Input: Solve the equation 1x - 16 = 0

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


Input:
Solve the equations:
1x + 5y = 113/14
6x + 5y = 39/7

Output:
1x + 5y = 113/14
6x + 5y = 39/7

Using elimination
6*(1x + 5y = 113/14)
1*(6x + 5y = 39/7)
6x + 30y = 339/7
6x + 5y = 39/7
Subtract equations
25y = 300/7
y = 300/7/25
y = 12/7

Substitute y
1x + 5(12/7) = 113/14
1x = -1/2
x = -1/2/1
x = -1/2


Input:
Solve the equations:
10x + 3y = 89
1x + 3y = 25/2

Output:
10x + 3y = 89
1x + 3y = 25/2

Using elimination
1*(10x + 3y = 89)
10*(1x + 3y = 25/2)
10x + 3y = 89
10x + 30y = 125
Subtract equations
-27y = -36
y = -36/-27
y = 4/3

Substitute y
10x + 3(4/3) = 89
10x = 85
x = 85/10
x = 17/2


Input:
Solve the system:
8x + 1y = 163/7
7x + 3y = 48

Output:
8x + 1y = 163/7
7x + 3y = 48

Using elimination
7*(8x + 1y = 163/7)
8*(7x + 3y = 48)
56x + 7y = 163
56x + 24y = 384
Subtract equations
-17y = -221
y = -221/-17
y = 13

Substitute y
8x + 1(13) = 163/7
8x = 72/7
x = 72/7/8
x = 9/7


Input: Find the solution to 6x - 20 = 0

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


Input:
Solve the equations:
5x + 5y = -55/8
7x + 10y = -19/4

Output:
5x + 5y = -55/8
7x + 10y = -19/4

Using elimination
7*(5x + 5y = -55/8)
5*(7x + 10y = -19/4)
35x + 35y = -385/8
35x + 50y = -95/4
Subtract equations
-15y = -195/8
y = -195/8/-15
y = 13/8

Substitute y
5x + 5(13/8) = -55/8
5x = -15
x = -15/5
x = -3


Input: Determine x in x^2 - 57/10x - 91/10 = 0

Output:
x^2 - 57/10x - 91/10 = 0
(x - -13/10)(x - 7) = 0
x - -13/10 = 0  or  x - 7 = 0
x = -13/10
x = 7


Input: Solve the equation x^3 + 317/70x^2 + 83/14x + 15/7 = 0

Output:
x^3 + 317/70x^2 + 83/14x + 15/7 = 0
(x - -3/5)(x - -5/2)(x - -10/7) = 0
x - -3/5 = 0
x - -5/2 = 0
x - -10/7 = 0
x = -3/5
x = -5/2
x = -10/7


Input: Find x for x^3 - 123/70x^2 - 319/70x + 57/7 = 0

Output:
x^3 - 123/70x^2 - 319/70x + 57/7 = 0
(x - 19/10)(x - -15/7)(x - 2) = 0
x - 19/10 = 0
x - -15/7 = 0
x - 2 = 0
x = 19/10
x = -15/7
x = 2


Input: Find x for 3x + 20/3 = 0

Output:
3x + 20/3 = 0
3x = -20/3
x = -20/3 / 3
x = -20/9


Input: Solve 8x - 68 = 0

Output:
8x - 68 = 0
8x = 68
x = 68 / 8
x = 17/2


Input: What value of x satisfies x^3 + 43/9x^2 + 244/81x - 32/81 = 0

Output:
x^3 + 43/9x^2 + 244/81x - 32/81 = 0
(x - -4)(x - -8/9)(x - 1/9) = 0
x - -4 = 0
x - -8/9 = 0
x - 1/9 = 0
x = -4
x = -8/9
x = 1/9


Input: Solve the equation 10x - 170/7 = 0

Output:
10x - 170/7 = 0
10x = 170/7
x = 170/7 / 10
x = 17/7


Input: Find the solution to x^2 - 25/9x + 16/9 = 0

Output:
x^2 - 25/9x + 16/9 = 0
(x - 16/9)(x - 1) = 0
x - 16/9 = 0  or  x - 1 = 0
x = 16/9
x = 1


Input: Solve x^2 - 73/20x + 17/20 = 0

Output:
x^2 - 73/20x + 17/20 = 0
(x - 1/4)(x - 17/5) = 0
x - 1/4 = 0  or  x - 17/5 = 0
x = 1/4
x = 17/5


Input: Compute the solution of x^3 + 9/8x^2 - 4x - 9/2 = 0

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


Input: Find x for x^3 + 14/9x^2 - 97/3x + 364/9 = 0

Output:
x^3 + 14/9x^2 - 97/3x + 364/9 = 0
(x - 13/9)(x - 4)(x - -7) = 0
x - 13/9 = 0
x - 4 = 0
x - -7 = 0
x = 13/9
x = 4
x = -7


Input: Compute the solution of x^3 + 79/20x^2 - 609/40x + 351/40 = 0

Output:
x^3 + 79/20x^2 - 609/40x + 351/40 = 0
(x - 9/5)(x - 3/4)(x - -13/2) = 0
x - 9/5 = 0
x - 3/4 = 0
x - -13/2 = 0
x = 9/5
x = 3/4
x = -13/2


Input: Compute the solution of x^3 - 337/36x^2 + 2417/108x - 221/27 = 0

Output:
x^3 - 337/36x^2 + 2417/108x - 221/27 = 0
(x - 13/4)(x - 4/9)(x - 17/3) = 0
x - 13/4 = 0
x - 4/9 = 0
x - 17/3 = 0
x = 13/4
x = 4/9
x = 17/3


Input: Solve the equation 8x - 136/3 = 0

Output:
8x - 136/3 = 0
8x = 136/3
x = 136/3 / 8
x = 17/3


Input: What value of x satisfies x^2 - 59/30x - 19/5 = 0

Output:
x^2 - 59/30x - 19/5 = 0
(x - 19/6)(x - -6/5) = 0
x - 19/6 = 0  or  x - -6/5 = 0
x = 19/6
x = -6/5


Input: Determine x in x^3 - 40/9x^2 - 269/27x + 34/9 = 0

Output:
x^3 - 40/9x^2 - 269/27x + 34/9 = 0
(x - 6)(x - 1/3)(x - -17/9) = 0
x - 6 = 0
x - 1/3 = 0
x - -17/9 = 0
x = 6
x = 1/3
x = -17/9


