Input: Determine x in x^2 + 2/35x - 33/7 = 0

Output:
x^2 + 2/35x - 33/7 = 0
(x - 15/7)(x - -11/5) = 0
x - 15/7 = 0  or  x - -11/5 = 0
x = 15/7
x = -11/5


Input: Find x in x^2 + 28/3x + 160/9 = 0

Output:
x^2 + 28/3x + 160/9 = 0
(x - -8/3)(x - -20/3) = 0
x - -8/3 = 0  or  x - -20/3 = 0
x = -8/3
x = -20/3


Input:
Find x and y such that
1x + 6y = -154/5
10x + 3y = 15

Output:
1x + 6y = -154/5
10x + 3y = 15

Using elimination
10*(1x + 6y = -154/5)
1*(10x + 3y = 15)
10x + 60y = -308
10x + 3y = 15
Subtract equations
57y = -323
y = -323/57
y = -17/3

Substitute y
1x + 6(-17/3) = -154/5
1x = 16/5
x = 16/5/1
x = 16/5


Input:
Solve the system:
8x + 9y = 84
1x + 4y = 45

Output:
8x + 9y = 84
1x + 4y = 45

Using elimination
1*(8x + 9y = 84)
8*(1x + 4y = 45)
8x + 9y = 84
8x + 32y = 360
Subtract equations
-23y = -276
y = -276/-23
y = 12

Substitute y
8x + 9(12) = 84
8x = -24
x = -24/8
x = -3


Input: Compute the solution of x^3 + 9/4x^2 - 23/18x - 455/144 = 0

Output:
x^3 + 9/4x^2 - 23/18x - 455/144 = 0
(x - -13/6)(x - 7/6)(x - -5/4) = 0
x - -13/6 = 0
x - 7/6 = 0
x - -5/4 = 0
x = -13/6
x = 7/6
x = -5/4


Input: Find x for x^2 - 14/9x - 5/27 = 0

Output:
x^2 - 14/9x - 5/27 = 0
(x - 5/3)(x - -1/9) = 0
x - 5/3 = 0  or  x - -1/9 = 0
x = 5/3
x = -1/9


Input: Solve x^2 + 20/7x + 75/49 = 0

Output:
x^2 + 20/7x + 75/49 = 0
(x - -5/7)(x - -15/7) = 0
x - -5/7 = 0  or  x - -15/7 = 0
x = -5/7
x = -15/7


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

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


Input: Solve the equation x^2 + 131/9x - 208/9 = 0

Output:
x^2 + 131/9x - 208/9 = 0
(x - -16)(x - 13/9) = 0
x - -16 = 0  or  x - 13/9 = 0
x = -16
x = 13/9


Input: Determine x in x^2 + 81/10x - 19 = 0

Output:
x^2 + 81/10x - 19 = 0
(x - -10)(x - 19/10) = 0
x - -10 = 0  or  x - 19/10 = 0
x = -10
x = 19/10


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

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


Input: Find x in x^3 - 1/3x^2 - 185/36x + 175/36 = 0

Output:
x^3 - 1/3x^2 - 185/36x + 175/36 = 0
(x - 5/3)(x - 7/6)(x - -5/2) = 0
x - 5/3 = 0
x - 7/6 = 0
x - -5/2 = 0
x = 5/3
x = 7/6
x = -5/2


Input: What value of x satisfies x^2 - 85/24x + 19/16 = 0

Output:
x^2 - 85/24x + 19/16 = 0
(x - 19/6)(x - 3/8) = 0
x - 19/6 = 0  or  x - 3/8 = 0
x = 19/6
x = 3/8


Input: Solve quickly: x^3 + 29/5x^2 + 41/4x + 5 = 0

Output:
x^3 + 29/5x^2 + 41/4x + 5 = 0
(x - -5/2)(x - -4/5)(x - -5/2) = 0
x - -5/2 = 0
x - -4/5 = 0
x - -5/2 = 0
x = -5/2
x = -4/5
x = -5/2


Input: Solve the equation 5x - 10 = 0

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


Input: Find x in x^3 - 2/15x^2 - 1313/405x - 266/135 = 0

Output:
x^3 - 2/15x^2 - 1313/405x - 266/135 = 0
(x - -6/5)(x - 19/9)(x - -7/9) = 0
x - -6/5 = 0
x - 19/9 = 0
x - -7/9 = 0
x = -6/5
x = 19/9
x = -7/9


Input:
Solve the equations:
9x + 2y = 40
6x + 6y = 29

Output:
9x + 2y = 40
6x + 6y = 29

Using elimination
6*(9x + 2y = 40)
9*(6x + 6y = 29)
54x + 12y = 240
54x + 54y = 261
Subtract equations
-42y = -21
y = -21/-42
y = 1/2

Substitute y
9x + 2(1/2) = 40
9x = 39
x = 39/9
x = 13/3


Input: Find x in x^3 - 167/63x^2 - 82/21x + 680/63 = 0

Output:
x^3 - 167/63x^2 - 82/21x + 680/63 = 0
(x - 20/9)(x - 17/7)(x - -2) = 0
x - 20/9 = 0
x - 17/7 = 0
x - -2 = 0
x = 20/9
x = 17/7
x = -2


Input:
Solve simultaneously:
7x + 1y = -199/18
5x + 7y = -205/18

Output:
7x + 1y = -199/18
5x + 7y = -205/18

Using elimination
5*(7x + 1y = -199/18)
7*(5x + 7y = -205/18)
35x + 5y = -995/18
35x + 49y = -1435/18
Subtract equations
-44y = 220/9
y = 220/9/-44
y = -5/9

Substitute y
7x + 1(-5/9) = -199/18
7x = -21/2
x = -21/2/7
x = -3/2


Input:
Solve the equations:
9x + 2y = -107/7
7x + 9y = -61/2

Output:
9x + 2y = -107/7
7x + 9y = -61/2

Using elimination
7*(9x + 2y = -107/7)
9*(7x + 9y = -61/2)
63x + 14y = -107
63x + 81y = -549/2
Subtract equations
-67y = 335/2
y = 335/2/-67
y = -5/2

Substitute y
9x + 2(-5/2) = -107/7
9x = -72/7
x = -72/7/9
x = -8/7


Input: Compute the solution of x^2 + 29/6x + 10/3 = 0

Output:
x^2 + 29/6x + 10/3 = 0
(x - -4)(x - -5/6) = 0
x - -4 = 0  or  x - -5/6 = 0
x = -4
x = -5/6


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

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


Input: Compute the solution of x^2 - 39/8x + 45/8 = 0

Output:
x^2 - 39/8x + 45/8 = 0
(x - 15/8)(x - 3) = 0
x - 15/8 = 0  or  x - 3 = 0
x = 15/8
x = 3


Input: Find x in 7x - 77/3 = 0

Output:
7x - 77/3 = 0
7x = 77/3
x = 77/3 / 7
x = 11/3


Input: What value of x satisfies 5x - 20/7 = 0

Output:
5x - 20/7 = 0
5x = 20/7
x = 20/7 / 5
x = 4/7


Input: Find x for 4x + 76/9 = 0

Output:
4x + 76/9 = 0
4x = -76/9
x = -76/9 / 4
x = -19/9


Input:
Solve the equations:
7x + 8y = -142/5
10x + 6y = -27

Output:
7x + 8y = -142/5
10x + 6y = -27

Using elimination
10*(7x + 8y = -142/5)
7*(10x + 6y = -27)
70x + 80y = -284
70x + 42y = -189
Subtract equations
38y = -95
y = -95/38
y = -5/2

Substitute y
7x + 8(-5/2) = -142/5
7x = -42/5
x = -42/5/7
x = -6/5


Input: Solve quickly: x^2 + 13x - 48 = 0

Output:
x^2 + 13x - 48 = 0
(x - -16)(x - 3) = 0
x - -16 = 0  or  x - 3 = 0
x = -16
x = 3


Input: Find x for x^2 + 1/6x - 35/6 = 0

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


Input: What value of x satisfies 9x - 33 = 0

Output:
9x - 33 = 0
9x = 33
x = 33 / 9
x = 11/3


Input: Solve x^3 + 89/30x^2 - 44/15x - 56/15 = 0

Output:
x^3 + 89/30x^2 - 44/15x - 56/15 = 0
(x - -7/2)(x - -4/5)(x - 4/3) = 0
x - -7/2 = 0
x - -4/5 = 0
x - 4/3 = 0
x = -7/2
x = -4/5
x = 4/3


Input: Find x for 8x + 20 = 0

Output:
8x + 20 = 0
8x = -20
x = -20 / 8
x = -5/2


Input: Determine x in x^3 + 629/168x^2 - 9/16x - 187/21 = 0

Output:
x^3 + 629/168x^2 - 9/16x - 187/21 = 0
(x - -17/6)(x - -16/7)(x - 11/8) = 0
x - -17/6 = 0
x - -16/7 = 0
x - 11/8 = 0
x = -17/6
x = -16/7
x = 11/8


Input:
Solve simultaneously:
1x + 3y = 9/5
10x + 1y = 441/10

Output:
1x + 3y = 9/5
10x + 1y = 441/10

Using elimination
10*(1x + 3y = 9/5)
1*(10x + 1y = 441/10)
10x + 30y = 18
10x + 1y = 441/10
Subtract equations
29y = -261/10
y = -261/10/29
y = -9/10

Substitute y
1x + 3(-9/10) = 9/5
1x = 9/2
x = 9/2/1
x = 9/2


Input: Find x for x^3 + 391/28x^2 + 603/28x - 171/7 = 0

Output:
x^3 + 391/28x^2 + 603/28x - 171/7 = 0
(x - 3/4)(x - -19/7)(x - -12) = 0
x - 3/4 = 0
x - -19/7 = 0
x - -12 = 0
x = 3/4
x = -19/7
x = -12


Input: What value of x satisfies x^2 + 35/9x + 88/27 = 0

Output:
x^2 + 35/9x + 88/27 = 0
(x - -11/9)(x - -8/3) = 0
x - -11/9 = 0  or  x - -8/3 = 0
x = -11/9
x = -8/3


Input: Solve 9x + 9 = 0

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


Input:
Solve the equations:
5x + 9y = -15/7
2x + 9y = -48/7

Output:
5x + 9y = -15/7
2x + 9y = -48/7

Using elimination
2*(5x + 9y = -15/7)
5*(2x + 9y = -48/7)
10x + 18y = -30/7
10x + 45y = -240/7
Subtract equations
-27y = 30
y = 30/-27
y = -10/9

Substitute y
5x + 9(-10/9) = -15/7
5x = 55/7
x = 55/7/5
x = 11/7


Input: Find x in x^3 + 817/56x^2 + 161/8x - 195/28 = 0

Output:
x^3 + 817/56x^2 + 161/8x - 195/28 = 0
(x - 2/7)(x - -13)(x - -15/8) = 0
x - 2/7 = 0
x - -13 = 0
x - -15/8 = 0
x = 2/7
x = -13
x = -15/8


Input: Solve x^3 - 81/28x^2 - 431/56x + 117/56 = 0

Output:
x^3 - 81/28x^2 - 431/56x + 117/56 = 0
(x - 9/2)(x - -13/7)(x - 1/4) = 0
x - 9/2 = 0
x - -13/7 = 0
x - 1/4 = 0
x = 9/2
x = -13/7
x = 1/4


Input:
Solve simultaneously:
5x + 1y = 68/5
5x + 6y = 83/5

Output:
5x + 1y = 68/5
5x + 6y = 83/5

Using elimination
5*(5x + 1y = 68/5)
5*(5x + 6y = 83/5)
25x + 5y = 68
25x + 30y = 83
Subtract equations
-25y = -15
y = -15/-25
y = 3/5

Substitute y
5x + 1(3/5) = 68/5
5x = 13
x = 13/5
x = 13/5


Input: Find the solution to 10x + 40/3 = 0

Output:
10x + 40/3 = 0
10x = -40/3
x = -40/3 / 10
x = -4/3


Input: Determine x in 2x - 18/5 = 0

Output:
2x - 18/5 = 0
2x = 18/5
x = 18/5 / 2
x = 9/5


Input: Determine x in x^2 + 16/7x + 9/7 = 0

Output:
x^2 + 16/7x + 9/7 = 0
(x - -9/7)(x - -1) = 0
x - -9/7 = 0  or  x - -1 = 0
x = -9/7
x = -1


Input: Determine x in x^3 - 1241/120x^2 + 2207/80x - 247/12 = 0

Output:
x^3 - 1241/120x^2 + 2207/80x - 247/12 = 0
(x - 20/3)(x - 19/8)(x - 13/10) = 0
x - 20/3 = 0
x - 19/8 = 0
x - 13/10 = 0
x = 20/3
x = 19/8
x = 13/10


Input: Solve quickly: x^2 - 1/8x - 95/16 = 0

Output:
x^2 - 1/8x - 95/16 = 0
(x - -19/8)(x - 5/2) = 0
x - -19/8 = 0  or  x - 5/2 = 0
x = -19/8
x = 5/2


Input: Compute the solution of x^3 + 83/45x^2 + 46/45x + 8/45 = 0

Output:
x^3 + 83/45x^2 + 46/45x + 8/45 = 0
(x - -2/5)(x - -4/9)(x - -1) = 0
x - -2/5 = 0
x - -4/9 = 0
x - -1 = 0
x = -2/5
x = -4/9
x = -1


Input: Find x in x^3 - 287/72x^2 - 1657/288x + 323/32 = 0

Output:
x^3 - 287/72x^2 - 1657/288x + 323/32 = 0
(x - -17/9)(x - 19/4)(x - 9/8) = 0
x - -17/9 = 0
x - 19/4 = 0
x - 9/8 = 0
x = -17/9
x = 19/4
x = 9/8


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

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


Input: Solve 7x + 77/9 = 0

Output:
7x + 77/9 = 0
7x = -77/9
x = -77/9 / 7
x = -11/9


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

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


Input: Find x in x^3 - 55/28x^2 - 283/14x - 24 = 0

Output:
x^3 - 55/28x^2 - 283/14x - 24 = 0
(x - -7/4)(x - -16/7)(x - 6) = 0
x - -7/4 = 0
x - -16/7 = 0
x - 6 = 0
x = -7/4
x = -16/7
x = 6


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

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


Input:
Find x and y such that
1x + 3y = -17/8
8x + 7y = 187/8

Output:
1x + 3y = -17/8
8x + 7y = 187/8

Using elimination
8*(1x + 3y = -17/8)
1*(8x + 7y = 187/8)
8x + 24y = -17
8x + 7y = 187/8
Subtract equations
17y = -323/8
y = -323/8/17
y = -19/8

Substitute y
1x + 3(-19/8) = -17/8
1x = 5
x = 5/1
x = 5


Input: Find x in x^3 - 23/105x^2 - 398/105x - 32/15 = 0

Output:
x^3 - 23/105x^2 - 398/105x - 32/15 = 0
(x - -7/5)(x - 16/7)(x - -2/3) = 0
x - -7/5 = 0
x - 16/7 = 0
x - -2/3 = 0
x = -7/5
x = 16/7
x = -2/3


Input: Compute the solution of x^3 + 659/210x^2 + 6/5x - 16/105 = 0

Output:
x^3 + 659/210x^2 + 6/5x - 16/105 = 0
(x - 1/10)(x - -8/3)(x - -4/7) = 0
x - 1/10 = 0
x - -8/3 = 0
x - -4/7 = 0
x = 1/10
x = -8/3
x = -4/7


Input: Solve the equation 8x + 104/7 = 0

Output:
8x + 104/7 = 0
8x = -104/7
x = -104/7 / 8
x = -13/7


Input:
Solve the equations:
6x + 9y = -426/5
4x + 8y = -374/5

Output:
6x + 9y = -426/5
4x + 8y = -374/5

Using elimination
4*(6x + 9y = -426/5)
6*(4x + 8y = -374/5)
24x + 36y = -1704/5
24x + 48y = -2244/5
Subtract equations
-12y = 108
y = 108/-12
y = -9

Substitute y
6x + 9(-9) = -426/5
6x = -21/5
x = -21/5/6
x = -7/10


Input: Solve the equation x^2 - 31/10x + 11/5 = 0

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


Input: What value of x satisfies 7x - 91/6 = 0

Output:
7x - 91/6 = 0
7x = 91/6
x = 91/6 / 7
x = 13/6


Input: Compute the solution of x^3 + 3/4x^2 - 61/4x - 15 = 0

Output:
x^3 + 3/4x^2 - 61/4x - 15 = 0
(x - -1)(x - -15/4)(x - 4) = 0
x - -1 = 0
x - -15/4 = 0
x - 4 = 0
x = -1
x = -15/4
x = 4


Input: Solve quickly: x^3 + 115/12x^2 + 24x + 65/12 = 0

Output:
x^3 + 115/12x^2 + 24x + 65/12 = 0
(x - -13/3)(x - -1/4)(x - -5) = 0
x - -13/3 = 0
x - -1/4 = 0
x - -5 = 0
x = -13/3
x = -1/4
x = -5


Input: Find x in x^2 + 5/6x - 17/3 = 0

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


Input: Solve the equation 3x + 12 = 0

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


Input: Compute the solution of 3x + 1 = 0

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


Input:
Solve the system:
4x + 1y = 17/3
6x + 2y = 9

Output:
4x + 1y = 17/3
6x + 2y = 9

Using elimination
6*(4x + 1y = 17/3)
4*(6x + 2y = 9)
24x + 6y = 34
24x + 8y = 36
Subtract equations
-2y = -2
y = -2/-2
y = 1

Substitute y
4x + 1(1) = 17/3
4x = 14/3
x = 14/3/4
x = 7/6


Input: Find x for 5x + 13/2 = 0

Output:
5x + 13/2 = 0
5x = -13/2
x = -13/2 / 5
x = -13/10


Input: Find x for 7x - 35/6 = 0

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


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

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


Input: Find x in x^3 - 61/15x^2 - 199/15x + 119/5 = 0

Output:
x^3 - 61/15x^2 - 199/15x + 119/5 = 0
(x - -3)(x - 7/5)(x - 17/3) = 0
x - -3 = 0
x - 7/5 = 0
x - 17/3 = 0
x = -3
x = 7/5
x = 17/3


