48y = 60
16x + 20y = 32
Subtract equations
28y = 28
y = 28/28
y = 1

Substitute y
2x + 6(1) = 15/2
2x = 3/2
x = 3/2/2
x = 3/4


Input: What value of x satisfies x^2 - 40/3x - 128/3 = 0

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


Input: Find the solution to x^2 - 36/5x - 32/5 = 0

Output:
x^2 - 36/5x - 32/5 = 0
(x - -4/5)(x - 8) = 0
x - -4/5 = 0  or  x - 8 = 0
x = -4/5
x = 8


Input: Find the solution to 2x - 10 = 0

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


Input: Solve x^3 + 71/14x^2 - 37x - 935/14 = 0

Output:
x^3 + 71/14x^2 - 37x - 935/14 = 0
(x - -17/2)(x - 5)(x - -11/7) = 0
x - -17/2 = 0
x - 5 = 0
x - -11/7 = 0
x = -17/2
x = 5
x = -11/7


Input:
Find x and y such that
1x + 5y = -101/7
9x + 2y = -221/7

Output:
1x + 5y = -101/7
9x + 2y = -221/7

Using elimination
9*(1x + 5y = -101/7)
1*(9x + 2y = -221/7)
9x + 45y = -909/7
9x + 2y = -221/7
Subtract equations
43y = -688/7
y = -688/7/43
y = -16/7

Substitute y
1x + 5(-16/7) = -101/7
1x = -3
x = -3/1
x = -3


Input: Solve quickly: x^3 - 71/24x^2 - 37/32x + 65/96 = 0

Output:
x^3 - 71/24x^2 - 37/32x + 65/96 = 0
(x - 13/4)(x - -5/8)(x - 1/3) = 0
x - 13/4 = 0
x - -5/8 = 0
x - 1/3 = 0
x = 13/4
x = -5/8
x = 1/3


Input: Solve x^3 + 13/4x^2 - 165/8x - 513/8 = 0

Output:
x^3 + 13/4x^2 - 165/8x - 513/8 = 0
(x - 9/2)(x - -19/4)(x - -3) = 0
x - 9/2 = 0
x - -19/4 = 0
x - -3 = 0
x = 9/2
x = -19/4
x = -3


Input: Solve quickly: x^2 - 4x + 20/9 = 0

Output:
x^2 - 4x + 20/9 = 0
(x - 10/3)(x - 2/3) = 0
x - 10/3 = 0  or  x - 2/3 = 0
x = 10/3
x = 2/3


Input:
Solve simultaneously:
6x + 7y = -37/5
5x + 10y = -12

Output:
6x + 7y = -37/5
5x + 10y = -12

Using elimination
5*(6x + 7y = -37/5)
6*(5x + 10y = -12)
30x + 35y = -37
30x + 60y = -72
Subtract equations
-25y = 35
y = 35/-25
y = -7/5

Substitute y
6x + 7(-7/5) = -37/5
6x = 12/5
x = 12/5/6
x = 2/5


Input:
Find x and y such that
4x + 4y = 38/3
3x + 5y = 113/6

Output:
4x + 4y = 38/3
3x + 5y = 113/6

Using elimination
3*(4x + 4y = 38/3)
4*(3x + 5y = 113/6)
12x + 12y = 38
12x + 20y = 226/3
Subtract equations
-8y = -112/3
y = -112/3/-8
y = 14/3

Substitute y
4x + 4(14/3) = 38/3
4x = -6
x = -6/4
x = -3/2


Input: Find x in 10x + 20 = 0

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


Input: Find x for x^3 + 217/24x^2 + 413/18x + 152/9 = 0

Output:
x^3 + 217/24x^2 + 413/18x + 152/9 = 0
(x - -16/3)(x - -4/3)(x - -19/8) = 0
x - -16/3 = 0
x - -4/3 = 0
x - -19/8 = 0
x = -16/3
x = -4/3
x = -19/8


Input: Determine x in x^2 + 13/8x + 5/8 = 0

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


Input: Find x in x^3 + 493/84x^2 + 78/7x + 27/4 = 0

Output:
x^3 + 493/84x^2 + 78/7x + 27/4 = 0
(x - -9/4)(x - -9/7)(x - -7/3) = 0
x - -9/4 = 0
x - -9/7 = 0
x - -7/3 = 0
x = -9/4
x = -9/7
x = -7/3


Input: Solve the equation x^2 + 31/63x - 44/21 = 0

Output:
x^2 + 31/63x - 44/21 = 0
(x - -12/7)(x - 11/9) = 0
x - -12/7 = 0  or  x - 11/9 = 0
x = -12/7
x = 11/9