Input: Determine x in x^3 - 29/30x^2 + 14/45x - 1/30 = 0

Output:
x^3 - 29/30x^2 + 14/45x - 1/30 = 0
(x - 1/3)(x - 1/3)(x - 3/10) = 0
x - 1/3 = 0
x - 1/3 = 0
x - 3/10 = 0
x = 1/3
x = 1/3
x = 3/10


Input: Solve x^2 + 8/9x + 5/27 = 0

Output:
x^2 + 8/9x + 5/27 = 0
(x - -1/3)(x - -5/9) = 0
x - -1/3 = 0  or  x - -5/9 = 0
x = -1/3
x = -5/9


Input: Solve quickly: 3x - 42 = 0

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


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

Output:
x^2 + 9/7x - 36/7 = 0
(x - -3)(x - 12/7) = 0
x - -3 = 0  or  x - 12/7 = 0
x = -3
x = 12/7


Input:
Find x and y such that
1x + 10y = -85/3
9x + 6y = -59

Output:
1x + 10y = -85/3
9x + 6y = -59

Using elimination
9*(1x + 10y = -85/3)
1*(9x + 6y = -59)
9x + 90y = -255
9x + 6y = -59
Subtract equations
84y = -196
y = -196/84
y = -7/3

Substitute y
1x + 10(-7/3) = -85/3
1x = -5
x = -5/1
x = -5


Input: Find x in 5x - 70/3 = 0

Output:
5x - 70/3 = 0
5x = 70/3
x = 70/3 / 5
x = 14/3


Input: What value of x satisfies x^2 - 19/12x - 11/24 = 0

Output:
x^2 - 19/12x - 11/24 = 0
(x - -1/4)(x - 11/6) = 0
x - -1/4 = 0  or  x - 11/6 = 0
x = -1/4
x = 11/6


Input: Find x in x^2 - 52/15x + 169/60 = 0

Output:
x^2 - 52/15x + 169/60 = 0
(x - 13/10)(x - 13/6) = 0
x - 13/10 = 0  or  x - 13/6 = 0
x = 13/10
x = 13/6


Input: Solve the equation x^3 - 131/21x^2 - 158/63x + 760/63 = 0

Output:
x^3 - 131/21x^2 - 158/63x + 760/63 = 0
(x - 19/3)(x - -10/7)(x - 4/3) = 0
x - 19/3 = 0
x - -10/7 = 0
x - 4/3 = 0
x = 19/3
x = -10/7
x = 4/3


Input: What value of x satisfies 7x + 140/3 = 0

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


Input:
Solve the equations:
7x + 10y = 29/3
7x + 8y = 4

Output:
7x + 10y = 29/3
7x + 8y = 4

Using elimination
7*(7x + 10y = 29/3)
7*(7x + 8y = 4)
49x + 70y = 203/3
49x + 56y = 28
Subtract equations
14y = 119/3
y = 119/3/14
y = 17/6

Substitute y
7x + 10(17/6) = 29/3
7x = -56/3
x = -56/3/7
x = -8/3


Input: Find x in x^2 - 137/30x + 33/10 = 0

Output:
x^2 - 137/30x + 33/10 = 0
(x - 11/3)(x - 9/10) = 0
x - 11/3 = 0  or  x - 9/10 = 0
x = 11/3
x = 9/10


Input: Solve 1x - 19/3 = 0

Output:
1x - 19/3 = 0
1x = 19/3
x = 19/3 / 1
x = 19/3


Input:
Solve the equations:
2x + 2y = -13/18
2x + 1y = -29/18

Output:
2x + 2y = -13/18
2x + 1y = -29/18

Using elimination
2*(2x + 2y = -13/18)
2*(2x + 1y = -29/18)
4x + 4y = -13/9
4x + 2y = -29/9
Subtract equations
2y = 16/9
y = 16/9/2
y = 8/9

Substitute y
2x + 2(8/9) = -13/18
2x = -5/2
x = -5/2/2
x = -5/4


Input: Solve x^3 + 17/9x^2 - 440/27x - 100/27 = 0

Output:
x^3 + 17/9x^2 - 440/27x - 100/27 = 0
(x - 10/3)(x - -5)(x - -2/9) = 0
x - 10/3 = 0
x - -5 = 0
x - -2/9 = 0
x = 10/3
x = -5
x = -2/9


Input: Determine x in 9x + 117/5 = 0

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


Input: Solve the equation 6x + 21 = 0

Output:
6x + 21 = 0
6x = -21
x = -21 / 6
x = -7/2


Input:
Solve the equations:
3x + 4y = -31/3
9x + 7y = -26

Output:
3x + 4y = -31/3
9x + 7y = -26

Using elimination
9*(3x + 4y = -31/3)
3*(9x + 7y = -26)
27x + 36y = -93
27x + 21y = -78
Subtract equations
15y = -15
y = -15/15
y = -1

Substitute y
3x + 4(-1) = -31/3
3x = -19/3
x = -19/3/3
x = -19/9


Input: Solve x^2 - 20/3x + 25/3 = 0

Output:
x^2 - 20/3x + 25/3 = 0
(x - 5)(x - 5/3) = 0
x - 5 = 0  or  x - 5/3 = 0
x = 5
x = 5/3


Input: Solve the equation x^3 + 49/30x^2 + 38/45x + 2/15 = 0

Output:
x^3 + 49/30x^2 + 38/45x + 2/15 = 0
(x - -2/3)(x - -2/3)(x - -3/10) = 0
x - -2/3 = 0
x - -2/3 = 0
x - -3/10 = 0
x = -2/3
x = -2/3
x = -3/10


Input: Find the solution to x^2 + 175/8x + 75/2 = 0

Output:
x^2 + 175/8x + 75/2 = 0
(x - -20)(x - -15/8) = 0
x - -20 = 0  or  x - -15/8 = 0
x = -20
x = -15/8


Input:
Solve the equations:
2x + 3y = 78/35
5x + 2y = 72/7

Output:
2x + 3y = 78/35
5x + 2y = 72/7

Using elimination
5*(2x + 3y = 78/35)
2*(5x + 2y = 72/7)
10x + 15y = 78/7
10x + 4y = 144/7
Subtract equations
11y = -66/7
y = -66/7/11
y = -6/7