Input: Find the solution to x^3 - 289/90x^2 + 911/450x - 14/75 = 0

Output:
x^3 - 289/90x^2 + 911/450x - 14/75 = 0
(x - 1/9)(x - 12/5)(x - 7/10) = 0
x - 1/9 = 0
x - 12/5 = 0
x - 7/10 = 0
x = 1/9
x = 12/5
x = 7/10


Input: Solve the equation x^3 - 73/15x^2 - 376/75x + 68/25 = 0

Output:
x^3 - 73/15x^2 - 376/75x + 68/25 = 0
(x - 2/5)(x - 17/3)(x - -6/5) = 0
x - 2/5 = 0
x - 17/3 = 0
x - -6/5 = 0
x = 2/5
x = 17/3
x = -6/5


Input: Solve x^3 - 161/10x^2 - 81/5x + 153/10 = 0

Output:
x^3 - 161/10x^2 - 81/5x + 153/10 = 0
(x - -3/2)(x - 17)(x - 3/5) = 0
x - -3/2 = 0
x - 17 = 0
x - 3/5 = 0
x = -3/2
x = 17
x = 3/5


Input: Find the solution to x^2 + 2/35x - 1/35 = 0

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


Input:
Solve simultaneously:
1x + 5y = -111/7
5x + 2y = -72/7

Output:
1x + 5y = -111/7
5x + 2y = -72/7

Using elimination
5*(1x + 5y = -111/7)
1*(5x + 2y = -72/7)
5x + 25y = -555/7
5x + 2y = -72/7
Subtract equations
23y = -69
y = -69/23
y = -3

Substitute y
1x + 5(-3) = -111/7
1x = -6/7
x = -6/7/1
x = -6/7


Input: Compute the solution of x^2 + 47/10x + 21/5 = 0

Output:
x^2 + 47/10x + 21/5 = 0
(x - -6/5)(x - -7/2) = 0
x - -6/5 = 0  or  x - -7/2 = 0
x = -6/5
x = -7/2


Input: Solve x^3 - 99/5x^2 + 487/5x - 117 = 0

Output:
x^3 - 99/5x^2 + 487/5x - 117 = 0
(x - 5)(x - 13)(x - 9/5) = 0
x - 5 = 0
x - 13 = 0
x - 9/5 = 0
x = 5
x = 13
x = 9/5


Input: Solve quickly: x^2 + 5/6x - 25/6 = 0

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


Input: Determine x in x^2 - 16/7x  = 0

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


Input: Find x for x^2 - 8/5x - 4/5 = 0

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


Input:
Solve simultaneously:
4x + 6y = -3
2x + 2y = 1/6

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

Using elimination
2*(4x + 6y = -3)
4*(2x + 2y = 1/6)
8x + 12y = -6
8x + 8y = 2/3
Subtract equations
4y = -20/3
y = -20/3/4
y = -5/3

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


Input: Find x in 7x + 84 = 0

Output:
7x + 84 = 0
7x = -84
x = -84 / 7
x = -12


Input:
Solve the equations:
6x + 3y = -5/4
8x + 2y = -13/6

Output:
6x + 3y = -5/4
8x + 2y = -13/6

Using elimination
8*(6x + 3y = -5/4)
6*(8x + 2y = -13/6)
48x + 24y = -10
48x + 12y = -13
Subtract equations
12y = 3
y = 3/12
y = 1/4

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


Input: What value of x satisfies 5x - 25/3 = 0

Output:
5x - 25/3 = 0
5x = 25/3
x = 25/3 / 5
x = 5/3


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

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


Input: Find x for x^3 - 385/18x^2 + 2009/18x + 38/3 = 0

Output:
x^3 - 385/18x^2 + 2009/18x + 38/3 = 0
(x - 19/2)(x - 12)(x - -1/9) = 0
x - 19/2 = 0
x - 12 = 0
x - -1/9 = 0
x = 19/2
x = 12
x = -1/9


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

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


Input: Compute the solution of x^3 + 29/4x^2 - 7/4x - 49/2 = 0

Output:
x^3 + 29/4x^2 - 7/4x - 49/2 = 0
(x - -2)(x - 7/4)(x - -7) = 0
x - -2 = 0
x - 7/4 = 0
x - -7 = 0
x = -2
x = 7/4
x = -7


Input:
Solve the equations:
1x + 10y = 129/10
8x + 8y = 84/5

Output:
1x + 10y = 129/10
8x + 8y = 84/5

Using elimination
8*(1x + 10y = 129/10)
1*(8x + 8y = 84/5)
8x + 80y = 516/5
8x + 8y = 84/5
Subtract equations
72y = 432/5
y = 432/5/72
y = 6/5

Substitute y
1x + 10(6/5) = 129/10
1x = 9/10
x = 9/10/1
x = 9/10


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

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


Input: Solve quickly: 3x - 9 = 0

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


Input: Find x in x^2 + 24/35x - 128/35 = 0

Output:
x^2 + 24/35x - 128/35 = 0
(x - -16/7)(x - 8/5) = 0
x - -16/7 = 0  or  x - 8/5 = 0
x = -16/7
x = 8/5


Input: Solve the equation x^3 - 218/21x^2 + 25/7x + 50/21 = 0

Output:
x^3 - 218/21x^2 + 25/7x + 50/21 = 0
(x - 5/7)(x - 10)(x - -1/3) = 0
x - 5/7 = 0
x - 10 = 0
x - -1/3 = 0
x = 5/7
x = 10
x = -1/3


Input: Compute the solution of 1x - 8/3 = 0

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


Input: Solve quickly: 8x + 64/5 = 0

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


Input: Find x in 8x - 136/9 = 0

Output:
8x - 136/9 = 0
8x = 136/9
x = 136/9 / 8
x = 17/9


Input:
Solve the equations:
5x + 8y = 13
10x + 4y = 20

Output:
5x + 8y = 13
10x + 4y = 20

Using elimination
10*(5x + 8y = 13)
5*(10x + 4y = 20)
50x + 80y = 130
50x + 20y = 100
Subtract equations
60y = 30
y = 30/60
y = 1/2

Substitute y
5x + 8(1/2) = 13
5x = 9
x = 9/5
x = 9/5


Input:
Find x and y such that
9x + 7y = -61/5
4x + 10y = -158/5

Output:
9x + 7y = -61/5
4x + 10y = -158/5

Using elimination
4*(9x + 7y = -61/5)
9*(4x + 10y = -158/5)
36x + 28y = -244/5
36x + 90y = -1422/5
Subtract equations
-62y = 1178/5
y = 1178/5/-62
y = -19/5

Substitute y
9x + 7(-19/5) = -61/5
9x = 72/5
x = 72/5/9
x = 8/5


Input: Determine x in x^2 + 7x - 30 = 0

Output:
x^2 + 7x - 30 = 0
(x - -10)(x - 3) = 0
x - -10 = 0  or  x - 3 = 0
x = -10
x = 3


Input: Find x in x^3 + 233/28x^2 + 67/28x - 969/14 = 0

Output:
x^3 + 233/28x^2 + 67/28x - 969/14 = 0
(x - -19/4)(x - 17/7)(x - -6) = 0
x - -19/4 = 0
x - 17/7 = 0
x - -6 = 0
x = -19/4
x = 17/7
x = -6


Input: Find x in x^3 - 19/10x^2 - 49/100x + 931/1000 = 0

Output:
x^3 - 19/10x^2 - 49/100x + 931/1000 = 0
(x - 19/10)(x - -7/10)(x - 7/10) = 0
x - 19/10 = 0
x - -7/10 = 0
x - 7/10 = 0
x = 19/10
x = -7/10
x = 7/10


Input: Find x for 9x - 27 = 0

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


Input: Find x in x^2 + 10/3x - 11/9 = 0

Output:
x^2 + 10/3x - 11/9 = 0
(x - 1/3)(x - -11/3) = 0
x - 1/3 = 0  or  x - -11/3 = 0
x = 1/3
x = -11/3


Input: Find x for 2x + 8 = 0

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


Input: Solve quickly: 7x - 77/6 = 0

Output:
7x - 77/6 = 0
7x = 77/6
x = 77/6 / 7
x = 11/6


Input:
Solve the equations:
5x + 3y = 544/7
7x + 8y = 830/7

Output:
5x + 3y = 544/7
7x + 8y = 830/7

Using elimination
7*(5x + 3y = 544/7)
5*(7x + 8y = 830/7)
35x + 21y = 544
35x + 40y = 4150/7
Subtract equations
-19y = -342/7
y = -342/7/-19
y = 18/7

Substitute y
5x + 3(18/7) = 544/7
5x = 70
x = 70/5
x = 14


Input: Solve the equation x^3 - 35/24x^2 - 13/6x + 7/24 = 0

Output:
x^3 - 35/24x^2 - 13/6x + 7/24 = 0
(x - 1/8)(x - 7/3)(x - -1) = 0
x - 1/8 = 0
x - 7/3 = 0
x - -1 = 0
x = 1/8
x = 7/3
x = -1


Input:
Solve simultaneously:
3x + 9y = 163/21
6x + 10y = 206/21

Output:
3x + 9y = 163/21
6x + 10y = 206/21

Using elimination
6*(3x + 9y = 163/21)
3*(6x + 10y = 206/21)
18x + 54y = 326/7
18x + 30y = 206/7
Subtract equations
24y = 120/7
y = 120/7/24
y = 5/7

Substitute y
3x + 9(5/7) = 163/21
3x = 4/3
x = 4/3/3
x = 4/9


Input:
Solve the system:
8x + 10y = 8
5x + 7y = 5

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

Using elimination
5*(8x + 10y = 8)
8*(5x + 7y = 5)
40x + 50y = 40
40x + 56y = 40
Subtract equations
-6y = 0
y = 0/-6
y = 0

Substitute y
8x + 10(0) = 8
8x = 8
x = 8/8
x = 1


Input: What value of x satisfies 7x - 7 = 0

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


Input:
Solve the equations:
10x + 6y = -34
10x + 8y = -72

Output:
10x + 6y = -34
10x + 8y = -72

Using elimination
10*(10x + 6y = -34)
10*(10x + 8y = -72)
100x + 60y = -340
100x + 80y = -720
Subtract equations
-20y = 380
y = 380/-20
y = -19

Substitute y
10x + 6(-19) = -34
10x = 80
x = 80/10
x = 8


Input: Compute the solution of x^3 - 257/10x^2 + 1151/10x - 22 = 0

Output:
x^3 - 257/10x^2 + 1151/10x - 22 = 0
(x - 20)(x - 1/5)(x - 11/2) = 0
x - 20 = 0
x - 1/5 = 0
x - 11/2 = 0
x = 20
x = 1/5
x = 11/2


Input: Determine x in 4x - 34 = 0

Output:
4x - 34 = 0
4x = 34
x = 34 / 4
x = 17/2


Input: Find the solution to x^3 - 83/20x^2 + 5x - 7/5 = 0

Output:
x^3 - 83/20x^2 + 5x - 7/5 = 0
(x - 2)(x - 2/5)(x - 7/4) = 0
x - 2 = 0
x - 2/5 = 0
x - 7/4 = 0
x = 2
x = 2/5
x = 7/4


Input: Find x in x^2 + 13/6x - 17/9 = 0

Output:
x^2 + 13/6x - 17/9 = 0
(x - -17/6)(x - 2/3) = 0
x - -17/6 = 0  or  x - 2/3 = 0
x = -17/6
x = 2/3


Input: Find x in 8x + 80/3 = 0

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


Input:
Solve simultaneously:
7x + 1y = -53/4
10x + 2y = -39/2

Output:
7x + 1y = -53/4
10x + 2y = -39/2

Using elimination
10*(7x + 1y = -53/4)
7*(10x + 2y = -39/2)
70x + 10y = -265/2
70x + 14y = -273/2
Subtract equations
-4y = 4
y = 4/-4
y = -1

Substitute y
7x + 1(-1) = -53/4
7x = -49/4
x = -49/4/7
x = -7/4


Input: Solve quickly: x^2 + 49/9x + 52/9 = 0

Output:
x^2 + 49/9x + 52/9 = 0
(x - -4)(x - -13/9) = 0
x - -4 = 0  or  x - -13/9 = 0
x = -4
x = -13/9


Input:
Solve the equations:
10x + 2y = 143/3
2x + 8y = 40/3

Output:
10x + 2y = 143/3
2x + 8y = 40/3

Using elimination
2*(10x + 2y = 143/3)
10*(2x + 8y = 40/3)
20x + 4y = 286/3
20x + 80y = 400/3
Subtract equations
-76y = -38
y = -38/-76
y = 1/2

Substitute y
10x + 2(1/2) = 143/3
10x = 140/3
x = 140/3/10
x = 14/3


Input: Determine x in 5x + 85/7 = 0

Output:
5x + 85/7 = 0
5x = -85/7
x = -85/7 / 5
x = -17/7


Input:
Solve the equations:
1x + 9y = -153
1x + 2y = -20

Output:
1x + 9y = -153
1x + 2y = -20

Using elimination
1*(1x + 9y = -153)
1*(1x + 2y = -20)
1x + 9y = -153
1x + 2y = -20
Subtract equations
7y = -133
y = -133/7
y = -19

Substitute y
1x + 9(-19) = -153
1x = 18
x = 18/1
x = 18


Input: Compute the solution of x^2 - 103/14x - 15/14 = 0

Output:
x^2 - 103/14x - 15/14 = 0
(x - -1/7)(x - 15/2) = 0
x - -1/7 = 0  or  x - 15/2 = 0
x = -1/7
x = 15/2


Input:
Find x and y such that
5x + 8y = 43/7
10x + 7y = 2

Output:
5x + 8y = 43/7
10x + 7y = 2

Using elimination
10*(5x + 8y = 43/7)
5*(10x + 7y = 2)
50x + 80y = 430/7
50x + 35y = 10
Subtract equations
45y = 360/7
y = 360/7/45
y = 8/7

Substitute y
5x + 8(8/7) = 43/7
5x = -3
x = -3/5
x = -3/5


Input: Find the solution to x^3 - 39/40x^2 - 269/80x - 9/8 = 0

Output:
x^3 - 39/40x^2 - 269/80x - 9/8 = 0
(x - -9/8)(x - 5/2)(x - -2/5) = 0
x - -9/8 = 0
x - 5/2 = 0
x - -2/5 = 0
x = -9/8
x = 5/2
x = -2/5


Input: Find x in 10x + 16 = 0

Output:
10x + 16 = 0
10x = -16
x = -16 / 10
x = -8/5


Input: What value of x satisfies x^2 + 5/14x - 39/14 = 0

Output:
x^2 + 5/14x - 39/14 = 0
(x - -13/7)(x - 3/2) = 0
x - -13/7 = 0  or  x - 3/2 = 0
x = -13/7
x = 3/2


Input:
Solve the system:
8x + 6y = -1144/7
6x + 8y = -872/7

Output:
8x + 6y = -1144/7
6x + 8y = -872/7

Using elimination
6*(8x + 6y = -1144/7)
8*(6x + 8y = -872/7)
48x + 36y = -6864/7
48x + 64y = -6976/7
Subtract equations
-28y = 16
y = 16/-28
y = -4/7

Substitute y
8x + 6(-4/7) = -1144/7
8x = -160
x = -160/8
x = -20


Input: Find x in x^2 - 74/9x + 40/3 = 0

Output:
x^2 - 74/9x + 40/3 = 0
(x - 6)(x - 20/9) = 0
x - 6 = 0  or  x - 20/9 = 0
x = 6
x = 20/9


Input: Find x in x^2 - 11/4x - 15/4 = 0

Output:
x^2 - 11/4x - 15/4 = 0
(x - -1)(x - 15/4) = 0
x - -1 = 0  or  x - 15/4 = 0
x = -1
x = 15/4


Input:
Solve the system:
5x + 9y = -253/8
7x + 10y = -917/24

Output:
5x + 9y = -253/8
7x + 10y = -917/24

Using elimination
7*(5x + 9y = -253/8)
5*(7x + 10y = -917/24)
35x + 63y = -1771/8
35x + 50y = -4585/24
Subtract equations
13y = -91/3
y = -91/3/13
y = -7/3

Substitute y
5x + 9(-7/3) = -253/8
5x = -85/8
x = -85/8/5
x = -17/8


Input: Solve x^2 - 5/3x + 56/81 = 0

Output:
x^2 - 5/3x + 56/81 = 0
(x - 7/9)(x - 8/9) = 0
x - 7/9 = 0  or  x - 8/9 = 0
x = 7/9
x = 8/9


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

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


Input:
Solve simultaneously:
3x + 4y = 37/10
10x + 9y = 67/10

Output:
3x + 4y = 37/10
10x + 9y = 67/10

Using elimination
10*(3x + 4y = 37/10)
3*(10x + 9y = 67/10)
30x + 40y = 37
30x + 27y = 201/10
Subtract equations
13y = 169/10
y = 169/10/13
y = 13/10

Substitute y
3x + 4(13/10) = 37/10
3x = -3/2
x = -3/2/3
x = -1/2


Input: Compute the solution of 6x + 15/4 = 0

Output:
6x + 15/4 = 0
6x = -15/4
x = -15/4 / 6
x = -5/8


Input: Determine x in 5x - 5/2 = 0

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


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

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


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

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


Input:
Solve the system:
5x + 9y = -29/2
9x + 8y = -179/10

Output:
5x + 9y = -29/2
9x + 8y = -179/10

Using elimination
9*(5x + 9y = -29/2)
5*(9x + 8y = -179/10)
45x + 81y = -261/2
45x + 40y = -179/2
Subtract equations
41y = -41
y = -41/41
y = -1

Substitute y
5x + 9(-1) = -29/2
5x = -11/2
x = -11/2/5
x = -11/10


Input: Find the solution to x^3 - 157/42x^2 - 1/42x + 22/21 = 0

Output:
x^3 - 157/42x^2 - 1/42x + 22/21 = 0
(x - 4/7)(x - 11/3)(x - -1/2) = 0
x - 4/7 = 0
x - 11/3 = 0
x - -1/2 = 0
x = 4/7
x = 11/3
x = -1/2