Input:
Solve simultaneously:
4x + 7y = 35
10x + 6y = 53

Output:
4x + 7y = 35
10x + 6y = 53

Using elimination
10*(4x + 7y = 35)
4*(10x + 6y = 53)
40x + 70y = 350
40x + 24y = 212
Subtract equations
46y = 138
y = 138/46
y = 3

Substitute y
4x + 7(3) = 35
4x = 14
x = 14/4
x = 7/2


Input: Find the solution to x^2 - 167/42x + 68/21 = 0

Output:
x^2 - 167/42x + 68/21 = 0
(x - 17/6)(x - 8/7) = 0
x - 17/6 = 0  or  x - 8/7 = 0
x = 17/6
x = 8/7


Input: Solve 8x + 72/5 = 0

Output:
8x + 72/5 = 0
8x = -72/5
x = -72/5 / 8
x = -9/5


Input:
Find x and y such that
8x + 7y = -7
5x + 8y = -535/56

Output:
8x + 7y = -7
5x + 8y = -535/56

Using elimination
5*(8x + 7y = -7)
8*(5x + 8y = -535/56)
40x + 35y = -35
40x + 64y = -535/7
Subtract equations
-29y = 290/7
y = 290/7/-29
y = -10/7

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


Input: Solve quickly: x^3 - 18x^2 + 335/4x - 75/2 = 0

Output:
x^3 - 18x^2 + 335/4x - 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:
Solve the system:
1x + 2y = -162/7
1x + 5y = -393/7

Output:
1x + 2y = -162/7
1x + 5y = -393/7

Using elimination
1*(1x + 2y = -162/7)
1*(1x + 5y = -393/7)
1x + 2y = -162/7
1x + 5y = -393/7
Subtract equations
-3y = 33
y = 33/-3
y = -11

Substitute y
1x + 2(-11) = -162/7
1x = -8/7
x = -8/7/1
x = -8/7


Input: Solve quickly: x^3 + 25/4x^2 + 99/8x + 63/8 = 0

Output:
x^3 + 25/4x^2 + 99/8x + 63/8 = 0
(x - -7/4)(x - -3/2)(x - -3) = 0
x - -7/4 = 0
x - -3/2 = 0
x - -3 = 0
x = -7/4
x = -3/2
x = -3


Input: What value of x satisfies x^3 - 25/24x^2 - 57/32x + 65/48 = 0

Output:
x^3 - 25/24x^2 - 57/32x + 65/48 = 0
(x - 13/8)(x - 2/3)(x - -5/4) = 0
x - 13/8 = 0
x - 2/3 = 0
x - -5/4 = 0
x = 13/8
x = 2/3
x = -5/4


Input: Compute the solution of x^3 + 11x^2 + 36x + 36 = 0

Output:
x^3 + 11x^2 + 36x + 36 = 0
(x - -2)(x - -3)(x - -6) = 0
x - -2 = 0
x - -3 = 0
x - -6 = 0
x = -2
x = -3
x = -6


Input:
Find x and y such that
1x + 8y = 41/14
6x + 4y = -9/7

Output:
1x + 8y = 41/14
6x + 4y = -9/7

Using elimination
6*(1x + 8y = 41/14)
1*(6x + 4y = -9/7)
6x + 48y = 123/7
6x + 4y = -9/7
Subtract equations
44y = 132/7
y = 132/7/44
y = 3/7

Substitute y
1x + 8(3/7) = 41/14
1x = -1/2
x = -1/2/1
x = -1/2


Input: Solve quickly: x^2 - 4x - 32 = 0

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


Input: Solve the equation 8x - 56/9 = 0

Output:
8x - 56/9 = 0
8x = 56/9
x = 56/9 / 8
x = 7/9


Input: What value of x satisfies 8x - 8 = 0

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


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

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


Input: What value of x satisfies x^3 - 9/10x^2 - 661/10x - 741/5 = 0

Output:
x^3 - 9/10x^2 - 661/10x - 741/5 = 0
(x - -13/5)(x - 19/2)(x - -6) = 0
x - -13/5 = 0
x - 19/2 = 0
x - -6 = 0
x = -13/5
x = 19/2
x = -6


Input: What value of x satisfies 7x - 91/3 = 0

Output:
7x - 91/3 = 0
7x = 91/3
x = 91/3 / 7
x = 13/3


Input:
Solve the equations:
9x + 5y = -67/7
4x + 4y = -92/7

Output:
9x + 5y = -67/7
4x + 4y = -92/7

Using elimination
4*(9x + 5y = -67/7)
9*(4x + 4y = -92/7)
36x + 20y = -268/7
36x + 36y = -828/7
Subtract equations
-16y = 80
y = 80/-16
y = -5