Substitute y
2x + 3(-6/7) = 78/35
2x = 24/5
x = 24/5/2
x = 12/5


Input: Determine x in x^2 + 21/4x + 5 = 0

Output:
x^2 + 21/4x + 5 = 0
(x - -4)(x - -5/4) = 0
x - -4 = 0  or  x - -5/4 = 0
x = -4
x = -5/4


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

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


Input:
Solve simultaneously:
1x + 9y = -52/3
6x + 8y = -16/9

Output:
1x + 9y = -52/3
6x + 8y = -16/9

Using elimination
6*(1x + 9y = -52/3)
1*(6x + 8y = -16/9)
6x + 54y = -104
6x + 8y = -16/9
Subtract equations
46y = -920/9
y = -920/9/46
y = -20/9

Substitute y
1x + 9(-20/9) = -52/3
1x = 8/3
x = 8/3/1
x = 8/3


Input:
Find x and y such that
2x + 3y = 49/2
10x + 9y = 203/2

Output:
2x + 3y = 49/2
10x + 9y = 203/2

Using elimination
10*(2x + 3y = 49/2)
2*(10x + 9y = 203/2)
20x + 30y = 245
20x + 18y = 203
Subtract equations
12y = 42
y = 42/12
y = 7/2

Substitute y
2x + 3(7/2) = 49/2
2x = 14
x = 14/2
x = 7


Input: Solve the equation x^2 + 37/6x + 19/2 = 0

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


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)(x - -7/4) = 0
x - 2 = 0
x - 7 = 0
x - -7/4 = 0
x = 2
x = 7
x = -7/4


Input: Determine x in 1x - 5/8 = 0

Output:
1x - 5/8 = 0
1x = 5/8
x = 5/8 / 1
x = 5/8


Input:
Solve the system:
6x + 3y = -39/2
6x + 9y = -87/2

Output:
6x + 3y = -39/2
6x + 9y = -87/2

Using elimination
6*(6x + 3y = -39/2)
6*(6x + 9y = -87/2)
36x + 18y = -117
36x + 54y = -261
Subtract equations
-36y = 144
y = 144/-36
y = -4

Substitute y
6x + 3(-4) = -39/2
6x = -15/2
x = -15/2/6
x = -5/4


Input:
Solve the equations:
1x + 9y = 667/20
8x + 6y = 193/10

Output:
1x + 9y = 667/20
8x + 6y = 193/10

Using elimination
8*(1x + 9y = 667/20)
1*(8x + 6y = 193/10)
8x + 72y = 1334/5
8x + 6y = 193/10
Subtract equations
66y = 495/2
y = 495/2/66
y = 15/4

Substitute y
1x + 9(15/4) = 667/20
1x = -2/5
x = -2/5/1
x = -2/5


Input: Compute the solution of x^3 - 2x^2 - 11x + 12 = 0

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


Input: Solve x^2 + 153/7x + 260/7 = 0

Output:
x^2 + 153/7x + 260/7 = 0
(x - -13/7)(x - -20) = 0
x - -13/7 = 0  or  x - -20 = 0
x = -13/7
x = -20


Input: Compute the solution of x^3 + 17/12x^2 - 111/8x - 165/8 = 0

Output:
x^3 + 17/12x^2 - 111/8x - 165/8 = 0
(x - -3/2)(x - -11/3)(x - 15/4) = 0
x - -3/2 = 0
x - -11/3 = 0
x - 15/4 = 0
x = -3/2
x = -11/3
x = 15/4


Input: Solve the equation 5x + 50/7 = 0

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


Input:
Solve the equations:
6x + 5y = 73
3x + 9y = 573/10

Output:
6x + 5y = 73
3x + 9y = 573/10

Using elimination
3*(6x + 5y = 73)
6*(3x + 9y = 573/10)
18x + 15y = 219
18x + 54y = 1719/5
Subtract equations
-39y = -624/5
y = -624/5/-39
y = 16/5

Substitute y
6x + 5(16/5) = 73
6x = 57
x = 57/6
x = 19/2


Input:
Solve simultaneously:
6x + 9y = 53/4
6x + 8y = 11

Output:
6x + 9y = 53/4
6x + 8y = 11

Using elimination
6*(6x + 9y = 53/4)
6*(6x + 8y = 11)
36x + 54y = 159/2
36x + 48y = 66
Subtract equations
6y = 27/2
y = 27/2/6
y = 9/4

Substitute y
6x + 9(9/4) = 53/4
6x = -7
x = -7/6
x = -7/6


Input:
Solve the system:
7x + 4y = 233/9
4x + 10y = 787/18

Output:
7x + 4y = 233/9
4x + 10y = 787/18

Using elimination
4*(7x + 4y = 233/9)
7*(4x + 10y = 787/18)
28x + 16y = 932/9
28x + 70y = 5509/18
Subtract equations
-54y = -405/2
y = -405/2/-54
y = 15/4

Substitute y
7x + 4(15/4) = 233/9
7x = 98/9
x = 98/9/7
x = 14/9


Input:
Solve simultaneously:
9x + 4y = -646/5
9x + 10y = -134

Output:
9x + 4y = -646/5
9x + 10y = -134

Using elimination
9*(9x + 4y = -646/5)
9*(9x + 10y = -134)
81x + 36y = -5814/5
81x + 90y = -1206
Subtract equations
-54y = 216/5
y = 216/5/-54
y = -4/5

Substitute y
9x + 4(-4/5) = -646/5
9x = -126
x = -126/9
x = -14


Input:
Solve simultaneously:
10x + 7y = -32/21
1x + 6y = -100/7

Output:
10x + 7y = -32/21
1x + 6y = -100/7

Using elimination
1*(10x + 7y = -32/21)
10*(1x + 6y = -100/7)
10x + 7y = -32/21
10x + 60y = -1000/7
Subtract equations
-53y = 424/3
y = 424/3/-53
y = -8/3

Substitute y
10x + 7(-8/3) = -32/21
10x = 120/7
x = 120/7/10
x = 12/7


Input: Solve x^2 + 23/2x + 19 = 0

Output:
x^2 + 23/2x + 19 = 0
(x - -19/2)(x - -2) = 0
x - -19/2 = 0  or  x - -2 = 0
x = -19/2
x = -2