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

Output:
5x + 11/2 = 0
5x = -11/2
x = -11/2 / 5
x = -11/10


Input: Solve 10x + 190 = 0

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


Input: Solve x^2 - 11/30x - 13/6 = 0

Output:
x^2 - 11/30x - 13/6 = 0
(x - -13/10)(x - 5/3) = 0
x - -13/10 = 0  or  x - 5/3 = 0
x = -13/10
x = 5/3


Input: Solve x^2 + 79/5x + 228/5 = 0

Output:
x^2 + 79/5x + 228/5 = 0
(x - -19/5)(x - -12) = 0
x - -19/5 = 0  or  x - -12 = 0
x = -19/5
x = -12


Input:
Find x and y such that
2x + 7y = -25/2
4x + 6y = -47/3

Output:
2x + 7y = -25/2
4x + 6y = -47/3

Using elimination
4*(2x + 7y = -25/2)
2*(4x + 6y = -47/3)
8x + 28y = -50
8x + 12y = -94/3
Subtract equations
16y = -56/3
y = -56/3/16
y = -7/6

Substitute y
2x + 7(-7/6) = -25/2
2x = -13/3
x = -13/3/2
x = -13/6


Input: Determine x in 6x - 2 = 0

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


Input: Compute the solution of 9x - 27 = 0

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


Input: Determine x in 1x + 19/9 = 0

Output:
1x + 19/9 = 0
1x = -19/9
x = -19/9 / 1
x = -19/9


Input:
Solve simultaneously:
8x + 2y = 89/18
8x + 5y = 205/36

Output:
8x + 2y = 89/18
8x + 5y = 205/36

Using elimination
8*(8x + 2y = 89/18)
8*(8x + 5y = 205/36)
64x + 16y = 356/9
64x + 40y = 410/9
Subtract equations
-24y = -6
y = -6/-24
y = 1/4

Substitute y
8x + 2(1/4) = 89/18
8x = 40/9
x = 40/9/8
x = 5/9


Input: Solve x^3 - 129/70x^2 - 68/35x + 39/14 = 0

Output:
x^3 - 129/70x^2 - 68/35x + 39/14 = 0
(x - -13/10)(x - 1)(x - 15/7) = 0
x - -13/10 = 0
x - 1 = 0
x - 15/7 = 0
x = -13/10
x = 1
x = 15/7


Input:
Solve simultaneously:
1x + 8y = -4
3x + 3y = 13/3

Output:
1x + 8y = -4
3x + 3y = 13/3

Using elimination
3*(1x + 8y = -4)
1*(3x + 3y = 13/3)
3x + 24y = -12
3x + 3y = 13/3
Subtract equations
21y = -49/3
y = -49/3/21
y = -7/9

Substitute y
1x + 8(-7/9) = -4
1x = 20/9
x = 20/9/1
x = 20/9


Input:
Solve simultaneously:
1x + 7y = -82/3
3x + 10y = -103/3

Output:
1x + 7y = -82/3
3x + 10y = -103/3

Using elimination
3*(1x + 7y = -82/3)
1*(3x + 10y = -103/3)
3x + 21y = -82
3x + 10y = -103/3
Subtract equations
11y = -143/3
y = -143/3/11
y = -13/3

Substitute y
1x + 7(-13/3) = -82/3
1x = 3
x = 3/1
x = 3


Input:
Solve the system:
2x + 2y = -4/5
9x + 5y = -10

Output:
2x + 2y = -4/5
9x + 5y = -10

Using elimination
9*(2x + 2y = -4/5)
2*(9x + 5y = -10)
18x + 18y = -36/5
18x + 10y = -20
Subtract equations
8y = 64/5
y = 64/5/8
y = 8/5

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


Input: Compute the solution of x^3 + 61/30x^2 + 109/150x + 4/75 = 0

Output:
x^3 + 61/30x^2 + 109/150x + 4/75 = 0
(x - -1/3)(x - -1/10)(x - -8/5) = 0
x - -1/3 = 0
x - -1/10 = 0
x - -8/5 = 0
x = -1/3
x = -1/10
x = -8/5


Input: Solve 8x - 96 = 0

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


Input: Find the solution to x^3 - 36/5x^2 - 25/4x - 6/5 = 0

Output:
x^3 - 36/5x^2 - 25/4x - 6/5 = 0
(x - -1/2)(x - 8)(x - -3/10) = 0
x - -1/2 = 0
x - 8 = 0
x - -3/10 = 0
x = -1/2
x = 8
x = -3/10


Input: Find x in x^2 + 28/9x - 55/27 = 0

Output:
x^2 + 28/9x - 55/27 = 0
(x - 5/9)(x - -11/3) = 0
x - 5/9 = 0  or  x - -11/3 = 0
x = 5/9
x = -11/3


Input: Determine x in 6x + 3 = 0

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


Input: Solve 2x + 8/9 = 0

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


Input: Compute the solution of x^3 - 169/72x^2 - 263/216x + 35/12 = 0

Output:
x^3 - 169/72x^2 - 263/216x + 35/12 = 0
(x - 7/3)(x - -10/9)(x - 9/8) = 0
x - 7/3 = 0
x - -10/9 = 0
x - 9/8 = 0
x = 7/3
x = -10/9
x = 9/8


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

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


Input: Find x for x^3 - 331/60x^2 + 63/8x - 11/15 = 0

Output:
x^3 - 331/60x^2 + 63/8x - 11/15 = 0
(x - 8/3)(x - 1/10)(x - 11/4) = 0
x - 8/3 = 0
x - 1/10 = 0
x - 11/4 = 0
x = 8/3
x = 1/10
x = 11/4


Input:
Find x and y such that
2x + 5y = 88/5
2x + 2y = 58/5

Output:
2x + 5y = 88/5
2x + 2y = 58/5

Using elimination
2*(2x + 5y = 88/5)
2*(2x + 2y = 58/5)
4x + 10y = 176/5
4x + 4y = 116/5
Subtract equations
6y = 12
y = 12/6
y = 2

Substitute y
2x + 5(2) = 88/5
2x = 38/5
x = 38/5/2
x = 19/5


Input:
Solve the system:
6x + 7y = -7/3
10x + 3y = 95/9

Output:
6x + 7y = -7/3
10x + 3y = 95/9

Using elimination
10*(6x + 7y = -7/3)
6*(10x + 3y = 95/9)
60x + 70y = -70/3
60x + 18y = 190/3
Subtract equations
52y = -260/3
y = -260/3/52
y = -5/3

Substitute y
6x + 7(-5/3) = -7/3
6x = 28/3
x = 28/3/6
x = 14/9


Input: Determine x in x^3 - 145/56x^2 - 1107/392x + 765/98 = 0

Output:
x^3 - 145/56x^2 - 1107/392x + 765/98 = 0
(x - 17/7)(x - 15/8)(x - -12/7) = 0
x - 17/7 = 0
x - 15/8 = 0
x - -12/7 = 0
x = 17/7
x = 15/8
x = -12/7


Input: Solve 6x + 54/7 = 0

Output:
6x + 54/7 = 0
6x = -54/7
x = -54/7 / 6
x = -9/7


Input: Find x for 10x + 130/7 = 0

Output:
10x + 130/7 = 0
10x = -130/7
x = -130/7 / 10
x = -13/7


Input: Solve quickly: 4x - 40/3 = 0

Output:
4x - 40/3 = 0
4x = 40/3
x = 40/3 / 4
x = 10/3


Input: Find the solution to x^3 - 106/5x^2 + 88x - 384/5 = 0

Output:
x^3 - 106/5x^2 + 88x - 384/5 = 0
(x - 16)(x - 4)(x - 6/5) = 0
x - 16 = 0
x - 4 = 0
x - 6/5 = 0
x = 16
x = 4
x = 6/5


Input: Solve x^2 - 15/4x - 27/2 = 0

Output:
x^2 - 15/4x - 27/2 = 0
(x - 6)(x - -9/4) = 0
x - 6 = 0  or  x - -9/4 = 0
x = 6
x = -9/4


Input: Find x for 1x + 6 = 0

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


Input:
Solve simultaneously:
2x + 4y = 130/9
8x + 7y = 196/9

Output:
2x + 4y = 130/9
8x + 7y = 196/9

Using elimination
8*(2x + 4y = 130/9)
2*(8x + 7y = 196/9)
16x + 32y = 1040/9
16x + 14y = 392/9
Subtract equations
18y = 72
y = 72/18
y = 4

Substitute y
2x + 4(4) = 130/9
2x = -14/9
x = -14/9/2
x = -7/9


Input: Find x in x^3 - 29/36x^2 + 23/108x - 1/54 = 0

Output:
x^3 - 29/36x^2 + 23/108x - 1/54 = 0
(x - 1/4)(x - 1/3)(x - 2/9) = 0
x - 1/4 = 0
x - 1/3 = 0
x - 2/9 = 0
x = 1/4
x = 1/3
x = 2/9


Input: Solve 8x - 8 = 0

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


Input: Solve x^2 - 4/3x + 4/9 = 0

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


Input:
Solve the system:
2x + 7y = 12
10x + 8y = 204/7

Output:
2x + 7y = 12
10x + 8y = 204/7

Using elimination
10*(2x + 7y = 12)
2*(10x + 8y = 204/7)
20x + 70y = 120
20x + 16y = 408/7
Subtract equations
54y = 432/7
y = 432/7/54
y = 8/7

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


Input: Find x for 10x + 85/2 = 0

Output:
10x + 85/2 = 0
10x = -85/2
x = -85/2 / 10
x = -17/4


Input: Solve quickly: x^2 - 97/14x + 153/14 = 0

Output:
x^2 - 97/14x + 153/14 = 0
(x - 17/7)(x - 9/2) = 0
x - 17/7 = 0  or  x - 9/2 = 0
x = 17/7
x = 9/2


Input: Determine x in 9x + 99/2 = 0

Output:
9x + 99/2 = 0
9x = -99/2
x = -99/2 / 9
x = -11/2


Input: Find x in x^2 + 85/24x + 19/16 = 0

Output:
x^2 + 85/24x + 19/16 = 0
(x - -19/6)(x - -3/8) = 0
x - -19/6 = 0  or  x - -3/8 = 0
x = -19/6
x = -3/8


Input: Solve quickly: x^3 - 47/3x^2 - 74x + 608/3 = 0

Output:
x^3 - 47/3x^2 - 74x + 608/3 = 0
(x - 2)(x - 19)(x - -16/3) = 0
x - 2 = 0
x - 19 = 0
x - -16/3 = 0
x = 2
x = 19
x = -16/3


Input:
Solve simultaneously:
2x + 5y = -8
3x + 2y = -12

Output:
2x + 5y = -8
3x + 2y = -12

Using elimination
3*(2x + 5y = -8)
2*(3x + 2y = -12)
6x + 15y = -24
6x + 4y = -24
Subtract equations
11y = 0
y = 0/11
y = 0

Substitute y
2x + 5(0) = -8
2x = -8
x = -8/2
x = -4


Input: Find the solution to x^3 + 1/24x^2 - 3287/648x + 361/324 = 0

Output:
x^3 + 1/24x^2 - 3287/648x + 361/324 = 0
(x - -19/8)(x - 19/9)(x - 2/9) = 0
x - -19/8 = 0
x - 19/9 = 0
x - 2/9 = 0
x = -19/8
x = 19/9
x = 2/9


Input: Find x for x^2 - 5/7x - 38/7 = 0

Output:
x^2 - 5/7x - 38/7 = 0
(x - 19/7)(x - -2) = 0
x - 19/7 = 0  or  x - -2 = 0
x = 19/7
x = -2


Input: Find x for x^2 - 20/3x + 28/3 = 0

Output:
x^2 - 20/3x + 28/3 = 0
(x - 14/3)(x - 2) = 0
x - 14/3 = 0  or  x - 2 = 0
x = 14/3
x = 2


Input:
Solve the equations:
5x + 2y = 121/6
1x + 7y = 77/6

Output:
5x + 2y = 121/6
1x + 7y = 77/6

Using elimination
1*(5x + 2y = 121/6)
5*(1x + 7y = 77/6)
5x + 2y = 121/6
5x + 35y = 385/6
Subtract equations
-33y = -44
y = -44/-33
y = 4/3

Substitute y
5x + 2(4/3) = 121/6
5x = 35/2
x = 35/2/5
x = 7/2


Input: Determine x in x^2 - 12/5x + 7/5 = 0

Output:
x^2 - 12/5x + 7/5 = 0
(x - 7/5)(x - 1) = 0
x - 7/5 = 0  or  x - 1 = 0
x = 7/5
x = 1


Input: Find x for x^3 + 18/7x^2 - 61/49x + 6/49 = 0

Output:
x^3 + 18/7x^2 - 61/49x + 6/49 = 0
(x - -3)(x - 1/7)(x - 2/7) = 0
x - -3 = 0
x - 1/7 = 0
x - 2/7 = 0
x = -3
x = 1/7
x = 2/7


Input: Determine x in 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:
Solve simultaneously:
8x + 4y = 104/3
7x + 1y = 137/6

Output:
8x + 4y = 104/3
7x + 1y = 137/6

Using elimination
7*(8x + 4y = 104/3)
8*(7x + 1y = 137/6)
56x + 28y = 728/3
56x + 8y = 548/3
Subtract equations
20y = 60
y = 60/20
y = 3

Substitute y
8x + 4(3) = 104/3
8x = 68/3
x = 68/3/8
x = 17/6


Input: Solve x^3 - 8/3x^2 - 89/9x + 104/9 = 0

Output:
x^3 - 8/3x^2 - 89/9x + 104/9 = 0
(x - -8/3)(x - 1)(x - 13/3) = 0
x - -8/3 = 0
x - 1 = 0
x - 13/3 = 0
x = -8/3
x = 1
x = 13/3


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

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

Using elimination
8*(9x + 8y = 76/7)
9*(8x + 4y = 73/7)
72x + 64y = 608/7
72x + 36y = 657/7
Subtract equations
28y = -7
y = -7/28
y = -1/4

Substitute y
9x + 8(-1/4) = 76/7
9x = 90/7
x = 90/7/9
x = 10/7


Input:
Solve simultaneously:
9x + 9y = 63
5x + 1y = 27

Output:
9x + 9y = 63
5x + 1y = 27

Using elimination
5*(9x + 9y = 63)
9*(5x + 1y = 27)
45x + 45y = 315
45x + 9y = 243
Subtract equations
36y = 72
y = 72/36
y = 2

Substitute y
9x + 9(2) = 63
9x = 45
x = 45/9
x = 5


Input: What value of x satisfies 6x - 42/5 = 0

Output:
6x - 42/5 = 0
6x = 42/5
x = 42/5 / 6
x = 7/5


Input:
Solve simultaneously:
2x + 10y = -2
9x + 5y = -65

Output:
2x + 10y = -2
9x + 5y = -65

Using elimination
9*(2x + 10y = -2)
2*(9x + 5y = -65)
18x + 90y = -18
18x + 10y = -130
Subtract equations
80y = 112
y = 112/80
y = 7/5

Substitute y
2x + 10(7/5) = -2
2x = -16
x = -16/2
x = -8


Input: Find the solution to x^3 - 217/45x^2 + 128/45x + 28/5 = 0

Output:
x^3 - 217/45x^2 + 128/45x + 28/5 = 0
(x - 2)(x - 18/5)(x - -7/9) = 0
x - 2 = 0
x - 18/5 = 0
x - -7/9 = 0
x = 2
x = 18/5
x = -7/9


Input:
Solve simultaneously:
9x + 3y = 135/2
7x + 9y = 65/2

Output:
9x + 3y = 135/2
7x + 9y = 65/2

Using elimination
7*(9x + 3y = 135/2)
9*(7x + 9y = 65/2)
63x + 21y = 945/2
63x + 81y = 585/2
Subtract equations
-60y = 180
y = 180/-60
y = -3

Substitute y
9x + 3(-3) = 135/2
9x = 153/2
x = 153/2/9
x = 17/2


Input: Determine x in 6x - 78/5 = 0

Output:
6x - 78/5 = 0
6x = 78/5
x = 78/5 / 6
x = 13/5


Input:
Solve the equations:
8x + 4y = 60
7x + 2y = 81

Output:
8x + 4y = 60
7x + 2y = 81

Using elimination
7*(8x + 4y = 60)
8*(7x + 2y = 81)
56x + 28y = 420
56x + 16y = 648
Subtract equations
12y = -228
y = -228/12
y = -19

Substitute y
8x + 4(-19) = 60
8x = 136
x = 136/8
x = 17


Input: Solve x^3 + 911/252x^2 + 71/21x + 40/63 = 0

Output:
x^3 + 911/252x^2 + 71/21x + 40/63 = 0
(x - -20/9)(x - -1/4)(x - -8/7) = 0
x - -20/9 = 0
x - -1/4 = 0
x - -8/7 = 0
x = -20/9
x = -1/4
x = -8/7


Input: Solve quickly: x^2 - 14/3x + 8/3 = 0

Output:
x^2 - 14/3x + 8/3 = 0
(x - 2/3)(x - 4) = 0
x - 2/3 = 0  or  x - 4 = 0
x = 2/3
x = 4


Input:
Find x and y such that
6x + 8y = -26/3
6x + 4y = 14/3

Output:
6x + 8y = -26/3
6x + 4y = 14/3

Using elimination
6*(6x + 8y = -26/3)
6*(6x + 4y = 14/3)
36x + 48y = -52
36x + 24y = 28
Subtract equations
24y = -80
y = -80/24
y = -10/3

Substitute y
6x + 8(-10/3) = -26/3
6x = 18
x = 18/6
x = 3


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

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


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

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


Input: What value of x satisfies 8x + 32 = 0

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


Input: Determine x in 8x + 4 = 0

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


Input:
Solve simultaneously:
4x + 7y = -1138/9
6x + 9y = -488/3

Output:
4x + 7y = -1138/9
6x + 9y = -488/3

Using elimination
6*(4x + 7y = -1138/9)
4*(6x + 9y = -488/3)
24x + 42y = -2276/3
24x + 36y = -1952/3
Subtract equations
6y = -108
y = -108/6
y = -18