Substitute y
9x + 5(-5) = -67/7
9x = 108/7
x = 108/7/9
x = 12/7


Input: Find x in x^3 - 33/8x^2 - 45/4x  = 0

Output:
x^3 - 33/8x^2 - 45/4x  = 0
(x - 6)(x - 0)(x - -15/8) = 0
x - 6 = 0
x - 0 = 0
x - -15/8 = 0
x = 6
x = 0
x = -15/8


Input: Find the solution to x^3 + 37/90x^2 - 791/270x - 8/9 = 0

Output:
x^3 + 37/90x^2 - 791/270x - 8/9 = 0
(x - 5/3)(x - -3/10)(x - -16/9) = 0
x - 5/3 = 0
x - -3/10 = 0
x - -16/9 = 0
x = 5/3
x = -3/10
x = -16/9


Input: Solve quickly: 7x + 91/4 = 0

Output:
7x + 91/4 = 0
7x = -91/4
x = -91/4 / 7
x = -13/4


Input: Find the solution to x^2 - 27/28x - 9/7 = 0

Output:
x^2 - 27/28x - 9/7 = 0
(x - -3/4)(x - 12/7) = 0
x - -3/4 = 0  or  x - 12/7 = 0
x = -3/4
x = 12/7


Input: Solve the equation 4x + 52/7 = 0

Output:
4x + 52/7 = 0
4x = -52/7
x = -52/7 / 4
x = -13/7


Input: Determine x in x^2 - 149/72x + 13/18 = 0

Output:
x^2 - 149/72x + 13/18 = 0
(x - 4/9)(x - 13/8) = 0
x - 4/9 = 0  or  x - 13/8 = 0
x = 4/9
x = 13/8


Input: Solve quickly: 8x - 8/7 = 0

Output:
8x - 8/7 = 0
8x = 8/7
x = 8/7 / 8
x = 1/7


Input: Find the solution to 10x + 70/3 = 0

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


Input:
Solve simultaneously:
3x + 5y = 100/7
6x + 9y = 180/7

Output:
3x + 5y = 100/7
6x + 9y = 180/7

Using elimination
6*(3x + 5y = 100/7)
3*(6x + 9y = 180/7)
18x + 30y = 600/7
18x + 27y = 540/7
Subtract equations
3y = 60/7
y = 60/7/3
y = 20/7

Substitute y
3x + 5(20/7) = 100/7
3x = 0
x = 0/3
x = 0


Input: Find x in 4x - 6 = 0

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


Input: Solve quickly: x^3 + 22/3x^2 - 76/3x + 40/3 = 0

Output:
x^3 + 22/3x^2 - 76/3x + 40/3 = 0
(x - 2)(x - 2/3)(x - -10) = 0
x - 2 = 0
x - 2/3 = 0
x - -10 = 0
x = 2
x = 2/3
x = -10


Input: Find the solution to x^3 - 23/4x^2 + 1123/200x + 323/100 = 0

Output:
x^3 - 23/4x^2 + 1123/200x + 323/100 = 0
(x - 17/4)(x - -2/5)(x - 19/10) = 0
x - 17/4 = 0
x - -2/5 = 0
x - 19/10 = 0
x = 17/4
x = -2/5
x = 19/10


Input:
Solve simultaneously:
1x + 3y = -81/8
3x + 4y = -47/2

Output:
1x + 3y = -81/8
3x + 4y = -47/2

Using elimination
3*(1x + 3y = -81/8)
1*(3x + 4y = -47/2)
3x + 9y = -243/8
3x + 4y = -47/2
Subtract equations
5y = -55/8
y = -55/8/5
y = -11/8

Substitute y
1x + 3(-11/8) = -81/8
1x = -6
x = -6/1
x = -6


Input: Compute the solution of x^3 - 63/5x^2 - 272/5x  = 0

Output:
x^3 - 63/5x^2 - 272/5x  = 0
(x - -17/5)(x - 0)(x - 16) = 0
x - -17/5 = 0
x - 0 = 0
x - 16 = 0
x = -17/5
x = 0
x = 16


Input: What value of x satisfies x^3 + 17/60x^2 - 299/40x + 169/24 = 0

Output:
x^3 + 17/60x^2 - 299/40x + 169/24 = 0
(x - 13/10)(x - -13/4)(x - 5/3) = 0
x - 13/10 = 0
x - -13/4 = 0
x - 5/3 = 0
x = 13/10
x = -13/4
x = 5/3