Input:
Solve the system:
9x + 4y = -179/9
2x + 1y = -41/9

Output:
9x + 4y = -179/9
2x + 1y = -41/9

Using elimination
2*(9x + 4y = -179/9)
9*(2x + 1y = -41/9)
18x + 8y = -358/9
18x + 9y = -41
Subtract equations
-1y = 11/9
y = 11/9/-1
y = -11/9

Substitute y
9x + 4(-11/9) = -179/9
9x = -15
x = -15/9
x = -5/3


Input: Compute the solution of 4x - 34/5 = 0

Output:
4x - 34/5 = 0
4x = 34/5
x = 34/5 / 4
x = 17/10


Input: Solve x^3 + 523/70x^2 + 177/10x + 459/35 = 0

Output:
x^3 + 523/70x^2 + 177/10x + 459/35 = 0
(x - -3/2)(x - -18/7)(x - -17/5) = 0
x - -3/2 = 0
x - -18/7 = 0
x - -17/5 = 0
x = -3/2
x = -18/7
x = -17/5


Input:
Solve the equations:
7x + 3y = -253/4
10x + 10y = -295/2

Output:
7x + 3y = -253/4
10x + 10y = -295/2

Using elimination
10*(7x + 3y = -253/4)
7*(10x + 10y = -295/2)
70x + 30y = -1265/2
70x + 70y = -2065/2
Subtract equations
-40y = 400
y = 400/-40
y = -10

Substitute y
7x + 3(-10) = -253/4
7x = -133/4
x = -133/4/7
x = -19/4


Input: Solve quickly: x^2 + 4x - 13/9 = 0

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


Input: Compute the solution of 3x + 15/2 = 0

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


Input: Find x in 4x + 44 = 0

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


Input:
Solve the equations:
1x + 8y = -64/7
2x + 9y = -23/7

Output:
1x + 8y = -64/7
2x + 9y = -23/7

Using elimination
2*(1x + 8y = -64/7)
1*(2x + 9y = -23/7)
2x + 16y = -128/7
2x + 9y = -23/7
Subtract equations
7y = -15
y = -15/7
y = -15/7

Substitute y
1x + 8(-15/7) = -64/7
1x = 8
x = 8/1
x = 8


Input:
Solve the equations:
10x + 1y = 53/3
6x + 8y = 11/15

Output:
10x + 1y = 53/3
6x + 8y = 11/15

Using elimination
6*(10x + 1y = 53/3)
10*(6x + 8y = 11/15)
60x + 6y = 106
60x + 80y = 22/3
Subtract equations
-74y = 296/3
y = 296/3/-74
y = -4/3

Substitute y
10x + 1(-4/3) = 53/3
10x = 19
x = 19/10
x = 19/10


Input: Compute the solution of x^3 + 107/30x^2 - 94/5x - 126/5 = 0

Output:
x^3 + 107/30x^2 - 94/5x - 126/5 = 0
(x - -7/6)(x - -6)(x - 18/5) = 0
x - -7/6 = 0
x - -6 = 0
x - 18/5 = 0
x = -7/6
x = -6
x = 18/5


Input:
Solve the equations:
2x + 10y = 55/9
7x + 2y = 44/9

Output:
2x + 10y = 55/9
7x + 2y = 44/9

Using elimination
7*(2x + 10y = 55/9)
2*(7x + 2y = 44/9)
14x + 70y = 385/9
14x + 4y = 88/9
Subtract equations
66y = 33
y = 33/66
y = 1/2

Substitute y
2x + 10(1/2) = 55/9
2x = 10/9
x = 10/9/2
x = 5/9


Input: Find x in x^3 + 402/35x^2 + 157/35x - 66/7 = 0

Output:
x^3 + 402/35x^2 + 157/35x - 66/7 = 0
(x - 5/7)(x - -11)(x - -6/5) = 0
x - 5/7 = 0
x - -11 = 0
x - -6/5 = 0
x = 5/7
x = -11
x = -6/5


Input: Determine x in x^2 - 17x + 70 = 0

Output:
x^2 - 17x + 70 = 0
(x - 10)(x - 7) = 0
x - 10 = 0  or  x - 7 = 0
x = 10
x = 7


Input:
Solve simultaneously:
9x + 9y = 414/7
2x + 7y = 302/7

Output:
9x + 9y = 414/7
2x + 7y = 302/7

Using elimination
2*(9x + 9y = 414/7)
9*(2x + 7y = 302/7)
18x + 18y = 828/7
18x + 63y = 2718/7
Subtract equations
-45y = -270
y = -270/-45
y = 6

Substitute y
9x + 9(6) = 414/7
9x = 36/7
x = 36/7/9
x = 4/7


Input: Find the solution to 1x - 12/7 = 0

Output:
1x - 12/7 = 0
1x = 12/7
x = 12/7 / 1
x = 12/7


Input: Solve the equation x^2 + 65/18x + 7/18 = 0

Output:
x^2 + 65/18x + 7/18 = 0
(x - -1/9)(x - -7/2) = 0
x - -1/9 = 0  or  x - -7/2 = 0
x = -1/9
x = -7/2


Input: Find the solution to x^3 - 21/8x^2 - 905/32x - 525/32 = 0

Output:
x^3 - 21/8x^2 - 905/32x - 525/32 = 0
(x - -5/8)(x - 7)(x - -15/4) = 0
x - -5/8 = 0
x - 7 = 0
x - -15/4 = 0
x = -5/8
x = 7
x = -15/4


Input: Find the solution to x^2 + 22/21x - 160/21 = 0

Output:
x^2 + 22/21x - 160/21 = 0
(x - -10/3)(x - 16/7) = 0
x - -10/3 = 0  or  x - 16/7 = 0
x = -10/3
x = 16/7


Input: Find x for x^3 - 13/7x^2 - 8/7x + 12/7 = 0

Output:
x^3 - 13/7x^2 - 8/7x + 12/7 = 0
(x - -1)(x - 2)(x - 6/7) = 0
x - -1 = 0
x - 2 = 0
x - 6/7 = 0
x = -1
x = 2
x = 6/7


Input: Determine x in x^3 - 159/10x^2 - 78x - 80 = 0

Output:
x^3 - 159/10x^2 - 78x - 80 = 0
(x - -8/5)(x - -5/2)(x - 20) = 0
x - -8/5 = 0
x - -5/2 = 0
x - 20 = 0
x = -8/5
x = -5/2
x = 20