Substitute y
4x + 7(-18) = -1138/9
4x = -4/9
x = -4/9/4
x = -1/9


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

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

Using elimination
5*(1x + 10y = -118/5)
1*(5x + 2y = -10)
5x + 50y = -118
5x + 2y = -10
Subtract equations
48y = -108
y = -108/48
y = -9/4

Substitute y
1x + 10(-9/4) = -118/5
1x = -11/10
x = -11/10/1
x = -11/10


Input: Determine x in x^2 + 19/8x + 3/4 = 0

Output:
x^2 + 19/8x + 3/4 = 0
(x - -2)(x - -3/8) = 0
x - -2 = 0  or  x - -3/8 = 0
x = -2
x = -3/8


Input: Find x in x^3 - 39/5x^2 + 319/20x - 39/4 = 0

Output:
x^3 - 39/5x^2 + 319/20x - 39/4 = 0
(x - 5)(x - 3/2)(x - 13/10) = 0
x - 5 = 0
x - 3/2 = 0
x - 13/10 = 0
x = 5
x = 3/2
x = 13/10


Input: Solve the equation x^2 - 151/90x - 19/45 = 0

Output:
x^2 - 151/90x - 19/45 = 0
(x - -2/9)(x - 19/10) = 0
x - -2/9 = 0  or  x - 19/10 = 0
x = -2/9
x = 19/10


Input:
Find x and y such that
1x + 9y = -99/2
8x + 1y = -41

Output:
1x + 9y = -99/2
8x + 1y = -41

Using elimination
8*(1x + 9y = -99/2)
1*(8x + 1y = -41)
8x + 72y = -396
8x + 1y = -41
Subtract equations
71y = -355
y = -355/71
y = -5

Substitute y
1x + 9(-5) = -99/2
1x = -9/2
x = -9/2/1
x = -9/2


Input:
Solve the equations:
4x + 7y = 1315/56
3x + 1y = 421/56

Output:
4x + 7y = 1315/56
3x + 1y = 421/56

Using elimination
3*(4x + 7y = 1315/56)
4*(3x + 1y = 421/56)
12x + 21y = 3945/56
12x + 4y = 421/14
Subtract equations
17y = 323/8
y = 323/8/17
y = 19/8

Substitute y
4x + 7(19/8) = 1315/56
4x = 48/7
x = 48/7/4
x = 12/7


Input: Solve 8x - 16 = 0

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


Input: Find x for x^3 - 39/40x^2 - 23/20x + 33/40 = 0

Output:
x^3 - 39/40x^2 - 23/20x + 33/40 = 0
(x - -1)(x - 3/5)(x - 11/8) = 0
x - -1 = 0
x - 3/5 = 0
x - 11/8 = 0
x = -1
x = 3/5
x = 11/8


Input: Solve 6x - 15/4 = 0

Output:
6x - 15/4 = 0
6x = 15/4
x = 15/4 / 6
x = 5/8


Input:
Find x and y such that
1x + 2y = -17/10
7x + 5y = -193/20

Output:
1x + 2y = -17/10
7x + 5y = -193/20

Using elimination
7*(1x + 2y = -17/10)
1*(7x + 5y = -193/20)
7x + 14y = -119/10
7x + 5y = -193/20
Subtract equations
9y = -9/4
y = -9/4/9
y = -1/4

Substitute y
1x + 2(-1/4) = -17/10
1x = -6/5
x = -6/5/1
x = -6/5


Input: Compute the solution of x^3 + 21/5x^2 + 91/20x + 3/4 = 0

Output:
x^3 + 21/5x^2 + 91/20x + 3/4 = 0
(x - -5/2)(x - -3/2)(x - -1/5) = 0
x - -5/2 = 0
x - -3/2 = 0
x - -1/5 = 0
x = -5/2
x = -3/2
x = -1/5


Input: Find the solution to x^3 - 7x^2 + 55/4x - 21/4 = 0

Output:
x^3 - 7x^2 + 55/4x - 21/4 = 0
(x - 7/2)(x - 1/2)(x - 3) = 0
x - 7/2 = 0
x - 1/2 = 0
x - 3 = 0
x = 7/2
x = 1/2
x = 3


Input:
Solve the equations:
9x + 2y = 97/6
5x + 2y = 29/6

Output:
9x + 2y = 97/6
5x + 2y = 29/6

Using elimination
5*(9x + 2y = 97/6)
9*(5x + 2y = 29/6)
45x + 10y = 485/6
45x + 18y = 87/2
Subtract equations
-8y = 112/3
y = 112/3/-8
y = -14/3

Substitute y
9x + 2(-14/3) = 97/6
9x = 51/2
x = 51/2/9
x = 17/6


Input:
Solve the equations:
6x + 1y = 119/10
7x + 1y = 139/10

Output:
6x + 1y = 119/10
7x + 1y = 139/10

Using elimination
7*(6x + 1y = 119/10)
6*(7x + 1y = 139/10)
42x + 7y = 833/10
42x + 6y = 417/5
Subtract equations
1y = -1/10
y = -1/10/1
y = -1/10

Substitute y
6x + 1(-1/10) = 119/10
6x = 12
x = 12/6
x = 2


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

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

Using elimination
7*(3x + 1y = 9)
3*(7x + 9y = 1)
21x + 7y = 63
21x + 27y = 3
Subtract equations
-20y = 60
y = 60/-20
y = -3

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


Input: Find x for x^3 + 33/10x^2 - 7x - 36/5 = 0

Output:
x^3 + 33/10x^2 - 7x - 36/5 = 0
(x - 2)(x - -4/5)(x - -9/2) = 0
x - 2 = 0
x - -4/5 = 0
x - -9/2 = 0
x = 2
x = -4/5
x = -9/2


Input: Find x for 10x - 20 = 0

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


Input: Solve the equation x^3 - 267/56x^2 + 225/32x - 675/224 = 0

Output:
x^3 - 267/56x^2 + 225/32x - 675/224 = 0
(x - 15/8)(x - 3/4)(x - 15/7) = 0
x - 15/8 = 0
x - 3/4 = 0
x - 15/7 = 0
x = 15/8
x = 3/4
x = 15/7


Input: Solve 9x + 99/8 = 0

Output:
9x + 99/8 = 0
9x = -99/8
x = -99/8 / 9
x = -11/8


Input: Find x in x^3 + 197/42x^2 + 305/42x + 26/7 = 0

Output:
x^3 + 197/42x^2 + 305/42x + 26/7 = 0
(x - -13/7)(x - -3/2)(x - -4/3) = 0
x - -13/7 = 0
x - -3/2 = 0
x - -4/3 = 0
x = -13/7
x = -3/2
x = -4/3


Input: What value of x satisfies x^3 + 309/140x^2 + 1/2x - 39/140 = 0

Output:
x^3 + 309/140x^2 + 1/2x - 39/140 = 0
(x - -13/7)(x - 1/4)(x - -3/5) = 0
x - -13/7 = 0
x - 1/4 = 0
x - -3/5 = 0
x = -13/7
x = 1/4
x = -3/5


Input: Solve 6x - 102 = 0

Output:
6x - 102 = 0
6x = 102
x = 102 / 6
x = 17


Input:
Solve the equations:
4x + 3y = 25/6
7x + 9y = 55/6

Output:
4x + 3y = 25/6
7x + 9y = 55/6

Using elimination
7*(4x + 3y = 25/6)
4*(7x + 9y = 55/6)
28x + 21y = 175/6
28x + 36y = 110/3
Subtract equations
-15y = -15/2
y = -15/2/-15
y = 1/2

Substitute y
4x + 3(1/2) = 25/6
4x = 8/3
x = 8/3/4
x = 2/3


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

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

Using elimination
9*(10x + 6y = 25/3)
10*(9x + 9y = -3/2)
90x + 54y = 75
90x + 90y = -15
Subtract equations
-36y = 90
y = 90/-36
y = -5/2

Substitute y
10x + 6(-5/2) = 25/3
10x = 70/3
x = 70/3/10
x = 7/3


Input:
Solve simultaneously:
6x + 9y = -1/2
2x + 8y = -83/18

Output:
6x + 9y = -1/2
2x + 8y = -83/18

Using elimination
2*(6x + 9y = -1/2)
6*(2x + 8y = -83/18)
12x + 18y = -1
12x + 48y = -83/3
Subtract equations
-30y = 80/3
y = 80/3/-30
y = -8/9

Substitute y
6x + 9(-8/9) = -1/2
6x = 15/2
x = 15/2/6
x = 5/4


Input: Find x for x^3 - 153/5x^2 + 227x - 627/5 = 0

Output:
x^3 - 153/5x^2 + 227x - 627/5 = 0
(x - 11)(x - 3/5)(x - 19) = 0
x - 11 = 0
x - 3/5 = 0
x - 19 = 0
x = 11
x = 3/5
x = 19


Input:
Find x and y such that
5x + 9y = 185/8
9x + 2y = 15

Output:
5x + 9y = 185/8
9x + 2y = 15

Using elimination
9*(5x + 9y = 185/8)
5*(9x + 2y = 15)
45x + 81y = 1665/8
45x + 10y = 75
Subtract equations
71y = 1065/8
y = 1065/8/71
y = 15/8

Substitute y
5x + 9(15/8) = 185/8
5x = 25/4
x = 25/4/5
x = 5/4


Input: What value of x satisfies x^3 - 163/72x^2 - 323/72x + 361/36 = 0

Output:
x^3 - 163/72x^2 - 323/72x + 361/36 = 0
(x - -19/9)(x - 2)(x - 19/8) = 0
x - -19/9 = 0
x - 2 = 0
x - 19/8 = 0
x = -19/9
x = 2
x = 19/8


Input: Find x in 2x - 5 = 0

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


Input: Solve the equation x^2 + 40/7x - 9 = 0

Output:
x^2 + 40/7x - 9 = 0
(x - 9/7)(x - -7) = 0
x - 9/7 = 0  or  x - -7 = 0
x = 9/7
x = -7


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

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


Input: Solve the equation x^2 + 19/36x - 7/36 = 0

Output:
x^2 + 19/36x - 7/36 = 0
(x - 1/4)(x - -7/9) = 0
x - 1/4 = 0  or  x - -7/9 = 0
x = 1/4
x = -7/9


Input:
Find x and y such that
7x + 8y = -173/7
4x + 10y = -50/7

Output:
7x + 8y = -173/7
4x + 10y = -50/7

Using elimination
4*(7x + 8y = -173/7)
7*(4x + 10y = -50/7)
28x + 32y = -692/7
28x + 70y = -50
Subtract equations
-38y = -342/7
y = -342/7/-38
y = 9/7

Substitute y
7x + 8(9/7) = -173/7
7x = -35
x = -35/7
x = -5


Input: Solve 6x + 3 = 0

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


Input:
Solve simultaneously:
6x + 7y = 253/6
2x + 1y = 31/6

Output:
6x + 7y = 253/6
2x + 1y = 31/6

Using elimination
2*(6x + 7y = 253/6)
6*(2x + 1y = 31/6)
12x + 14y = 253/3
12x + 6y = 31
Subtract equations
8y = 160/3
y = 160/3/8
y = 20/3

Substitute y
6x + 7(20/3) = 253/6
6x = -9/2
x = -9/2/6
x = -3/4


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

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


Input: Compute the solution of x^3 - 365/63x^2 - 91/27x - 19/63 = 0

Output:
x^3 - 365/63x^2 - 91/27x - 19/63 = 0
(x - -1/9)(x - -3/7)(x - 19/3) = 0
x - -1/9 = 0
x - -3/7 = 0
x - 19/3 = 0
x = -1/9
x = -3/7
x = 19/3


Input: Find x in x^3 - 211/30x^2 + 133/30x  = 0

Output:
x^3 - 211/30x^2 + 133/30x  = 0
(x - 19/3)(x - 7/10)(x - 0) = 0
x - 19/3 = 0
x - 7/10 = 0
x - 0 = 0
x = 19/3
x = 7/10
x = 0


Input: Compute the solution of x^3 - 137/40x^2 - 1117/80x - 357/40 = 0

Output:
x^3 - 137/40x^2 - 1117/80x - 357/40 = 0
(x - -7/8)(x - 6)(x - -17/10) = 0
x - -7/8 = 0
x - 6 = 0
x - -17/10 = 0
x = -7/8
x = 6
x = -17/10


Input:
Solve the system:
5x + 3y = 107/6
3x + 1y = 167/18

Output:
5x + 3y = 107/6
3x + 1y = 167/18

Using elimination
3*(5x + 3y = 107/6)
5*(3x + 1y = 167/18)
15x + 9y = 107/2
15x + 5y = 835/18
Subtract equations
4y = 64/9
y = 64/9/4
y = 16/9

Substitute y
5x + 3(16/9) = 107/6
5x = 25/2
x = 25/2/5
x = 5/2


Input:
Find x and y such that
5x + 8y = 164/7
5x + 2y = 146/7

Output:
5x + 8y = 164/7
5x + 2y = 146/7

Using elimination
5*(5x + 8y = 164/7)
5*(5x + 2y = 146/7)
25x + 40y = 820/7
25x + 10y = 730/7
Subtract equations
30y = 90/7
y = 90/7/30
y = 3/7

Substitute y
5x + 8(3/7) = 164/7
5x = 20
x = 20/5
x = 4


Input: What value of x satisfies 5x + 19/2 = 0

Output:
5x + 19/2 = 0
5x = -19/2
x = -19/2 / 5
x = -19/10


Input:
Solve simultaneously:
7x + 5y = -268/3
8x + 4y = -272/3

Output:
7x + 5y = -268/3
8x + 4y = -272/3

Using elimination
8*(7x + 5y = -268/3)
7*(8x + 4y = -272/3)
56x + 40y = -2144/3
56x + 28y = -1904/3
Subtract equations
12y = -80
y = -80/12
y = -20/3

Substitute y
7x + 5(-20/3) = -268/3
7x = -56
x = -56/7
x = -8


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

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


Input: Compute the solution of 10x + 18 = 0

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


Input:
Solve simultaneously:
8x + 6y = -43
10x + 5y = -65/2

Output:
8x + 6y = -43
10x + 5y = -65/2

Using elimination
10*(8x + 6y = -43)
8*(10x + 5y = -65/2)
80x + 60y = -430
80x + 40y = -260
Subtract equations
20y = -170
y = -170/20
y = -17/2

Substitute y
8x + 6(-17/2) = -43
8x = 8
x = 8/8
x = 1


Input: Find the solution to x^3 + 1x^2 + 7/64x  = 0

Output:
x^3 + 1x^2 + 7/64x  = 0
(x - -7/8)(x - -1/8)(x - 0) = 0
x - -7/8 = 0
x - -1/8 = 0
x - 0 = 0
x = -7/8
x = -1/8
x = 0


Input: Solve quickly: x^2 - 16x - 17 = 0

Output:
x^2 - 16x - 17 = 0
(x - -1)(x - 17) = 0
x - -1 = 0  or  x - 17 = 0
x = -1
x = 17


Input: Find x in x^2 - 1/2x - 15/2 = 0

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


Input:
Solve simultaneously:
2x + 5y = 49/5
5x + 9y = 189/10

Output:
2x + 5y = 49/5
5x + 9y = 189/10

Using elimination
5*(2x + 5y = 49/5)
2*(5x + 9y = 189/10)
10x + 25y = 49
10x + 18y = 189/5
Subtract equations
7y = 56/5
y = 56/5/7
y = 8/5

Substitute y
2x + 5(8/5) = 49/5
2x = 9/5
x = 9/5/2
x = 9/10


Input: Solve quickly: 2x + 10/3 = 0

Output:
2x + 10/3 = 0
2x = -10/3
x = -10/3 / 2
x = -5/3


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

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


Input: Find the solution to 4x - 16/5 = 0

Output:
4x - 16/5 = 0
4x = 16/5
x = 16/5 / 4
x = 4/5


Input:
Find x and y such that
8x + 1y = -140/9
3x + 5y = -295/3

Output:
8x + 1y = -140/9
3x + 5y = -295/3

Using elimination
3*(8x + 1y = -140/9)
8*(3x + 5y = -295/3)
24x + 3y = -140/3
24x + 40y = -2360/3
Subtract equations
-37y = 740
y = 740/-37
y = -20

Substitute y
8x + 1(-20) = -140/9
8x = 40/9
x = 40/9/8
x = 5/9


Input:
Find x and y such that
5x + 1y = 248/3
1x + 6y = 3

Output:
5x + 1y = 248/3
1x + 6y = 3

Using elimination
1*(5x + 1y = 248/3)
5*(1x + 6y = 3)
5x + 1y = 248/3
5x + 30y = 15
Subtract equations
-29y = 203/3
y = 203/3/-29
y = -7/3

Substitute y
5x + 1(-7/3) = 248/3
5x = 85
x = 85/5
x = 17


Input: Determine x in 7x + 133/8 = 0

Output:
7x + 133/8 = 0
7x = -133/8
x = -133/8 / 7
x = -19/8


Input:
Solve the equations:
6x + 7y = -131/12
3x + 3y = -67/12

Output:
6x + 7y = -131/12
3x + 3y = -67/12

Using elimination
3*(6x + 7y = -131/12)
6*(3x + 3y = -67/12)
18x + 21y = -131/4
18x + 18y = -67/2
Subtract equations
3y = 3/4
y = 3/4/3
y = 1/4

Substitute y
6x + 7(1/4) = -131/12
6x = -38/3
x = -38/3/6
x = -19/9


Input: Find x for x^3 + 23/60x^2 - 29/12x - 5/3 = 0

Output:
x^3 + 23/60x^2 - 29/12x - 5/3 = 0
(x - -5/4)(x - -4/5)(x - 5/3) = 0
x - -5/4 = 0
x - -4/5 = 0
x - 5/3 = 0
x = -5/4
x = -4/5
x = 5/3