Input: Compute the solution of 1x + 20 = 0

Output:
1x + 20 = 0
1x = -20
x = -20 / 1
x = -20


Input: Solve quickly: 6x - 24 = 0

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


Input: Determine x in x^2 - 3/4x - 5/2 = 0

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


Input: Solve quickly: 7x - 11 = 0

Output:
7x - 11 = 0
7x = 11
x = 11 / 7
x = 11/7


Input: Determine x in 2x + 1/2 = 0

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


Input:
Solve the system:
10x + 3y = 559/14
6x + 9y = 249/14

Output:
10x + 3y = 559/14
6x + 9y = 249/14

Using elimination
6*(10x + 3y = 559/14)
10*(6x + 9y = 249/14)
60x + 18y = 1677/7
60x + 90y = 1245/7
Subtract equations
-72y = 432/7
y = 432/7/-72
y = -6/7

Substitute y
10x + 3(-6/7) = 559/14
10x = 85/2
x = 85/2/10
x = 17/4


Input: Find x in 6x - 15/2 = 0

Output:
6x - 15/2 = 0
6x = 15/2
x = 15/2 / 6
x = 5/4


Input: Solve the equation x^3 + 71/45x^2 - 52/27x - 76/45 = 0

Output:
x^3 + 71/45x^2 - 52/27x - 76/45 = 0
(x - -2/3)(x - 6/5)(x - -19/9) = 0
x - -2/3 = 0
x - 6/5 = 0
x - -19/9 = 0
x = -2/3
x = 6/5
x = -19/9


Input:
Find x and y such that
9x + 1y = -39/10
9x + 9y = -279/10

Output:
9x + 1y = -39/10
9x + 9y = -279/10

Using elimination
9*(9x + 1y = -39/10)
9*(9x + 9y = -279/10)
81x + 9y = -351/10
81x + 81y = -2511/10
Subtract equations
-72y = 216
y = 216/-72
y = -3

Substitute y
9x + 1(-3) = -39/10
9x = -9/10
x = -9/10/9
x = -1/10


Input:
Find x and y such that
6x + 3y = 9
4x + 6y = 66/5

Output:
6x + 3y = 9
4x + 6y = 66/5

Using elimination
4*(6x + 3y = 9)
6*(4x + 6y = 66/5)
24x + 12y = 36
24x + 36y = 396/5
Subtract equations
-24y = -216/5
y = -216/5/-24
y = 9/5

Substitute y
6x + 3(9/5) = 9
6x = 18/5
x = 18/5/6
x = 3/5


Input: Find x for x^3 + 63/8x^2 + 11/4x - 51 = 0

Output:
x^3 + 63/8x^2 + 11/4x - 51 = 0
(x - 17/8)(x - -6)(x - -4) = 0
x - 17/8 = 0
x - -6 = 0
x - -4 = 0
x = 17/8
x = -6
x = -4


Input: Solve quickly: 9x - 13 = 0

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


Input: Find x in x^3 + 9/10x^2 - 2/5x - 3/10 = 0

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


Input: Find the solution to x^3 + 141/10x^2 - 71/5x - 21/2 = 0

Output:
x^3 + 141/10x^2 - 71/5x - 21/2 = 0
(x - -15)(x - 7/5)(x - -1/2) = 0
x - -15 = 0
x - 7/5 = 0
x - -1/2 = 0
x = -15
x = 7/5
x = -1/2


Input: Solve x^3 + 81/40x^2 - 177/20x - 19/5 = 0

Output:
x^3 + 81/40x^2 - 177/20x - 19/5 = 0
(x - -4)(x - -2/5)(x - 19/8) = 0
x - -4 = 0
x - -2/5 = 0
x - 19/8 = 0
x = -4
x = -2/5
x = 19/8


Input: Solve quickly: x^2 + 71/21x + 20/7 = 0

Output:
x^2 + 71/21x + 20/7 = 0
(x - -5/3)(x - -12/7) = 0
x - -5/3 = 0  or  x - -12/7 = 0
x = -5/3
x = -12/7


Input: Solve the equation x^3 + 12x^2 - 445/4x - 117/2 = 0

Output:
x^3 + 12x^2 - 445/4x - 117/2 = 0
(x - -18)(x - 13/2)(x - -1/2) = 0
x - -18 = 0
x - 13/2 = 0
x - -1/2 = 0
x = -18
x = 13/2
x = -1/2


Input: Find x for 8x + 4 = 0

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