Input: Solve quickly: x^2 - 31/21x + 8/21 = 0

Output:
x^2 - 31/21x + 8/21 = 0
(x - 1/3)(x - 8/7) = 0
x - 1/3 = 0  or  x - 8/7 = 0
x = 1/3
x = 8/7


Input: Determine x in x^3 - 17/2x^2 + 23x - 20 = 0

Output:
x^3 - 17/2x^2 + 23x - 20 = 0
(x - 2)(x - 5/2)(x - 4) = 0
x - 2 = 0
x - 5/2 = 0
x - 4 = 0
x = 2
x = 5/2
x = 4


Input: What value of x satisfies 6x + 36/5 = 0

Output:
6x + 36/5 = 0
6x = -36/5
x = -36/5 / 6
x = -6/5


Input: Solve 5x - 35 = 0

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


Input: Solve quickly: 10x - 30 = 0

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


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

Output:
2x + 7/5 = 0
2x = -7/5
x = -7/5 / 2
x = -7/10


Input: Find x for 6x + 9 = 0

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


Input:
Solve the system:
3x + 3y = 30
3x + 6y = 66

Output:
3x + 3y = 30
3x + 6y = 66

Using elimination
3*(3x + 3y = 30)
3*(3x + 6y = 66)
9x + 9y = 90
9x + 18y = 198
Subtract equations
-9y = -108
y = -108/-9
y = 12

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


Input: Determine x in x^3 - 11/9x^2 - 1334/441x - 8/7 = 0

Output:
x^3 - 11/9x^2 - 1334/441x - 8/7 = 0
(x - -4/7)(x - 18/7)(x - -7/9) = 0
x - -4/7 = 0
x - 18/7 = 0
x - -7/9 = 0
x = -4/7
x = 18/7
x = -7/9


Input: What value of x satisfies x^2 + 29/6x + 35/6 = 0

Output:
x^2 + 29/6x + 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: Determine x in x^2 - 33/5x + 8 = 0

Output:
x^2 - 33/5x + 8 = 0
(x - 8/5)(x - 5) = 0
x - 8/5 = 0  or  x - 5 = 0
x = 8/5
x = 5


Input: Solve 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:
Solve the equations:
8x + 4y = 80/3
9x + 5y = 65/2

Output:
8x + 4y = 80/3
9x + 5y = 65/2

Using elimination
9*(8x + 4y = 80/3)
8*(9x + 5y = 65/2)
72x + 36y = 240
72x + 40y = 260
Subtract equations
-4y = -20
y = -20/-4
y = 5

Substitute y
8x + 4(5) = 80/3
8x = 20/3
x = 20/3/8
x = 5/6


Input:
Solve simultaneously:
4x + 7y = -78/5
2x + 6y = -64/5

Output:
4x + 7y = -78/5
2x + 6y = -64/5

Using elimination
2*(4x + 7y = -78/5)
4*(2x + 6y = -64/5)
8x + 14y = -156/5
8x + 24y = -256/5
Subtract equations
-10y = 20
y = 20/-10
y = -2

Substitute y
4x + 7(-2) = -78/5
4x = -8/5
x = -8/5/4
x = -2/5


Input: Find x in x^2 + 25/4x - 13/8 = 0

Output:
x^2 + 25/4x - 13/8 = 0
(x - 1/4)(x - -13/2) = 0
x - 1/4 = 0  or  x - -13/2 = 0
x = 1/4
x = -13/2


Input:
Solve simultaneously:
7x + 5y = 33
3x + 10y = -33

Output:
7x + 5y = 33
3x + 10y = -33

Using elimination
3*(7x + 5y = 33)
7*(3x + 10y = -33)
21x + 15y = 99
21x + 70y = -231
Subtract equations
-55y = 330
y = 330/-55
y = -6

Substitute y
7x + 5(-6) = 33
7x = 63
x = 63/7
x = 9


Input: Solve the equation 9x + 18/7 = 0

Output:
9x + 18/7 = 0
9x = -18/7
x = -18/7 / 9
x = -2/7


Input: Solve quickly: x^2 - 67/70x + 3/35 = 0

Output:
x^2 - 67/70x + 3/35 = 0
(x - 1/10)(x - 6/7) = 0
x - 1/10 = 0  or  x - 6/7 = 0
x = 1/10
x = 6/7


Input: Find x for x^3 - 331/90x^2 + 16/75x + 6/25 = 0

Output:
x^3 - 331/90x^2 + 16/75x + 6/25 = 0
(x - -2/9)(x - 3/10)(x - 18/5) = 0
x - -2/9 = 0
x - 3/10 = 0
x - 18/5 = 0
x = -2/9
x = 3/10
x = 18/5


Input: Solve x^3 + 157/30x^2 + 5x - 51/10 = 0

Output:
x^3 + 157/30x^2 + 5x - 51/10 = 0
(x - -3)(x - 3/5)(x - -17/6) = 0
x - -3 = 0
x - 3/5 = 0
x - -17/6 = 0
x = -3
x = 3/5
x = -17/6


Input: Solve x^2 - 7x + 45/4 = 0

Output:
x^2 - 7x + 45/4 = 0
(x - 9/2)(x - 5/2) = 0
x - 9/2 = 0  or  x - 5/2 = 0
x = 9/2
x = 5/2


Input: Solve x^3 + 286/35x^2 - 289/35x - 36/5 = 0

Output:
x^3 + 286/35x^2 - 289/35x - 36/5 = 0
(x - -9)(x - -4/7)(x - 7/5) = 0
x - -9 = 0
x - -4/7 = 0
x - 7/5 = 0
x = -9
x = -4/7
x = 7/5


Input: Solve quickly: 10x + 24 = 0

Output:
10x + 24 = 0
10x = -24
x = -24 / 10
x = -12/5


Input: Determine x in 2x + 10 = 0

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


Input: Find x in x^3 + 837/140x^2 + 1501/140x + 51/10 = 0

Output:
x^3 + 837/140x^2 + 1501/140x + 51/10 = 0
(x - -17/7)(x - -14/5)(x - -3/4) = 0
x - -17/7 = 0
x - -14/5 = 0
x - -3/4 = 0
x = -17/7
x = -14/5
x = -3/4