Input: Solve x^2 - 43/8x + 57/8 = 0

Output:
x^2 - 43/8x + 57/8 = 0
(x - 3)(x - 19/8) = 0
x - 3 = 0  or  x - 19/8 = 0
x = 3
x = 19/8


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

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


Input: Find x in x^3 - 307/120x^2 + 103/60x - 13/40 = 0

Output:
x^3 - 307/120x^2 + 103/60x - 13/40 = 0
(x - 3/5)(x - 1/3)(x - 13/8) = 0
x - 3/5 = 0
x - 1/3 = 0
x - 13/8 = 0
x = 3/5
x = 1/3
x = 13/8


Input: What value of x satisfies x^2 - 8/9x + 16/81 = 0

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


Input: Solve the equation x^2 + 4x - 320 = 0

Output:
x^2 + 4x - 320 = 0
(x - -20)(x - 16) = 0
x - -20 = 0  or  x - 16 = 0
x = -20
x = 16


Input: Solve x^3 - 101/30x^2 + 89/30x - 7/15 = 0

Output:
x^3 - 101/30x^2 + 89/30x - 7/15 = 0
(x - 2)(x - 1/5)(x - 7/6) = 0
x - 2 = 0
x - 1/5 = 0
x - 7/6 = 0
x = 2
x = 1/5
x = 7/6


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 the system:
5x + 4y = -23/10
5x + 10y = 5/2

Output:
5x + 4y = -23/10
5x + 10y = 5/2

Using elimination
5*(5x + 4y = -23/10)
5*(5x + 10y = 5/2)
25x + 20y = -23/2
25x + 50y = 25/2
Subtract equations
-30y = -24
y = -24/-30
y = 4/5

Substitute y
5x + 4(4/5) = -23/10
5x = -11/2
x = -11/2/5
x = -11/10


Input: Solve 3x - 17/3 = 0

Output:
3x - 17/3 = 0
3x = 17/3
x = 17/3 / 3
x = 17/9


Input: Solve the equation 3x - 13/2 = 0

Output:
3x - 13/2 = 0
3x = 13/2
x = 13/2 / 3
x = 13/6


Input: Solve 9x + 1 = 0

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


Input: Compute the solution of x^3 - 10/3x^2 - 257/36x + 77/18 = 0

Output:
x^3 - 10/3x^2 - 257/36x + 77/18 = 0
(x - 14/3)(x - 1/2)(x - -11/6) = 0
x - 14/3 = 0
x - 1/2 = 0
x - -11/6 = 0
x = 14/3
x = 1/2
x = -11/6


Input: Determine x in 10x + 65/3 = 0

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


Input:
Solve the system:
6x + 5y = 35/3
3x + 2y = 37/6

Output:
6x + 5y = 35/3
3x + 2y = 37/6

Using elimination
3*(6x + 5y = 35/3)
6*(3x + 2y = 37/6)
18x + 15y = 35
18x + 12y = 37
Subtract equations
3y = -2
y = -2/3
y = -2/3

Substitute y
6x + 5(-2/3) = 35/3
6x = 15
x = 15/6
x = 5/2


Input: Find x in x^2 - 14/3x - 39 = 0

Output:
x^2 - 14/3x - 39 = 0
(x - 9)(x - -13/3) = 0
x - 9 = 0  or  x - -13/3 = 0
x = 9
x = -13/3


Input: Solve quickly: x^3 + 107/30x^2 - 211/30x + 2/3 = 0

Output:
x^3 + 107/30x^2 - 211/30x + 2/3 = 0
(x - 4/3)(x - 1/10)(x - -5) = 0
x - 4/3 = 0
x - 1/10 = 0
x - -5 = 0
x = 4/3
x = 1/10
x = -5


Input: What value of x satisfies 5x + 30 = 0

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


Input: Determine x in x^2 + 41/40x + 1/4 = 0

Output:
x^2 + 41/40x + 1/4 = 0
(x - -5/8)(x - -2/5) = 0
x - -5/8 = 0  or  x - -2/5 = 0
x = -5/8
x = -2/5


Input:
Solve simultaneously:
4x + 5y = 143/9
3x + 2y = 317/36

Output:
4x + 5y = 143/9
3x + 2y = 317/36

Using elimination
3*(4x + 5y = 143/9)
4*(3x + 2y = 317/36)
12x + 15y = 143/3
12x + 8y = 317/9
Subtract equations
7y = 112/9
y = 112/9/7
y = 16/9

Substitute y
4x + 5(16/9) = 143/9
4x = 7
x = 7/4
x = 7/4


Input:
Solve the system:
9x + 6y = 15
1x + 7y = -11

Output:
9x + 6y = 15
1x + 7y = -11

Using elimination
1*(9x + 6y = 15)
9*(1x + 7y = -11)
9x + 6y = 15
9x + 63y = -99
Subtract equations
-57y = 114
y = 114/-57
y = -2

Substitute y
9x + 6(-2) = 15
9x = 27
x = 27/9
x = 3


Input: What value of x satisfies x^2 + 19/2x + 39/2 = 0

Output:
x^2 + 19/2x + 39/2 = 0
(x - -13/2)(x - -3) = 0
x - -13/2 = 0  or  x - -3 = 0
x = -13/2
x = -3


Input: Find x for x^2 - 65/21x + 34/21 = 0

Output:
x^2 - 65/21x + 34/21 = 0
(x - 17/7)(x - 2/3) = 0
x - 17/7 = 0  or  x - 2/3 = 0
x = 17/7
x = 2/3


Input:
Find x and y such that
4x + 8y = 38
2x + 8y = 43

Output:
4x + 8y = 38
2x + 8y = 43

Using elimination
2*(4x + 8y = 38)
4*(2x + 8y = 43)
8x + 16y = 76
8x + 32y = 172
Subtract equations
-16y = -96
y = -96/-16
y = 6

Substitute y
4x + 8(6) = 38
4x = -10
x = -10/4
x = -5/2


Input: Find the solution to 9x - 117/2 = 0

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


Input:
Find x and y such that
3x + 4y = 318/7
5x + 3y = 508/7

Output:
3x + 4y = 318/7
5x + 3y = 508/7

Using elimination
5*(3x + 4y = 318/7)
3*(5x + 3y = 508/7)
15x + 20y = 1590/7
15x + 9y = 1524/7
Subtract equations
11y = 66/7
y = 66/7/11
y = 6/7

Substitute y
3x + 4(6/7) = 318/7
3x = 42
x = 42/3
x = 14


Input: Solve x^3 + 317/280x^2 - 151/80x - 57/70 = 0

Output:
x^3 + 317/280x^2 - 151/80x - 57/70 = 0
(x - 8/7)(x - -19/10)(x - -3/8) = 0
x - 8/7 = 0
x - -19/10 = 0
x - -3/8 = 0
x = 8/7
x = -19/10
x = -3/8


Input: Find x for 10x - 40 = 0

Output:
10x - 40 = 0
10x = 40
x = 40 / 10
x = 4


Input:
Solve the equations:
10x + 1y = 62/3
4x + 3y = -2/5

Output:
10x + 1y = 62/3
4x + 3y = -2/5

Using elimination
4*(10x + 1y = 62/3)
10*(4x + 3y = -2/5)
40x + 4y = 248/3
40x + 30y = -4
Subtract equations
-26y = 260/3
y = 260/3/-26
y = -10/3

Substitute y
10x + 1(-10/3) = 62/3
10x = 24
x = 24/10
x = 12/5


Input: Find x for x^3 + 7/2x^2 + 49/25x  = 0

Output:
x^3 + 7/2x^2 + 49/25x  = 0
(x - 0)(x - -14/5)(x - -7/10) = 0
x - 0 = 0
x - -14/5 = 0
x - -7/10 = 0
x = 0
x = -14/5
x = -7/10


Input: Compute the solution of x^2 - 7/12x - 143/24 = 0

Output:
x^2 - 7/12x - 143/24 = 0
(x - -13/6)(x - 11/4) = 0
x - -13/6 = 0  or  x - 11/4 = 0
x = -13/6
x = 11/4


Input: What value of x satisfies x^3 + 61/8x^2 + 12x - 45/8 = 0

Output:
x^3 + 61/8x^2 + 12x - 45/8 = 0
(x - 3/8)(x - -5)(x - -3) = 0
x - 3/8 = 0
x - -5 = 0
x - -3 = 0
x = 3/8
x = -5
x = -3


Input:
Solve the equations:
5x + 8y = 21
1x + 2y = 5

Output:
5x + 8y = 21
1x + 2y = 5

Using elimination
1*(5x + 8y = 21)
5*(1x + 2y = 5)
5x + 8y = 21
5x + 10y = 25
Subtract equations
-2y = -4
y = -4/-2
y = 2

Substitute y
5x + 8(2) = 21
5x = 5
x = 5/5
x = 1


Input: Solve x^3 - 35/12x^2 + 7/24x + 11/24 = 0

Output:
x^3 - 35/12x^2 + 7/24x + 11/24 = 0
(x - 1/2)(x - 11/4)(x - -1/3) = 0
x - 1/2 = 0
x - 11/4 = 0
x - -1/3 = 0
x = 1/2
x = 11/4
x = -1/3


Input:
Solve the equations:
2x + 1y = 43/24
9x + 3y = 75/8

Output:
2x + 1y = 43/24
9x + 3y = 75/8

Using elimination
9*(2x + 1y = 43/24)
2*(9x + 3y = 75/8)
18x + 9y = 129/8
18x + 6y = 75/4
Subtract equations
3y = -21/8
y = -21/8/3
y = -7/8

Substitute y
2x + 1(-7/8) = 43/24
2x = 8/3
x = 8/3/2
x = 4/3


Input:
Solve simultaneously:
6x + 7y = 25/3
10x + 10y = 50/3

Output:
6x + 7y = 25/3
10x + 10y = 50/3

Using elimination
10*(6x + 7y = 25/3)
6*(10x + 10y = 50/3)
60x + 70y = 250/3
60x + 60y = 100
Subtract equations
10y = -50/3
y = -50/3/10
y = -5/3

Substitute y
6x + 7(-5/3) = 25/3
6x = 20
x = 20/6
x = 10/3


Input: Find the solution to x^2 + 32/5x + 7 = 0

Output:
x^2 + 32/5x + 7 = 0
(x - -7/5)(x - -5) = 0
x - -7/5 = 0  or  x - -5 = 0
x = -7/5
x = -5


Input: What value of x satisfies x^3 + 2939/504x^2 + 803/72x + 442/63 = 0

Output:
x^3 + 2939/504x^2 + 803/72x + 442/63 = 0
(x - -17/7)(x - -13/8)(x - -16/9) = 0
x - -17/7 = 0
x - -13/8 = 0
x - -16/9 = 0
x = -17/7
x = -13/8
x = -16/9


Input: Solve x^2 - 32/35x + 1/7 = 0

Output:
x^2 - 32/35x + 1/7 = 0
(x - 5/7)(x - 1/5) = 0
x - 5/7 = 0  or  x - 1/5 = 0
x = 5/7
x = 1/5


Input: What value of x satisfies x^2 - 1/5x - 42/5 = 0

Output:
x^2 - 1/5x - 42/5 = 0
(x - -14/5)(x - 3) = 0
x - -14/5 = 0  or  x - 3 = 0
x = -14/5
x = 3


Input:
Solve the equations:
8x + 9y = 197/3
5x + 10y = 395/6

Output:
8x + 9y = 197/3
5x + 10y = 395/6

Using elimination
5*(8x + 9y = 197/3)
8*(5x + 10y = 395/6)
40x + 45y = 985/3
40x + 80y = 1580/3
Subtract equations
-35y = -595/3
y = -595/3/-35
y = 17/3

Substitute y
8x + 9(17/3) = 197/3
8x = 44/3
x = 44/3/8
x = 11/6


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

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


Input: Solve 2x - 13/3 = 0

Output:
2x - 13/3 = 0
2x = 13/3
x = 13/3 / 2
x = 13/6


Input: What value of x satisfies x^2 + 17/14x - 3/7 = 0

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


Input: Solve quickly: x^3 - 14x^2 + 1949/36x - 2261/36 = 0

Output:
x^3 - 14x^2 + 1949/36x - 2261/36 = 0
(x - 7/3)(x - 17/2)(x - 19/6) = 0
x - 7/3 = 0
x - 17/2 = 0
x - 19/6 = 0
x = 7/3
x = 17/2
x = 19/6


Input: Solve the equation x^2 - 91/5x + 18/5 = 0

Output:
x^2 - 91/5x + 18/5 = 0
(x - 1/5)(x - 18) = 0
x - 1/5 = 0  or  x - 18 = 0
x = 1/5
x = 18


Input:
Solve the system:
9x + 7y = -164/5
5x + 3y = -268/15

Output:
9x + 7y = -164/5
5x + 3y = -268/15

Using elimination
5*(9x + 7y = -164/5)
9*(5x + 3y = -268/15)
45x + 35y = -164
45x + 27y = -804/5
Subtract equations
8y = -16/5
y = -16/5/8
y = -2/5

Substitute y
9x + 7(-2/5) = -164/5
9x = -30
x = -30/9
x = -10/3


Input: Compute the solution of 9x - 72/5 = 0

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


Input: Find the solution to 4x - 16/3 = 0

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


Input: Solve quickly: 10x + 80 = 0

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


Input: Find x in 3x - 27 = 0

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


Input:
Solve simultaneously:
10x + 1y = -61/4
5x + 8y = -17

Output:
10x + 1y = -61/4
5x + 8y = -17

Using elimination
5*(10x + 1y = -61/4)
10*(5x + 8y = -17)
50x + 5y = -305/4
50x + 80y = -170
Subtract equations
-75y = 375/4
y = 375/4/-75
y = -5/4

Substitute y
10x + 1(-5/4) = -61/4
10x = -14
x = -14/10
x = -7/5


Input: What value of x satisfies x^3 + 19/4x^2 + 55/8x + 25/8 = 0

Output:
x^3 + 19/4x^2 + 55/8x + 25/8 = 0
(x - -1)(x - -5/2)(x - -5/4) = 0
x - -1 = 0
x - -5/2 = 0
x - -5/4 = 0
x = -1
x = -5/2
x = -5/4


Input:
Find x and y such that
2x + 2y = 14
1x + 6y = 32

Output:
2x + 2y = 14
1x + 6y = 32

Using elimination
1*(2x + 2y = 14)
2*(1x + 6y = 32)
2x + 2y = 14
2x + 12y = 64
Subtract equations
-10y = -50
y = -50/-10
y = 5

Substitute y
2x + 2(5) = 14
2x = 4
x = 4/2
x = 2


Input:
Find x and y such that
8x + 8y = 56/5
3x + 9y = 33/5

Output:
8x + 8y = 56/5
3x + 9y = 33/5

Using elimination
3*(8x + 8y = 56/5)
8*(3x + 9y = 33/5)
24x + 24y = 168/5
24x + 72y = 264/5
Subtract equations
-48y = -96/5
y = -96/5/-48
y = 2/5

Substitute y
8x + 8(2/5) = 56/5
8x = 8
x = 8/8
x = 1


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

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


Input: What value of x satisfies 8x + 8 = 0

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


Input: Solve quickly: 4x - 44/5 = 0

Output:
4x - 44/5 = 0
4x = 44/5
x = 44/5 / 4
x = 11/5


Input:
Solve simultaneously:
1x + 9y = -77/6
10x + 3y = 13/6

Output:
1x + 9y = -77/6
10x + 3y = 13/6

Using elimination
10*(1x + 9y = -77/6)
1*(10x + 3y = 13/6)
10x + 90y = -385/3
10x + 3y = 13/6
Subtract equations
87y = -261/2
y = -261/2/87
y = -3/2

Substitute y
1x + 9(-3/2) = -77/6
1x = 2/3
x = 2/3/1
x = 2/3


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

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


Input: Find x in x^2 + 46/5x + 119/20 = 0

Output:
x^2 + 46/5x + 119/20 = 0
(x - -7/10)(x - -17/2) = 0
x - -7/10 = 0  or  x - -17/2 = 0
x = -7/10
x = -17/2


Input: Solve quickly: 8x + 96 = 0

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


Input: What value of x satisfies 7x + 112/5 = 0

Output:
7x + 112/5 = 0
7x = -112/5
x = -112/5 / 7
x = -16/5


Input: Solve quickly: x^3 + 169/180x^2 - 2021/360x - 209/120 = 0

Output:
x^3 + 169/180x^2 - 2021/360x - 209/120 = 0
(x - -3/10)(x - 19/9)(x - -11/4) = 0
x - -3/10 = 0
x - 19/9 = 0
x - -11/4 = 0
x = -3/10
x = 19/9
x = -11/4


Input:
Solve the equations:
9x + 3y = -174/7
1x + 7y = -346/7

Output:
9x + 3y = -174/7
1x + 7y = -346/7

Using elimination
1*(9x + 3y = -174/7)
9*(1x + 7y = -346/7)
9x + 3y = -174/7
9x + 63y = -3114/7
Subtract equations
-60y = 420
y = 420/-60
y = -7

Substitute y
9x + 3(-7) = -174/7
9x = -27/7
x = -27/7/9
x = -3/7


Input: Solve quickly: 4x + 72 = 0

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


Input: Solve x^2 - 83/10x - 57/5 = 0

Output:
x^2 - 83/10x - 57/5 = 0
(x - 19/2)(x - -6/5) = 0
x - 19/2 = 0  or  x - -6/5 = 0
x = 19/2
x = -6/5


Input: Find the solution to x^2 - 88/15x - 16/3 = 0

Output:
x^2 - 88/15x - 16/3 = 0
(x - -4/5)(x - 20/3) = 0
x - -4/5 = 0  or  x - 20/3 = 0
x = -4/5
x = 20/3


Input:
Solve the equations:
9x + 6y = -63/5
8x + 10y = -56/3

Output:
9x + 6y = -63/5
8x + 10y = -56/3

Using elimination
8*(9x + 6y = -63/5)
9*(8x + 10y = -56/3)
72x + 48y = -504/5
72x + 90y = -168
Subtract equations
-42y = 336/5
y = 336/5/-42
y = -8/5

Substitute y
9x + 6(-8/5) = -63/5
9x = -3
x = -3/9
x = -1/3


Input:
Solve the system:
10x + 5y = 475/12
4x + 3y = 43/2

Output:
10x + 5y = 475/12
4x + 3y = 43/2

Using elimination
4*(10x + 5y = 475/12)
10*(4x + 3y = 43/2)
40x + 20y = 475/3
40x + 30y = 215
Subtract equations
-10y = -170/3
y = -170/3/-10
y = 17/3

Substitute y
10x + 5(17/3) = 475/12
10x = 45/4
x = 45/4/10
x = 9/8


Input:
Find x and y such that
8x + 1y = -47/12
9x + 4y = -8

Output:
8x + 1y = -47/12
9x + 4y = -8

Using elimination
9*(8x + 1y = -47/12)
8*(9x + 4y = -8)
72x + 9y = -141/4
72x + 32y = -64
Subtract equations
-23y = 115/4
y = 115/4/-23
y = -5/4

Substitute y
8x + 1(-5/4) = -47/12
8x = -8/3
x = -8/3/8
x = -1/3


Input: Solve the equation 6x + 14 = 0

Output:
6x + 14 = 0
6x = -14
x = -14 / 6
x = -7/3


Input: Find x in 2x - 36/7 = 0

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


Input: Find the solution to 5x - 50/7 = 0

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


Input: Solve x^2 - 26/9x + 160/81 = 0

Output:
x^2 - 26/9x + 160/81 = 0
(x - 16/9)(x - 10/9) = 0
x - 16/9 = 0  or  x - 10/9 = 0
x = 16/9
x = 10/9


Input: Solve the equation 5x + 20 = 0

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


Input: Determine x in x^2 - 131/7x - 180/7 = 0

Output:
x^2 - 131/7x - 180/7 = 0
(x - 20)(x - -9/7) = 0
x - 20 = 0  or  x - -9/7 = 0
x = 20
x = -9/7


Input: Determine x in x^3 + 17/10x^2 - 9/10x - 9/5 = 0

Output:
x^3 + 17/10x^2 - 9/10x - 9/5 = 0
(x - -6/5)(x - -3/2)(x - 1) = 0
x - -6/5 = 0
x - -3/2 = 0
x - 1 = 0
x = -6/5
x = -3/2
x = 1


Input: Find x for x^3 + 109/28x^2 - 21/2x - 855/28 = 0

Output:
x^3 + 109/28x^2 - 21/2x - 855/28 = 0
(x - 3)(x - -15/7)(x - -19/4) = 0
x - 3 = 0
x - -15/7 = 0
x - -19/4 = 0
x = 3
x = -15/7
x = -19/4


Input:
Solve the system:
10x + 9y = -707/20
3x + 6y = -741/40

Output:
10x + 9y = -707/20
3x + 6y = -741/40

Using elimination
3*(10x + 9y = -707/20)
10*(3x + 6y = -741/40)
30x + 27y = -2121/20
30x + 60y = -741/4
Subtract equations
-33y = 396/5
y = 396/5/-33
y = -12/5

Substitute y
10x + 9(-12/5) = -707/20
10x = -55/4
x = -55/4/10
x = -11/8


Input: Solve quickly: x^3 + 27/10x^2 - 53/5x + 9/2 = 0

Output:
x^3 + 27/10x^2 - 53/5x + 9/2 = 0
(x - -5)(x - 9/5)(x - 1/2) = 0
x - -5 = 0
x - 9/5 = 0
x - 1/2 = 0
x = -5
x = 9/5
x = 1/2


Input:
Solve the system:
2x + 10y = -2
9x + 5y = 31

Output:
2x + 10y = -2
9x + 5y = 31

Using elimination
9*(2x + 10y = -2)
2*(9x + 5y = 31)
18x + 90y = -18
18x + 10y = 62
Subtract equations
80y = -80
y = -80/80
y = -1

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


Input: Find the solution to x^3 - 25/6x^2 + 29/6x - 5/3 = 0

Output:
x^3 - 25/6x^2 + 29/6x - 5/3 = 0
(x - 2/3)(x - 5/2)(x - 1) = 0
x - 2/3 = 0
x - 5/2 = 0
x - 1 = 0
x = 2/3
x = 5/2
x = 1


Input: Find x in 7x + 133/5 = 0

Output:
7x + 133/5 = 0
7x = -133/5
x = -133/5 / 7
x = -19/5


Input: Solve the equation x^2 - 41/35x - 22/35 = 0

Output:
x^2 - 41/35x - 22/35 = 0
(x - -2/5)(x - 11/7) = 0
x - -2/5 = 0  or  x - 11/7 = 0
x = -2/5
x = 11/7


Input:
Solve simultaneously:
4x + 2y = 23/10
9x + 6y = 33/10

Output:
4x + 2y = 23/10
9x + 6y = 33/10

Using elimination
9*(4x + 2y = 23/10)
4*(9x + 6y = 33/10)
36x + 18y = 207/10
36x + 24y = 66/5
Subtract equations
-6y = 15/2
y = 15/2/-6
y = -5/4

Substitute y
4x + 2(-5/4) = 23/10
4x = 24/5
x = 24/5/4
x = 6/5


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

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


Input: Determine x in x^2 - 5/4x - 51/4 = 0

Output:
x^2 - 5/4x - 51/4 = 0
(x - 17/4)(x - -3) = 0
x - 17/4 = 0  or  x - -3 = 0
x = 17/4
x = -3


Input: Compute the solution of x^3 + 101/56x^2 - 249/112x - 135/112 = 0

Output:
x^3 + 101/56x^2 - 249/112x - 135/112 = 0
(x - 9/8)(x - -3/7)(x - -5/2) = 0
x - 9/8 = 0
x - -3/7 = 0
x - -5/2 = 0
x = 9/8
x = -3/7
x = -5/2


Input: Find x for 4x + 38/5 = 0

Output:
4x + 38/5 = 0
4x = -38/5
x = -38/5 / 4
x = -19/10


Input: Find the solution to 4x + 10/3 = 0

Output:
4x + 10/3 = 0
4x = -10/3
x = -10/3 / 4
x = -5/6


Input: Solve the equation x^2 + 109/36x + 7/4 = 0

Output:
x^2 + 109/36x + 7/4 = 0
(x - -7/9)(x - -9/4) = 0
x - -7/9 = 0  or  x - -9/4 = 0
x = -7/9
x = -9/4


Input:
Find x and y such that
3x + 2y = 127/10
2x + 8y = 209/5

Output:
3x + 2y = 127/10
2x + 8y = 209/5

Using elimination
2*(3x + 2y = 127/10)
3*(2x + 8y = 209/5)
6x + 4y = 127/5
6x + 24y = 627/5
Subtract equations
-20y = -100
y = -100/-20
y = 5

Substitute y
3x + 2(5) = 127/10
3x = 27/10
x = 27/10/3
x = 9/10


Input:
Solve the system:
3x + 1y = -91/15
7x + 8y = 241/15

Output:
3x + 1y = -91/15
7x + 8y = 241/15

Using elimination
7*(3x + 1y = -91/15)
3*(7x + 8y = 241/15)
21x + 7y = -637/15
21x + 24y = 241/5
Subtract equations
-17y = -272/3
y = -272/3/-17
y = 16/3

Substitute y
3x + 1(16/3) = -91/15
3x = -57/5
x = -57/5/3
x = -19/5


Input: Find the solution to x^2 + 4/3x - 160/81 = 0

Output:
x^2 + 4/3x - 160/81 = 0
(x - 8/9)(x - -20/9) = 0
x - 8/9 = 0  or  x - -20/9 = 0
x = 8/9
x = -20/9


Input: Find the solution to x^2 - 251/72x + 209/72 = 0

Output:
x^2 - 251/72x + 209/72 = 0
(x - 11/8)(x - 19/9) = 0
x - 11/8 = 0  or  x - 19/9 = 0
x = 11/8
x = 19/9


Input: Find the solution to x^3 - 59/7x^2 - 23/28x + 51/28 = 0

Output:
x^3 - 59/7x^2 - 23/28x + 51/28 = 0
(x - -1/2)(x - 17/2)(x - 3/7) = 0
x - -1/2 = 0
x - 17/2 = 0
x - 3/7 = 0
x = -1/2
x = 17/2
x = 3/7


Input: Compute the solution of x^2 - 157/36x + 65/18 = 0

Output:
x^2 - 157/36x + 65/18 = 0
(x - 13/4)(x - 10/9) = 0
x - 13/4 = 0  or  x - 10/9 = 0
x = 13/4
x = 10/9


Input: Find x for 3x + 9 = 0

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


Input: Find the solution to x^3 - 131/30x^2 + 1601/300x - 247/200 = 0

Output:
x^3 - 131/30x^2 + 1601/300x - 247/200 = 0
(x - 19/10)(x - 13/6)(x - 3/10) = 0
x - 19/10 = 0
x - 13/6 = 0
x - 3/10 = 0
x = 19/10
x = 13/6
x = 3/10


Input: Solve x^2 + 16/3x - 4 = 0

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


Input:
Solve the system:
6x + 3y = 153/20
8x + 1y = 279/20

Output:
6x + 3y = 153/20
8x + 1y = 279/20

Using elimination
8*(6x + 3y = 153/20)
6*(8x + 1y = 279/20)
48x + 24y = 306/5
48x + 6y = 837/10
Subtract equations
18y = -45/2
y = -45/2/18
y = -5/4

Substitute y
6x + 3(-5/4) = 153/20
6x = 57/5
x = 57/5/6
x = 19/10


Input:
Solve the equations:
4x + 1y = -25/18
10x + 7y = -319/18

Output:
4x + 1y = -25/18
10x + 7y = -319/18

Using elimination
10*(4x + 1y = -25/18)
4*(10x + 7y = -319/18)
40x + 10y = -125/9
40x + 28y = -638/9
Subtract equations
-18y = 57
y = 57/-18
y = -19/6

Substitute y
4x + 1(-19/6) = -25/18
4x = 16/9
x = 16/9/4
x = 4/9


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

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


Input: Determine x in x^2 + 7/4x - 65/4 = 0

Output:
x^2 + 7/4x - 65/4 = 0
(x - -5)(x - 13/4) = 0
x - -5 = 0  or  x - 13/4 = 0
x = -5
x = 13/4


Input:
Solve the equations:
3x + 9y = -315/2
7x + 10y = -339/2

Output:
3x + 9y = -315/2
7x + 10y = -339/2

Using elimination
7*(3x + 9y = -315/2)
3*(7x + 10y = -339/2)
21x + 63y = -2205/2
21x + 30y = -1017/2
Subtract equations
33y = -594
y = -594/33
y = -18

Substitute y
3x + 9(-18) = -315/2
3x = 9/2
x = 9/2/3
x = 3/2


Input: Find x for 5x + 65/9 = 0

Output:
5x + 65/9 = 0
5x = -65/9
x = -65/9 / 5
x = -13/9


Input: Solve the equation 4x + 32/9 = 0

Output:
4x + 32/9 = 0
4x = -32/9
x = -32/9 / 4
x = -8/9


Input:
Solve the system:
2x + 5y = 11/2
3x + 6y = 12

Output:
2x + 5y = 11/2
3x + 6y = 12

Using elimination
3*(2x + 5y = 11/2)
2*(3x + 6y = 12)
6x + 15y = 33/2
6x + 12y = 24
Subtract equations
3y = -15/2
y = -15/2/3
y = -5/2

Substitute y
2x + 5(-5/2) = 11/2
2x = 18
x = 18/2
x = 9


Input:
Solve the equations:
10x + 4y = 38/3
2x + 5y = -26/3

Output:
10x + 4y = 38/3
2x + 5y = -26/3

Using elimination
2*(10x + 4y = 38/3)
10*(2x + 5y = -26/3)
20x + 8y = 76/3
20x + 50y = -260/3
Subtract equations
-42y = 112
y = 112/-42
y = -8/3

Substitute y
10x + 4(-8/3) = 38/3
10x = 70/3
x = 70/3/10
x = 7/3


Input: Find the solution to 7x + 63 = 0

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


Input: Compute the solution of x^3 + 27/10x^2 - 24/5x + 8/5 = 0

Output:
x^3 + 27/10x^2 - 24/5x + 8/5 = 0
(x - 1/2)(x - 4/5)(x - -4) = 0
x - 1/2 = 0
x - 4/5 = 0
x - -4 = 0
x = 1/2
x = 4/5
x = -4


Input: Solve the equation x^2 + 112/15x + 16/3 = 0

Output:
x^2 + 112/15x + 16/3 = 0
(x - -20/3)(x - -4/5) = 0
x - -20/3 = 0  or  x - -4/5 = 0
x = -20/3
x = -4/5


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

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

Using elimination
2*(4x + 2y = 3)
4*(2x + 5y = 3/2)
8x + 4y = 6
8x + 20y = 6
Subtract equations
-16y = 0
y = 0/-16
y = 0

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


Input: Solve quickly: x^3 + 69/20x^2 + 27/10x  = 0

Output:
x^3 + 69/20x^2 + 27/10x  = 0
(x - 0)(x - -9/4)(x - -6/5) = 0
x - 0 = 0
x - -9/4 = 0
x - -6/5 = 0
x = 0
x = -9/4
x = -6/5


Input: Find x for x^3 + 43/36x^2 - 518/27x + 416/27 = 0

Output:
x^3 + 43/36x^2 - 518/27x + 416/27 = 0
(x - 13/4)(x - 8/9)(x - -16/3) = 0
x - 13/4 = 0
x - 8/9 = 0
x - -16/3 = 0
x = 13/4
x = 8/9
x = -16/3


Input:
Find x and y such that
10x + 10y = 63/2
7x + 8y = 469/20

Output:
10x + 10y = 63/2
7x + 8y = 469/20

Using elimination
7*(10x + 10y = 63/2)
10*(7x + 8y = 469/20)
70x + 70y = 441/2
70x + 80y = 469/2
Subtract equations
-10y = -14
y = -14/-10
y = 7/5

Substitute y
10x + 10(7/5) = 63/2
10x = 35/2
x = 35/2/10
x = 7/4


Input:
Solve simultaneously:
10x + 4y = -5
4x + 1y = -5

Output:
10x + 4y = -5
4x + 1y = -5

Using elimination
4*(10x + 4y = -5)
10*(4x + 1y = -5)
40x + 16y = -20
40x + 10y = -50
Subtract equations
6y = 30
y = 30/6
y = 5

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


Input:
Find x and y such that
2x + 1y = -40/9
5x + 9y = -15/2

Output:
2x + 1y = -40/9
5x + 9y = -15/2

Using elimination
5*(2x + 1y = -40/9)
2*(5x + 9y = -15/2)
10x + 5y = -200/9
10x + 18y = -15
Subtract equations
-13y = -65/9
y = -65/9/-13
y = 5/9

Substitute y
2x + 1(5/9) = -40/9
2x = -5
x = -5/2
x = -5/2


Input: Find the solution to x^3 + 23/10x^2 + 13/18x - 11/45 = 0

Output:
x^3 + 23/10x^2 + 13/18x - 11/45 = 0
(x - -11/6)(x - 1/5)(x - -2/3) = 0
x - -11/6 = 0
x - 1/5 = 0
x - -2/3 = 0
x = -11/6
x = 1/5
x = -2/3


Input: Solve 9x + 18 = 0

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


Input: Solve 4x + 44/5 = 0

Output:
4x + 44/5 = 0
4x = -44/5
x = -44/5 / 4
x = -11/5


Input: What value of x satisfies 3x + 9/8 = 0

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


Input: What value of x satisfies x^2 - 5/4x - 7/8 = 0

Output:
x^2 - 5/4x - 7/8 = 0
(x - 7/4)(x - -1/2) = 0
x - 7/4 = 0  or  x - -1/2 = 0
x = 7/4
x = -1/2


Input: Solve the equation x^3 - 49/8x^2 + 189/16x - 117/16 = 0

Output:
x^3 - 49/8x^2 + 189/16x - 117/16 = 0
(x - 3)(x - 13/8)(x - 3/2) = 0
x - 3 = 0
x - 13/8 = 0
x - 3/2 = 0
x = 3
x = 13/8
x = 3/2


Input:
Solve simultaneously:
9x + 9y = -57/5
7x + 8y = -113/15

Output:
9x + 9y = -57/5
7x + 8y = -113/15

Using elimination
7*(9x + 9y = -57/5)
9*(7x + 8y = -113/15)
63x + 63y = -399/5
63x + 72y = -339/5
Subtract equations
-9y = -12
y = -12/-9
y = 4/3

Substitute y
9x + 9(4/3) = -57/5
9x = -117/5
x = -117/5/9
x = -13/5


Input: Determine x in x^2 + 11/4x + 3/2 = 0

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


Input: Solve the equation x^2 - 23/7x + 6/7 = 0

Output:
x^2 - 23/7x + 6/7 = 0
(x - 2/7)(x - 3) = 0
x - 2/7 = 0  or  x - 3 = 0
x = 2/7
x = 3


Input: Solve quickly: 9x + 117/4 = 0

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


Input: Compute the solution of 9x - 7 = 0

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


Input: Solve the equation x^2 - 33/8x + 91/32 = 0

Output:
x^2 - 33/8x + 91/32 = 0
(x - 13/4)(x - 7/8) = 0
x - 13/4 = 0  or  x - 7/8 = 0
x = 13/4
x = 7/8


Input: Find x for x^2 - 16/15x - 1 = 0

Output:
x^2 - 16/15x - 1 = 0
(x - 5/3)(x - -3/5) = 0
x - 5/3 = 0  or  x - -3/5 = 0
x = 5/3
x = -3/5


Input: What value of x satisfies 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: Find x for 1x + 17/10 = 0

Output:
1x + 17/10 = 0
1x = -17/10
x = -17/10 / 1
x = -17/10


Input: Compute the solution of 8x - 12 = 0

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


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

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


Input: Find x in 7x  = 0

Output:
7x  = 0
7x = 0
x = 0 / 7
x = 0


Input: Solve quickly: 8x - 8 = 0

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


Input: Compute the solution of x^2 + 22/9x - 221/27 = 0

Output:
x^2 + 22/9x - 221/27 = 0
(x - -13/3)(x - 17/9) = 0
x - -13/3 = 0  or  x - 17/9 = 0
x = -13/3
x = 17/9