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

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


Input:
Solve simultaneously:
1x + 9y = -99/5
5x + 10y = -52/3

Output:
1x + 9y = -99/5
5x + 10y = -52/3

Using elimination
5*(1x + 9y = -99/5)
1*(5x + 10y = -52/3)
5x + 45y = -99
5x + 10y = -52/3
Subtract equations
35y = -245/3
y = -245/3/35
y = -7/3

Substitute y
1x + 9(-7/3) = -99/5
1x = 6/5
x = 6/5/1
x = 6/5


Input:
Find x and y such that
3x + 4y = 4
1x + 9y = 131/12

Output:
3x + 4y = 4
1x + 9y = 131/12

Using elimination
1*(3x + 4y = 4)
3*(1x + 9y = 131/12)
3x + 4y = 4
3x + 27y = 131/4
Subtract equations
-23y = -115/4
y = -115/4/-23
y = 5/4

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


Input:
Solve the equations:
7x + 2y = 158/9
5x + 4y = 136/9

Output:
7x + 2y = 158/9
5x + 4y = 136/9

Using elimination
5*(7x + 2y = 158/9)
7*(5x + 4y = 136/9)
35x + 10y = 790/9
35x + 28y = 952/9
Subtract equations
-18y = -18
y = -18/-18
y = 1

Substitute y
7x + 2(1) = 158/9
7x = 140/9
x = 140/9/7
x = 20/9


Input:
Find x and y such that
5x + 3y = 211/21
6x + 3y = 235/21

Output:
5x + 3y = 211/21
6x + 3y = 235/21

Using elimination
6*(5x + 3y = 211/21)
5*(6x + 3y = 235/21)
30x + 18y = 422/7
30x + 15y = 1175/21
Subtract equations
3y = 13/3
y = 13/3/3
y = 13/9

Substitute y
5x + 3(13/9) = 211/21
5x = 40/7
x = 40/7/5
x = 8/7


Input: Find x in 8x + 32/3 = 0

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


Input: Solve x^3 + 3/5x^2 - 2066/405x - 136/27 = 0

Output:
x^3 + 3/5x^2 - 2066/405x - 136/27 = 0
(x - 12/5)(x - -10/9)(x - -17/9) = 0
x - 12/5 = 0
x - -10/9 = 0
x - -17/9 = 0
x = 12/5
x = -10/9
x = -17/9


Input: Find the solution to x^2 - 11/2x - 13/2 = 0

Output:
x^2 - 11/2x - 13/2 = 0
(x - -1)(x - 13/2) = 0
x - -1 = 0  or  x - 13/2 = 0
x = -1
x = 13/2


Input: Solve the equation x^2 + 79/18x + 119/27 = 0

Output:
x^2 + 79/18x + 119/27 = 0
(x - -17/6)(x - -14/9) = 0
x - -17/6 = 0  or  x - -14/9 = 0
x = -17/6
x = -14/9


Input: What value of x satisfies x^3 + 75/14x^2 + 79/14x - 30/7 = 0

Output:
x^3 + 75/14x^2 + 79/14x - 30/7 = 0
(x - -20/7)(x - 1/2)(x - -3) = 0
x - -20/7 = 0
x - 1/2 = 0
x - -3 = 0
x = -20/7
x = 1/2
x = -3


Input: Compute the solution of 2x - 32/9 = 0

Output:
2x - 32/9 = 0
2x = 32/9
x = 32/9 / 2
x = 16/9


Input: Determine x in x^2 + 20x + 36 = 0

Output:
x^2 + 20x + 36 = 0
(x - -18)(x - -2) = 0
x - -18 = 0  or  x - -2 = 0
x = -18
x = -2


Input: Compute the solution of x^3 - 47/5x^2 + 134/5x - 24 = 0

Output:
x^3 - 47/5x^2 + 134/5x - 24 = 0
(x - 2)(x - 12/5)(x - 5) = 0
x - 2 = 0
x - 12/5 = 0
x - 5 = 0
x = 2
x = 12/5
x = 5


Input: Find x in x^3 - 297/14x^2 + 283/14x + 570/7 = 0

Output:
x^3 - 297/14x^2 + 283/14x + 570/7 = 0
(x - -3/2)(x - 20)(x - 19/7) = 0
x - -3/2 = 0
x - 20 = 0
x - 19/7 = 0
x = -3/2
x = 20
x = 19/7


Input:
Solve the equations:
10x + 2y = 23
5x + 8y = 22

Output:
10x + 2y = 23
5x + 8y = 22

Using elimination
5*(10x + 2y = 23)
10*(5x + 8y = 22)
50x + 10y = 115
50x + 80y = 220
Subtract equations
-70y = -105
y = -105/-70
y = 3/2

Substitute y
10x + 2(3/2) = 23
10x = 20
x = 20/10
x = 2


Input:
Solve simultaneously:
8x + 1y = -81/7
3x + 7y = -3/2

Output:
8x + 1y = -81/7
3x + 7y = -3/2

Using elimination
3*(8x + 1y = -81/7)
8*(3x + 7y = -3/2)
24x + 3y = -243/7
24x + 56y = -12
Subtract equations
-53y = -159/7
y = -159/7/-53
y = 3/7

Substitute y
8x + 1(3/7) = -81/7
8x = -12
x = -12/8
x = -3/2


Input:
Find x and y such that
1x + 9y = -45/8
10x + 4y = -91/2

Output:
1x + 9y = -45/8
10x + 4y = -91/2

Using elimination
10*(1x + 9y = -45/8)
1*(10x + 4y = -91/2)
10x + 90y = -225/4
10x + 4y = -91/2
Subtract equations
86y = -43/4
y = -43/4/86
y = -1/8

Substitute y
1x + 9(-1/8) = -45/8
1x = -9/2
x = -9/2/1
x = -9/2


Input:
Find x and y such that
1x + 5y = 49/4
7x + 1y = 71/4

Output:
1x + 5y = 49/4
7x + 1y = 71/4

Using elimination
7*(1x + 5y = 49/4)
1*(7x + 1y = 71/4)
7x + 35y = 343/4
7x + 1y = 71/4
Subtract equations
34y = 68
y = 68/34
y = 2

Substitute y
1x + 5(2) = 49/4
1x = 9/4
x = 9/4/1
x = 9/4


Input:
Find x and y such that
10x + 9y = 23/3
4x + 3y = 11/3

Output:
10x + 9y = 23/3
4x + 3y = 11/3

Using elimination
4*(10x + 9y = 23/3)
10*(4x + 3y = 11/3)
40x + 36y = 92/3
40x + 30y = 110/3
Subtract equations
6y = -6
y = -6/6
y = -1