Input: Solve x^2 - 11/4x - 5 = 0

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


Input: Find the solution to x^2 - 7/15x - 13/12 = 0

Output:
x^2 - 7/15x - 13/12 = 0
(x - -5/6)(x - 13/10) = 0
x - -5/6 = 0  or  x - 13/10 = 0
x = -5/6
x = 13/10


Input: Solve x^3 - 11/2x^2 + 15/2x  = 0

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


Input: Solve 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: Determine x in 4x - 17 = 0

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


Input:
Solve the system:
4x + 4y = 12/5
7x + 8y = 57/10

Output:
4x + 4y = 12/5
7x + 8y = 57/10

Using elimination
7*(4x + 4y = 12/5)
4*(7x + 8y = 57/10)
28x + 28y = 84/5
28x + 32y = 114/5
Subtract equations
-4y = -6
y = -6/-4
y = 3/2

Substitute y
4x + 4(3/2) = 12/5
4x = -18/5
x = -18/5/4
x = -9/10


Input: Determine x in x^2 - 26/5x + 133/25 = 0

Output:
x^2 - 26/5x + 133/25 = 0
(x - 7/5)(x - 19/5) = 0
x - 7/5 = 0  or  x - 19/5 = 0
x = 7/5
x = 19/5


Input: Compute the solution of x^2 + 61/15x + 22/15 = 0

Output:
x^2 + 61/15x + 22/15 = 0
(x - -2/5)(x - -11/3) = 0
x - -2/5 = 0  or  x - -11/3 = 0
x = -2/5
x = -11/3


Input: Find the solution to 3x - 15/4 = 0

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


Input:
Solve the system:
7x + 3y = 11
1x + 4y = -64/7

Output:
7x + 3y = 11
1x + 4y = -64/7

Using elimination
1*(7x + 3y = 11)
7*(1x + 4y = -64/7)
7x + 3y = 11
7x + 28y = -64
Subtract equations
-25y = 75
y = 75/-25
y = -3

Substitute y
7x + 3(-3) = 11
7x = 20
x = 20/7
x = 20/7


Input: Find the solution to 5x - 25/2 = 0

Output:
5x - 25/2 = 0
5x = 25/2
x = 25/2 / 5
x = 5/2


Input: Solve the equation x^2 - 5/4x - 63/8 = 0

Output:
x^2 - 5/4x - 63/8 = 0
(x - -9/4)(x - 7/2) = 0
x - -9/4 = 0  or  x - 7/2 = 0
x = -9/4
x = 7/2


Input: Determine x in 7x - 7 = 0

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


Input: Find the solution to x^3 - 267/35x^2 + 477/35x - 17/7 = 0

Output:
x^3 - 267/35x^2 + 477/35x - 17/7 = 0
(x - 17/7)(x - 5)(x - 1/5) = 0
x - 17/7 = 0
x - 5 = 0
x - 1/5 = 0
x = 17/7
x = 5
x = 1/5


Input: Solve the equation 9x + 2 = 0

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


Input: Determine x in 3x + 21/2 = 0

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


Input: Solve quickly: x^2 + 89/28x + 51/28 = 0

Output:
x^2 + 89/28x + 51/28 = 0
(x - -3/4)(x - -17/7) = 0
x - -3/4 = 0  or  x - -17/7 = 0
x = -3/4
x = -17/7


Input:
Solve the system:
8x + 7y = 11/3
10x + 4y = 151/6

Output:
8x + 7y = 11/3
10x + 4y = 151/6

Using elimination
10*(8x + 7y = 11/3)
8*(10x + 4y = 151/6)
80x + 70y = 110/3
80x + 32y = 604/3
Subtract equations
38y = -494/3
y = -494/3/38
y = -13/3

Substitute y
8x + 7(-13/3) = 11/3
8x = 34
x = 34/8
x = 17/4


Input: What value of x satisfies x^2 - 41/12x + 13/24 = 0

Output:
x^2 - 41/12x + 13/24 = 0
(x - 13/4)(x - 1/6) = 0
x - 13/4 = 0  or  x - 1/6 = 0
x = 13/4
x = 1/6


Input:
Solve the system:
4x + 9y = -147/2
3x + 5y = -42

Output:
4x + 9y = -147/2
3x + 5y = -42

Using elimination
3*(4x + 9y = -147/2)
4*(3x + 5y = -42)
12x + 27y = -441/2
12x + 20y = -168
Subtract equations
7y = -105/2
y = -105/2/7
y = -15/2

Substitute y
4x + 9(-15/2) = -147/2
4x = -6
x = -6/4
x = -3/2


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

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


Input:
Solve the system:
2x + 9y = 163/10
6x + 2y = 7/5

Output:
2x + 9y = 163/10
6x + 2y = 7/5

Using elimination
6*(2x + 9y = 163/10)
2*(6x + 2y = 7/5)
12x + 54y = 489/5
12x + 4y = 14/5
Subtract equations
50y = 95
y = 95/50
y = 19/10

Substitute y
2x + 9(19/10) = 163/10
2x = -4/5
x = -4/5/2
x = -2/5


Input: Solve 9x - 27/4 = 0

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


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

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


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

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


Input: Solve the equation 1x - 5/4 = 0

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


Input: Solve x^2 + 25/12x + 1 = 0

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


Input:
Find x and y such that
10x + 10y = 105
7x + 3y = 127/2

Output:
10x + 10y = 105
7x + 3y = 127/2

Using elimination
7*(10x + 10y = 105)
10*(7x + 3y = 127/2)
70x + 70y = 735
70x + 30y = 635
Subtract equations
40y = 100
y = 100/40
y = 5/2

Substitute y
10x + 10(5/2) = 105
10x = 80
x = 80/10
x = 8


Input: Solve 9x - 36 = 0

Output:
9x - 36 = 0
9x = 36
x = 36 / 9
x = 4


Input: Find the solution to x^3 + 155/21x^2 + 46/21x - 120/7 = 0

Output:
x^3 + 155/21x^2 + 46/21x - 120/7 = 0
(x - 9/7)(x - -2)(x - -20/3) = 0
x - 9/7 = 0
x - -2 = 0
x - -20/3 = 0
x = 9/7
x = -2
x = -20/3


Input:
Solve the system:
4x + 7y = 201/4
10x + 5y = 415/4

Output:
4x + 7y = 201/4
10x + 5y = 415/4

Using elimination
10*(4x + 7y = 201/4)
4*(10x + 5y = 415/4)
40x + 70y = 1005/2
40x + 20y = 415
Subtract equations
50y = 175/2
y = 175/2/50
y = 7/4

Substitute y
4x + 7(7/4) = 201/4
4x = 38
x = 38/4
x = 19/2


Input:
Solve simultaneously:
1x + 2y = 46/5
4x + 7y = 164/5

Output:
1x + 2y = 46/5
4x + 7y = 164/5

Using elimination
4*(1x + 2y = 46/5)
1*(4x + 7y = 164/5)
4x + 8y = 184/5
4x + 7y = 164/5
Subtract equations
1y = 4
y = 4/1
y = 4

Substitute y
1x + 2(4) = 46/5
1x = 6/5
x = 6/5/1
x = 6/5


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: Compute the solution of x^3 - 31/10x^2 - 9/5x + 63/10 = 0

Output:
x^3 - 31/10x^2 - 9/5x + 63/10 = 0
(x - 3/2)(x - -7/5)(x - 3) = 0
x - 3/2 = 0
x - -7/5 = 0
x - 3 = 0
x = 3/2
x = -7/5
x = 3


Input:
Solve the equations:
3x + 4y = -11/2
5x + 10y = -25/2

Output:
3x + 4y = -11/2
5x + 10y = -25/2

Using elimination
5*(3x + 4y = -11/2)
3*(5x + 10y = -25/2)
15x + 20y = -55/2
15x + 30y = -75/2
Subtract equations
-10y = 10
y = 10/-10
y = -1

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


Input: Solve quickly: x^3 - 15/8x^2 - 63/16x + 27/16 = 0

Output:
x^3 - 15/8x^2 - 63/16x + 27/16 = 0
(x - -3/2)(x - 3/8)(x - 3) = 0
x - -3/2 = 0
x - 3/8 = 0
x - 3 = 0
x = -3/2
x = 3/8
x = 3


Input: Determine x in x^3 + 18/7x^2 - 165/28x - 425/28 = 0

Output:
x^3 + 18/7x^2 - 165/28x - 425/28 = 0
(x - -5/2)(x - 17/7)(x - -5/2) = 0
x - -5/2 = 0
x - 17/7 = 0
x - -5/2 = 0
x = -5/2
x = 17/7
x = -5/2


Input: Find x for x^2 - 1x - 10/9 = 0

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


Input: Solve the equation 2x + 5 = 0

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


Input:
Find x and y such that
10x + 9y = -135/4
9x + 10y = -178/5

Output:
10x + 9y = -135/4
9x + 10y = -178/5

Using elimination
9*(10x + 9y = -135/4)
10*(9x + 10y = -178/5)
90x + 81y = -1215/4
90x + 100y = -356
Subtract equations
-19y = 209/4
y = 209/4/-19
y = -11/4

Substitute y
10x + 9(-11/4) = -135/4
10x = -9
x = -9/10
x = -9/10


Input:
Find x and y such that
7x + 9y = 9
4x + 10y = 23/4

Output:
7x + 9y = 9
4x + 10y = 23/4

Using elimination
4*(7x + 9y = 9)
7*(4x + 10y = 23/4)
28x + 36y = 36
28x + 70y = 161/4
Subtract equations
-34y = -17/4
y = -17/4/-34
y = 1/8

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


Input: Solve quickly: x^2 - 9/2x - 209/18 = 0

Output:
x^2 - 9/2x - 209/18 = 0
(x - -11/6)(x - 19/3) = 0
x - -11/6 = 0  or  x - 19/3 = 0
x = -11/6
x = 19/3


Input: Determine x in 2x + 7/5 = 0

Output:
2x + 7/5 = 0
2x = -7/5
x = -7/5 / 2
x = -7/10


Input:
Solve the system:
3x + 2y = 14
7x + 3y = 73/3

Output:
3x + 2y = 14
7x + 3y = 73/3

Using elimination
7*(3x + 2y = 14)
3*(7x + 3y = 73/3)
21x + 14y = 98
21x + 9y = 73
Subtract equations
5y = 25
y = 25/5
y = 5

Substitute y
3x + 2(5) = 14
3x = 4
x = 4/3
x = 4/3


Input: Find x for x^2 - 8/5x - 48/5 = 0

Output:
x^2 - 8/5x - 48/5 = 0
(x - 4)(x - -12/5) = 0
x - 4 = 0  or  x - -12/5 = 0
x = 4
x = -12/5


Input: Find x in x^3 + 677/84x^2 + 415/21x + 425/28 = 0

Output:
x^3 + 677/84x^2 + 415/21x + 425/28 = 0
(x - -5/3)(x - -15/7)(x - -17/4) = 0
x - -5/3 = 0
x - -15/7 = 0
x - -17/4 = 0
x = -5/3
x = -15/7
x = -17/4


Input: What value of x satisfies x^3 + 499/60x^2 + 1363/60x + 102/5 = 0

Output:
x^3 + 499/60x^2 + 1363/60x + 102/5 = 0
(x - -9/4)(x - -17/5)(x - -8/3) = 0
x - -9/4 = 0
x - -17/5 = 0
x - -8/3 = 0
x = -9/4
x = -17/5
x = -8/3


Input:
Solve the equations:
1x + 10y = 641/21
6x + 10y = 521/21

Output:
1x + 10y = 641/21
6x + 10y = 521/21

Using elimination
6*(1x + 10y = 641/21)
1*(6x + 10y = 521/21)
6x + 60y = 1282/7
6x + 10y = 521/21
Subtract equations
50y = 475/3
y = 475/3/50
y = 19/6

Substitute y
1x + 10(19/6) = 641/21
1x = -8/7
x = -8/7/1
x = -8/7


Input: Solve the equation 9x + 18 = 0

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


Input: Solve x^3 + 44/21x^2 - 25/3x - 66/7 = 0

Output:
x^3 + 44/21x^2 - 25/3x - 66/7 = 0
(x - -1)(x - -11/3)(x - 18/7) = 0
x - -1 = 0
x - -11/3 = 0
x - 18/7 = 0
x = -1
x = -11/3
x = 18/7


Input: What value of x satisfies x^2 - 132/35x + 108/35 = 0

Output:
x^2 - 132/35x + 108/35 = 0
(x - 18/7)(x - 6/5) = 0
x - 18/7 = 0  or  x - 6/5 = 0
x = 18/7
x = 6/5


Input:
Find x and y such that
8x + 2y = 20/3
2x + 10y = -52/3

Output:
8x + 2y = 20/3
2x + 10y = -52/3

Using elimination
2*(8x + 2y = 20/3)
8*(2x + 10y = -52/3)
16x + 4y = 40/3
16x + 80y = -416/3
Subtract equations
-76y = 152
y = 152/-76
y = -2

Substitute y
8x + 2(-2) = 20/3
8x = 32/3
x = 32/3/8
x = 4/3


Input: Find x in 5x - 65/7 = 0

Output:
5x - 65/7 = 0
5x = 65/7
x = 65/7 / 5
x = 13/7


Input: Solve the equation 9x + 171/7 = 0

Output:
9x + 171/7 = 0
9x = -171/7
x = -171/7 / 9
x = -19/7


Input:
Solve simultaneously:
7x + 3y = 31/3
8x + 10y = 1618/63

Output:
7x + 3y = 31/3
8x + 10y = 1618/63

Using elimination
8*(7x + 3y = 31/3)
7*(8x + 10y = 1618/63)
56x + 24y = 248/3
56x + 70y = 1618/9
Subtract equations
-46y = -874/9
y = -874/9/-46
y = 19/9

Substitute y
7x + 3(19/9) = 31/3
7x = 4
x = 4/7
x = 4/7


Input:
Solve simultaneously:
5x + 6y = 16
6x + 4y = 16

Output:
5x + 6y = 16
6x + 4y = 16

Using elimination
6*(5x + 6y = 16)
5*(6x + 4y = 16)
30x + 36y = 96
30x + 20y = 80
Subtract equations
16y = 16
y = 16/16
y = 1

Substitute y
5x + 6(1) = 16
5x = 10
x = 10/5
x = 2


Input: Solve quickly: 8x + 7 = 0

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


Input: Solve the equation x^2 + 77/24x + 49/24 = 0

Output:
x^2 + 77/24x + 49/24 = 0
(x - -7/8)(x - -7/3) = 0
x - -7/8 = 0  or  x - -7/3 = 0
x = -7/8
x = -7/3


Input: What value of x satisfies x^2 - 5x + 144/25 = 0

Output:
x^2 - 5x + 144/25 = 0
(x - 16/5)(x - 9/5) = 0
x - 16/5 = 0  or  x - 9/5 = 0
x = 16/5
x = 9/5


Input: Determine x in x^2 + 55/24x + 21/16 = 0

Output:
x^2 + 55/24x + 21/16 = 0
(x - -9/8)(x - -7/6) = 0
x - -9/8 = 0  or  x - -7/6 = 0
x = -9/8
x = -7/6


Input: Find x in 1x - 1 = 0

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


Input: What value of x satisfies x^3 - 47/4x^2 - 337/4x - 85 = 0

Output:
x^3 - 47/4x^2 - 337/4x - 85 = 0
(x - -5/4)(x - 17)(x - -4) = 0
x - -5/4 = 0
x - 17 = 0
x - -4 = 0
x = -5/4
x = 17
x = -4


Input: Solve 8x + 16 = 0

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


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

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


Input:
Solve the equations:
10x + 5y = 20
5x + 8y = 65

Output:
10x + 5y = 20
5x + 8y = 65

Using elimination
5*(10x + 5y = 20)
10*(5x + 8y = 65)
50x + 25y = 100
50x + 80y = 650
Subtract equations
-55y = -550
y = -550/-55
y = 10

Substitute y
10x + 5(10) = 20
10x = -30
x = -30/10
x = -3


Input: Find the solution to 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 1x - 13/3 = 0

Output:
1x - 13/3 = 0
1x = 13/3
x = 13/3 / 1
x = 13/3


Input: Solve quickly: x^2 - 10/9x - 200/27 = 0

Output:
x^2 - 10/9x - 200/27 = 0
(x - -20/9)(x - 10/3) = 0
x - -20/9 = 0  or  x - 10/3 = 0
x = -20/9
x = 10/3


Input: Solve the equation x^3 + 73/10x^2 + 18/5x - 126/5 = 0

Output:
x^3 + 73/10x^2 + 18/5x - 126/5 = 0
(x - 3/2)(x - -14/5)(x - -6) = 0
x - 3/2 = 0
x - -14/5 = 0
x - -6 = 0
x = 3/2
x = -14/5
x = -6


Input:
Solve simultaneously:
9x + 9y = 549/5
8x + 9y = 504/5

Output:
9x + 9y = 549/5
8x + 9y = 504/5

Using elimination
8*(9x + 9y = 549/5)
9*(8x + 9y = 504/5)
72x + 72y = 4392/5
72x + 81y = 4536/5
Subtract equations
-9y = -144/5
y = -144/5/-9
y = 16/5

Substitute y
9x + 9(16/5) = 549/5
9x = 81
x = 81/9
x = 9


Input: Solve x^2 - 29/72x - 22/9 = 0

Output:
x^2 - 29/72x - 22/9 = 0
(x - 16/9)(x - -11/8) = 0
x - 16/9 = 0  or  x - -11/8 = 0
x = 16/9
x = -11/8


Input:
Solve the equations:
10x + 3y = -117/8
2x + 1y = -131/40

Output:
10x + 3y = -117/8
2x + 1y = -131/40

Using elimination
2*(10x + 3y = -117/8)
10*(2x + 1y = -131/40)
20x + 6y = -117/4
20x + 10y = -131/4
Subtract equations
-4y = 7/2
y = 7/2/-4
y = -7/8

Substitute y
10x + 3(-7/8) = -117/8
10x = -12
x = -12/10
x = -6/5


Input: Compute the solution of x^3 - 1x^2 - 16x + 16 = 0

Output:
x^3 - 1x^2 - 16x + 16 = 0
(x - -4)(x - 1)(x - 4) = 0
x - -4 = 0
x - 1 = 0
x - 4 = 0
x = -4
x = 1
x = 4


Input:
Find x and y such that
1x + 8y = 58/5
10x + 1y = -5/2

Output:
1x + 8y = 58/5
10x + 1y = -5/2

Using elimination
10*(1x + 8y = 58/5)
1*(10x + 1y = -5/2)
10x + 80y = 116
10x + 1y = -5/2
Subtract equations
79y = 237/2
y = 237/2/79
y = 3/2

Substitute y
1x + 8(3/2) = 58/5
1x = -2/5
x = -2/5/1
x = -2/5


Input: Solve the equation 8x - 24 = 0

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


Input: Find x for x^2 + 79/40x + 77/80 = 0

Output:
x^2 + 79/40x + 77/80 = 0
(x - -11/10)(x - -7/8) = 0
x - -11/10 = 0  or  x - -7/8 = 0
x = -11/10
x = -7/8


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

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


Input: Solve 6x - 4 = 0

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


Input: Compute the solution of x^3 - 20/3x^2 - 1517/12x + 85/4 = 0

Output:
x^3 - 20/3x^2 - 1517/12x + 85/4 = 0
(x - -17/2)(x - 1/6)(x - 15) = 0
x - -17/2 = 0
x - 1/6 = 0
x - 15 = 0
x = -17/2
x = 1/6
x = 15


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

Output:
2x - 5/4 = 0
2x = 5/4
x = 5/4 / 2
x = 5/8


Input: Find x for x^3 + 47/10x^2 + 367/50x + 476/125 = 0

Output:
x^3 + 47/10x^2 + 367/50x + 476/125 = 0
(x - -7/5)(x - -8/5)(x - -17/10) = 0
x - -7/5 = 0
x - -8/5 = 0
x - -17/10 = 0
x = -7/5
x = -8/5
x = -17/10


Input:
Solve the system:
3x + 5y = 15
3x + 7y = 13

Output:
3x + 5y = 15
3x + 7y = 13

Using elimination
3*(3x + 5y = 15)
3*(3x + 7y = 13)
9x + 15y = 45
9x + 21y = 39
Subtract equations
-6y = 6
y = 6/-6
y = -1

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


Input: Solve the equation x^2 - 113/6x - 19/6 = 0

Output:
x^2 - 113/6x - 19/6 = 0
(x - 19)(x - -1/6) = 0
x - 19 = 0  or  x - -1/6 = 0
x = 19
x = -1/6


Input: Find the solution to x^3 + 625/84x^2 + 689/56x - 95/42 = 0

Output:
x^3 + 625/84x^2 + 689/56x - 95/42 = 0
(x - 1/6)(x - -19/4)(x - -20/7) = 0
x - 1/6 = 0
x - -19/4 = 0
x - -20/7 = 0
x = 1/6
x = -19/4
x = -20/7


Input: Solve the equation x^3 + 181/90x^2 - 9/10x - 19/9 = 0

Output:
x^3 + 181/90x^2 - 9/10x - 19/9 = 0
(x - -10/9)(x - -19/10)(x - 1) = 0
x - -10/9 = 0
x - -19/10 = 0
x - 1 = 0
x = -10/9
x = -19/10
x = 1


Input:
Solve simultaneously:
2x + 6y = 242/35
8x + 7y = 849/35

Output:
2x + 6y = 242/35
8x + 7y = 849/35

Using elimination
8*(2x + 6y = 242/35)
2*(8x + 7y = 849/35)
16x + 48y = 1936/35
16x + 14y = 1698/35
Subtract equations
34y = 34/5
y = 34/5/34
y = 1/5

Substitute y
2x + 6(1/5) = 242/35
2x = 40/7
x = 40/7/2
x = 20/7


Input:
Solve the system:
3x + 4y = 15
9x + 5y = 55/2

Output:
3x + 4y = 15
9x + 5y = 55/2

Using elimination
9*(3x + 4y = 15)
3*(9x + 5y = 55/2)
27x + 36y = 135
27x + 15y = 165/2
Subtract equations
21y = 105/2
y = 105/2/21
y = 5/2

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


Input: Solve quickly: x^3 - 31/40x^2 - 9/20x + 9/40 = 0

Output:
x^3 - 31/40x^2 - 9/20x + 9/40 = 0
(x - 3/8)(x - -3/5)(x - 1) = 0
x - 3/8 = 0
x - -3/5 = 0
x - 1 = 0
x = 3/8
x = -3/5
x = 1


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

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


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

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


Input: Solve quickly: x^3 + 334/35x^2 - 569/35x - 88/35 = 0

Output:
x^3 + 334/35x^2 - 569/35x - 88/35 = 0
(x - 8/5)(x - -1/7)(x - -11) = 0
x - 8/5 = 0
x - -1/7 = 0
x - -11 = 0
x = 8/5
x = -1/7
x = -11


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

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


Input:
Solve the system:
7x + 10y = 45
9x + 8y = 320/7

Output:
7x + 10y = 45
9x + 8y = 320/7

Using elimination
9*(7x + 10y = 45)
7*(9x + 8y = 320/7)
63x + 90y = 405
63x + 56y = 320
Subtract equations
34y = 85
y = 85/34
y = 5/2

Substitute y
7x + 10(5/2) = 45
7x = 20
x = 20/7
x = 20/7


Input:
Solve simultaneously:
9x + 4y = 81/2
5x + 2y = 37/2

Output:
9x + 4y = 81/2
5x + 2y = 37/2

Using elimination
5*(9x + 4y = 81/2)
9*(5x + 2y = 37/2)
45x + 20y = 405/2
45x + 18y = 333/2
Subtract equations
2y = 36
y = 36/2
y = 18

Substitute y
9x + 4(18) = 81/2
9x = -63/2
x = -63/2/9
x = -7/2


Input: Find x in x^3 - 7/20x^2 - 113/20x - 209/80 = 0

Output:
x^3 - 7/20x^2 - 113/20x - 209/80 = 0
(x - 11/4)(x - -1/2)(x - -19/10) = 0
x - 11/4 = 0
x - -1/2 = 0
x - -19/10 = 0
x = 11/4
x = -1/2
x = -19/10


Input: Solve the equation 10x - 55/4 = 0

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


Input: Solve the equation x^3 - 133/36x^2 + 917/216x - 55/36 = 0

Output:
x^3 - 133/36x^2 + 917/216x - 55/36 = 0
(x - 3/4)(x - 10/9)(x - 11/6) = 0
x - 3/4 = 0
x - 10/9 = 0
x - 11/6 = 0
x = 3/4
x = 10/9
x = 11/6


Input: Solve quickly: 8x + 24 = 0

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


Input:
Solve simultaneously:
9x + 9y = -130/7
1x + 2y = -242/63

Output:
9x + 9y = -130/7
1x + 2y = -242/63

Using elimination
1*(9x + 9y = -130/7)
9*(1x + 2y = -242/63)
9x + 9y = -130/7
9x + 18y = -242/7
Subtract equations
-9y = 16
y = 16/-9
y = -16/9

Substitute y
9x + 9(-16/9) = -130/7
9x = -18/7
x = -18/7/9
x = -2/7


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

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


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

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


Input: Find x for x^2 + 11/15x + 2/15 = 0

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


Input:
Solve the system:
8x + 7y = 5/3
10x + 5y = 10/3

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

Using elimination
10*(8x + 7y = 5/3)
8*(10x + 5y = 10/3)
80x + 70y = 50/3
80x + 40y = 80/3
Subtract equations
30y = -10
y = -10/30
y = -1/3

Substitute y
8x + 7(-1/3) = 5/3
8x = 4
x = 4/8
x = 1/2


Input: Determine x in x^2 + 5x + 6 = 0

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


Input: Find x in x^3 + 25/7x^2 + 100/49x  = 0

Output:
x^3 + 25/7x^2 + 100/49x  = 0
(x - -20/7)(x - -5/7)(x - 0) = 0
x - -20/7 = 0
x - -5/7 = 0
x - 0 = 0
x = -20/7
x = -5/7
x = 0


Input:
Solve the system:
9x + 9y = -648/5
7x + 1y = -24/5

Output:
9x + 9y = -648/5
7x + 1y = -24/5

Using elimination
7*(9x + 9y = -648/5)
9*(7x + 1y = -24/5)
63x + 63y = -4536/5
63x + 9y = -216/5
Subtract equations
54y = -864
y = -864/54
y = -16

Substitute y
9x + 9(-16) = -648/5
9x = 72/5
x = 72/5/9
x = 8/5


Input: Find x in 7x - 133/3 = 0

Output:
7x - 133/3 = 0
7x = 133/3
x = 133/3 / 7
x = 19/3


Input:
Find x and y such that
3x + 9y = 91/4
1x + 4y = 37/3

Output:
3x + 9y = 91/4
1x + 4y = 37/3

Using elimination
1*(3x + 9y = 91/4)
3*(1x + 4y = 37/3)
3x + 9y = 91/4
3x + 12y = 37
Subtract equations
-3y = -57/4
y = -57/4/-3
y = 19/4

Substitute y
3x + 9(19/4) = 91/4
3x = -20
x = -20/3
x = -20/3


Input: Determine x in x^2 - 47/6x - 17/3 = 0

Output:
x^2 - 47/6x - 17/3 = 0
(x - 17/2)(x - -2/3) = 0
x - 17/2 = 0  or  x - -2/3 = 0
x = 17/2
x = -2/3


Input: Determine x in x^2 + 8/9x - 1/9 = 0

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


Input: Find x in x^3 + 281/70x^2 - 20/7x - 408/35 = 0

Output:
x^3 + 281/70x^2 - 20/7x - 408/35 = 0
(x - -4)(x - 17/10)(x - -12/7) = 0
x - -4 = 0
x - 17/10 = 0
x - -12/7 = 0
x = -4
x = 17/10
x = -12/7


Input:
Solve the equations:
5x + 7y = -63/4
7x + 7y = -77/4

Output:
5x + 7y = -63/4
7x + 7y = -77/4

Using elimination
7*(5x + 7y = -63/4)
5*(7x + 7y = -77/4)
35x + 49y = -441/4
35x + 35y = -385/4
Subtract equations
14y = -14
y = -14/14
y = -1

Substitute y
5x + 7(-1) = -63/4
5x = -35/4
x = -35/4/5
x = -7/4


Input: What value of x satisfies 8x + 24 = 0

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


Input: Determine x in x^3 + 81/14x^2 + 9/14x - 162/7 = 0

Output:
x^3 + 81/14x^2 + 9/14x - 162/7 = 0
(x - -9/2)(x - 12/7)(x - -3) = 0
x - -9/2 = 0
x - 12/7 = 0
x - -3 = 0
x = -9/2
x = 12/7
x = -3


Input:
Solve the system:
3x + 6y = -11/3
7x + 3y = 22/9

Output:
3x + 6y = -11/3
7x + 3y = 22/9

Using elimination
7*(3x + 6y = -11/3)
3*(7x + 3y = 22/9)
21x + 42y = -77/3
21x + 9y = 22/3
Subtract equations
33y = -33
y = -33/33
y = -1

Substitute y
3x + 6(-1) = -11/3
3x = 7/3
x = 7/3/3
x = 7/9


Input: Compute the solution of 1x + 17/2 = 0

Output:
1x + 17/2 = 0
1x = -17/2
x = -17/2 / 1
x = -17/2


Input: Determine x in x^2 + 9/2x - 13 = 0

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


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

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


Input: Find the solution to x^3 - 65/72x^2 + 7/72x  = 0

Output:
x^3 - 65/72x^2 + 7/72x  = 0
(x - 7/9)(x - 0)(x - 1/8) = 0
x - 7/9 = 0
x - 0 = 0
x - 1/8 = 0
x = 7/9
x = 0
x = 1/8


Input: Determine x in x^3 + 29/9x^2 + 8/3x + 4/9 = 0

Output:
x^3 + 29/9x^2 + 8/3x + 4/9 = 0
(x - -1)(x - -2/9)(x - -2) = 0
x - -1 = 0
x - -2/9 = 0
x - -2 = 0
x = -1
x = -2/9
x = -2


Input: Find x for x^3 - 31/3x^2 + 29/3x + 21 = 0

Output:
x^3 - 31/3x^2 + 29/3x + 21 = 0
(x - 9)(x - -1)(x - 7/3) = 0
x - 9 = 0
x - -1 = 0
x - 7/3 = 0
x = 9
x = -1
x = 7/3


Input: Solve 6x - 27/2 = 0

Output:
6x - 27/2 = 0
6x = 27/2
x = 27/2 / 6
x = 9/4


Input: Determine x in x^2 + 65/18x - 4 = 0

Output:
x^2 + 65/18x - 4 = 0
(x - -9/2)(x - 8/9) = 0
x - -9/2 = 0  or  x - 8/9 = 0
x = -9/2
x = 8/9


Input: Determine x in x^2 - 25/72x - 25/6 = 0

Output:
x^2 - 25/72x - 25/6 = 0
(x - -15/8)(x - 20/9) = 0
x - -15/8 = 0  or  x - 20/9 = 0
x = -15/8
x = 20/9


Input: Determine x in x^3 - 73/42x^2 - 10/3x + 16/7 = 0

Output:
x^3 - 73/42x^2 - 10/3x + 16/7 = 0
(x - 8/3)(x - 4/7)(x - -3/2) = 0
x - 8/3 = 0
x - 4/7 = 0
x - -3/2 = 0
x = 8/3
x = 4/7
x = -3/2


Input: Compute the solution of 6x - 6/7 = 0

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


Input: Find the solution to x^3 + 19x^2 + 367/4x + 165/4 = 0

Output:
x^3 + 19x^2 + 367/4x + 165/4 = 0
(x - -15/2)(x - -11)(x - -1/2) = 0
x - -15/2 = 0
x - -11 = 0
x - -1/2 = 0
x = -15/2
x = -11
x = -1/2


Input: Solve 10x + 30 = 0

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


Input: Find x in 4x + 4 = 0

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


Input: Solve 3x + 5/3 = 0

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


Input: Determine x in 7x + 4 = 0

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


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

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


Input: Compute the solution of x^3 - 17/8x^2 - 725/392x + 19/28 = 0

Output:
x^3 - 17/8x^2 - 725/392x + 19/28 = 0
(x - 2/7)(x - -7/8)(x - 19/7) = 0
x - 2/7 = 0
x - -7/8 = 0
x - 19/7 = 0
x = 2/7
x = -7/8
x = 19/7


Input: Solve x^3 - 122/15x^2 + 43/5x + 266/15 = 0

Output:
x^3 - 122/15x^2 + 43/5x + 266/15 = 0
(x - 19/3)(x - -1)(x - 14/5) = 0
x - 19/3 = 0
x - -1 = 0
x - 14/5 = 0
x = 19/3
x = -1
x = 14/5


Input: Determine x in x^2 + 200/9x + 400/9 = 0

Output:
x^2 + 200/9x + 400/9 = 0
(x - -20)(x - -20/9) = 0
x - -20 = 0  or  x - -20/9 = 0
x = -20
x = -20/9


Input: Solve quickly: x^2 + 23/35x - 44/7 = 0

Output:
x^2 + 23/35x - 44/7 = 0
(x - 11/5)(x - -20/7) = 0
x - 11/5 = 0  or  x - -20/7 = 0
x = 11/5
x = -20/7


Input: Solve x^3 - 715/42x^2 - 13/42x + 85/7 = 0

Output:
x^3 - 715/42x^2 - 13/42x + 85/7 = 0
(x - 17)(x - -5/6)(x - 6/7) = 0
x - 17 = 0
x - -5/6 = 0
x - 6/7 = 0
x = 17
x = -5/6
x = 6/7


Input: Determine x in x^3 + 7/30x^2 - 58/5x + 208/15 = 0

Output:
x^3 + 7/30x^2 - 58/5x + 208/15 = 0
(x - -4)(x - 8/5)(x - 13/6) = 0
x - -4 = 0
x - 8/5 = 0
x - 13/6 = 0
x = -4
x = 8/5
x = 13/6


Input: Solve the equation x^3 + 37/30x^2 - 709/75x - 1064/75 = 0

Output:
x^3 + 37/30x^2 - 709/75x - 1064/75 = 0
(x - -14/5)(x - -8/5)(x - 19/6) = 0
x - -14/5 = 0
x - -8/5 = 0
x - 19/6 = 0
x = -14/5
x = -8/5
x = 19/6


Input: Solve x^3 + 169/105x^2 - 68/35x - 12/7 = 0

Output:
x^3 + 169/105x^2 - 68/35x - 12/7 = 0
(x - -2/3)(x - 6/5)(x - -15/7) = 0
x - -2/3 = 0
x - 6/5 = 0
x - -15/7 = 0
x = -2/3
x = 6/5
x = -15/7


Input:
Find x and y such that
7x + 10y = 143/6
3x + 6y = 29/2

Output:
7x + 10y = 143/6
3x + 6y = 29/2

Using elimination
3*(7x + 10y = 143/6)
7*(3x + 6y = 29/2)
21x + 30y = 143/2
21x + 42y = 203/2
Subtract equations
-12y = -30
y = -30/-12
y = 5/2

Substitute y
7x + 10(5/2) = 143/6
7x = -7/6
x = -7/6/7
x = -1/6


Input:
Find x and y such that
7x + 5y = -137/6
4x + 5y = -52/3

Output:
7x + 5y = -137/6
4x + 5y = -52/3

Using elimination
4*(7x + 5y = -137/6)
7*(4x + 5y = -52/3)
28x + 20y = -274/3
28x + 35y = -364/3
Subtract equations
-15y = 30
y = 30/-15
y = -2

Substitute y
7x + 5(-2) = -137/6
7x = -77/6
x = -77/6/7
x = -11/6