Substitute y
10x + 9(-1) = 23/3
10x = 50/3
x = 50/3/10
x = 5/3


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

Output:
x^3  - 9x  = 0
(x - 0)(x - 3)(x - -3) = 0
x - 0 = 0
x - 3 = 0
x - -3 = 0
x = 0
x = 3
x = -3


Input: Solve quickly: 8x + 72 = 0

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


Input:
Find x and y such that
2x + 6y = -47/5
1x + 4y = -51/10

Output:
2x + 6y = -47/5
1x + 4y = -51/10

Using elimination
1*(2x + 6y = -47/5)
2*(1x + 4y = -51/10)
2x + 6y = -47/5
2x + 8y = -51/5
Subtract equations
-2y = 4/5
y = 4/5/-2
y = -2/5

Substitute y
2x + 6(-2/5) = -47/5
2x = -7
x = -7/2
x = -7/2


Input: What value of x satisfies x^3 - 29/6x^2 - 281/18x + 1045/27 = 0

Output:
x^3 - 29/6x^2 - 281/18x + 1045/27 = 0
(x - -10/3)(x - 11/6)(x - 19/3) = 0
x - -10/3 = 0
x - 11/6 = 0
x - 19/3 = 0
x = -10/3
x = 11/6
x = 19/3


Input: Solve the equation 8x + 36 = 0

Output:
8x + 36 = 0
8x = -36
x = -36 / 8
x = -9/2


Input: Solve quickly: x^3 + 191/35x^2 - 1177/140x - 741/70 = 0

Output:
x^3 + 191/35x^2 - 1177/140x - 741/70 = 0
(x - 19/10)(x - -13/2)(x - -6/7) = 0
x - 19/10 = 0
x - -13/2 = 0
x - -6/7 = 0
x = 19/10
x = -13/2
x = -6/7


Input:
Solve simultaneously:
10x + 6y = -139/4
2x + 5y = -67/8

Output:
10x + 6y = -139/4
2x + 5y = -67/8

Using elimination
2*(10x + 6y = -139/4)
10*(2x + 5y = -67/8)
20x + 12y = -139/2
20x + 50y = -335/4
Subtract equations
-38y = 57/4
y = 57/4/-38
y = -3/8

Substitute y
10x + 6(-3/8) = -139/4
10x = -65/2
x = -65/2/10
x = -13/4


Input:
Solve simultaneously:
1x + 6y = 127/6
9x + 9y = 21/2

Output:
1x + 6y = 127/6
9x + 9y = 21/2

Using elimination
9*(1x + 6y = 127/6)
1*(9x + 9y = 21/2)
9x + 54y = 381/2
9x + 9y = 21/2
Subtract equations
45y = 180
y = 180/45
y = 4

Substitute y
1x + 6(4) = 127/6
1x = -17/6
x = -17/6/1
x = -17/6


Input:
Find x and y such that
4x + 7y = 76/3
6x + 4y = 10/3

Output:
4x + 7y = 76/3
6x + 4y = 10/3

Using elimination
6*(4x + 7y = 76/3)
4*(6x + 4y = 10/3)
24x + 42y = 152
24x + 16y = 40/3
Subtract equations
26y = 416/3
y = 416/3/26
y = 16/3

Substitute y
4x + 7(16/3) = 76/3
4x = -12
x = -12/4
x = -3


Input: Solve quickly: 4x - 9 = 0

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


Input: Compute the solution of x^3 + 9/2x^2 + 313/50x + 63/25 = 0

Output:
x^3 + 9/2x^2 + 313/50x + 63/25 = 0
(x - -7/10)(x - -2)(x - -9/5) = 0
x - -7/10 = 0
x - -2 = 0
x - -9/5 = 0
x = -7/10
x = -2
x = -9/5


Input: What value of x satisfies 6x - 114 = 0

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


Input: Solve x^2 - 119/15x + 152/15 = 0

Output:
x^2 - 119/15x + 152/15 = 0
(x - 19/3)(x - 8/5) = 0
x - 19/3 = 0  or  x - 8/5 = 0
x = 19/3
x = 8/5


Input: Solve the equation x^3 - 212/21x^2 + 1159/84x - 85/42 = 0

Output:
x^3 - 212/21x^2 + 1159/84x - 85/42 = 0
(x - 10/7)(x - 1/6)(x - 17/2) = 0
x - 10/7 = 0
x - 1/6 = 0
x - 17/2 = 0
x = 10/7
x = 1/6
x = 17/2


Input: Solve quickly: x^2 - 2/5x - 63/25 = 0

Output:
x^2 - 2/5x - 63/25 = 0
(x - 9/5)(x - -7/5) = 0
x - 9/5 = 0  or  x - -7/5 = 0
x = 9/5
x = -7/5


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

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


Input: Compute the solution of x^3 + 37/14x^2 - 1585/14x + 1950/7 = 0

Output:
x^3 + 37/14x^2 - 1585/14x + 1950/7 = 0
(x - -13)(x - 20/7)(x - 15/2) = 0
x - -13 = 0
x - 20/7 = 0
x - 15/2 = 0
x = -13
x = 20/7
x = 15/2


Input: Solve the equation 10x + 85/2 = 0

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


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

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


Input: What value of x satisfies x^2 + 5x + 44/9 = 0

Output:
x^2 + 5x + 44/9 = 0
(x - -11/3)(x - -4/3) = 0
x - -11/3 = 0  or  x - -4/3 = 0
x = -11/3
x = -4/3


Input: What value of x satisfies x^2 - 49/6x + 85/6 = 0

Output:
x^2 - 49/6x + 85/6 = 0
(x - 17/3)(x - 5/2) = 0
x - 17/3 = 0  or  x - 5/2 = 0
x = 17/3
x = 5/2


Input: Solve quickly: x^2 + 17/2x + 18 = 0

Output:
x^2 + 17/2x + 18 = 0
(x - -9/2)(x - -4) = 0
x - -9/2 = 0  or  x - -4 = 0
x = -9/2
x = -4


Input: Find x in 6x + 54/5 = 0

Output:
6x + 54/5 = 0
6x = -54/5
x = -54/5 / 6
x = -9/5


Input: Solve quickly: 10x  = 0

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


Input: Solve quickly: x^2 + 19/4x + 11/2 = 0

Output:
x^2 + 19/4x + 11/2 = 0
(x - -2)(x - -11/4) = 0
x - -2 = 0  or  x - -11/4 = 0
x = -2
x = -11/4


Input: Solve quickly: x^2 - 23/4x + 45/8 = 0

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


Input:
Solve the system:
2x + 1y = -2
10x + 3y = -11

Output:
2x + 1y = -2
10x + 3y = -11

Using elimination
10*(2x + 1y = -2)
2*(10x + 3y = -11)
20x + 10y = -20
20x + 6y = -22
Subtract equations
4y = 2
y = 2/4
y = 1/2

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


Input: Find the solution to x^2 - 13/18x - 35/27 = 0

Output:
x^2 - 13/18x - 35/27 = 0
(x - -5/6)(x - 14/9) = 0
x - -5/6 = 0  or  x - 14/9 = 0
x = -5/6
x = 14/9


Input:
Solve the equations:
2x + 7y = -193/3
3x + 10y = -92

Output:
2x + 7y = -193/3
3x + 10y = -92

Using elimination
3*(2x + 7y = -193/3)
2*(3x + 10y = -92)
6x + 21y = -193
6x + 20y = -184
Subtract equations
1y = -9
y = -9/1
y = -9

Substitute y
2x + 7(-9) = -193/3
2x = -4/3
x = -4/3/2
x = -2/3


Input:
Solve the system:
6x + 6y = 372/7
10x + 5y = 340/7

Output:
6x + 6y = 372/7
10x + 5y = 340/7

Using elimination
10*(6x + 6y = 372/7)
6*(10x + 5y = 340/7)
60x + 60y = 3720/7
60x + 30y = 2040/7
Subtract equations
30y = 240
y = 240/30
y = 8

Substitute y
6x + 6(8) = 372/7
6x = 36/7
x = 36/7/6
x = 6/7


Input:
Solve the equations:
2x + 10y = -5/12
2x + 7y = -19/24

Output:
2x + 10y = -5/12
2x + 7y = -19/24

Using elimination
2*(2x + 10y = -5/12)
2*(2x + 7y = -19/24)
4x + 20y = -5/6
4x + 14y = -19/12
Subtract equations
6y = 3/4
y = 3/4/6
y = 1/8

Substitute y
2x + 10(1/8) = -5/12
2x = -5/3
x = -5/3/2
x = -5/6


Input: Find x for x^3 - 188/15x^2 + 41/15x + 44 = 0

Output:
x^3 - 188/15x^2 + 41/15x + 44 = 0
(x - -5/3)(x - 12)(x - 11/5) = 0
x - -5/3 = 0
x - 12 = 0
x - 11/5 = 0
x = -5/3
x = 12
x = 11/5


Input: Compute the solution of x^3 + 72/7x^2 - 460/7x - 192 = 0

Output:
x^3 + 72/7x^2 - 460/7x - 192 = 0
(x - 6)(x - -16/7)(x - -14) = 0
x - 6 = 0
x - -16/7 = 0
x - -14 = 0
x = 6
x = -16/7
x = -14


Input: What value of x satisfies 9x - 72/5 = 0

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


Input:
Solve the system:
7x + 5y = 75/4
4x + 10y = 425/14

Output:
7x + 5y = 75/4
4x + 10y = 425/14

Using elimination
4*(7x + 5y = 75/4)
7*(4x + 10y = 425/14)
28x + 20y = 75
28x + 70y = 425/2
Subtract equations
-50y = -275/2
y = -275/2/-50
y = 11/4

Substitute y
7x + 5(11/4) = 75/4
7x = 5
x = 5/7
x = 5/7


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

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


Input: Find the solution to x^2 - 10/9x - 32/27 = 0

Output:
x^2 - 10/9x - 32/27 = 0
(x - 16/9)(x - -2/3) = 0
x - 16/9 = 0  or  x - -2/3 = 0
x = 16/9
x = -2/3


Input: Find x for x^2 - 1x + 12/49 = 0

Output:
x^2 - 1x + 12/49 = 0
(x - 3/7)(x - 4/7) = 0
x - 3/7 = 0  or  x - 4/7 = 0
x = 3/7
x = 4/7


Input: Determine x in 7x + 63/2 = 0

Output:
7x + 63/2 = 0
7x = -63/2
x = -63/2 / 7
x = -9/2


Input: Compute the solution of x^3 + 391/72x^2 - 961/144x + 65/36 = 0

Output:
x^3 + 391/72x^2 - 961/144x + 65/36 = 0
(x - -13/2)(x - 4/9)(x - 5/8) = 0
x - -13/2 = 0
x - 4/9 = 0
x - 5/8 = 0
x = -13/2
x = 4/9
x = 5/8


Input: Solve x^2 - 107/35x + 78/35 = 0

Output:
x^2 - 107/35x + 78/35 = 0
(x - 6/5)(x - 13/7) = 0
x - 6/5 = 0  or  x - 13/7 = 0
x = 6/5
x = 13/7


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

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


Input: Find the solution to 6x + 11 = 0

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


Input:
Find x and y such that
3x + 9y = 405/56
2x + 10y = 183/28

Output:
3x + 9y = 405/56
2x + 10y = 183/28

Using elimination
2*(3x + 9y = 405/56)
3*(2x + 10y = 183/28)
6x + 18y = 405/28
6x + 30y = 549/28
Subtract equations
-12y = -36/7
y = -36/7/-12
y = 3/7

Substitute y
3x + 9(3/7) = 405/56
3x = 27/8
x = 27/8/3
x = 9/8


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

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


Input: Find the solution to x^3 - 23/10x^2 - 243/80x + 567/80 = 0

Output:
x^3 - 23/10x^2 - 243/80x + 567/80 = 0
(x - 9/4)(x - 9/5)(x - -7/4) = 0
x - 9/4 = 0
x - 9/5 = 0
x - -7/4 = 0
x = 9/4
x = 9/5
x = -7/4


Input: Find x for x^3 + 31/70x^2 - 52/7x - 40/7 = 0

Output:
x^3 + 31/70x^2 - 52/7x - 40/7 = 0
(x - -4/5)(x - 20/7)(x - -5/2) = 0
x - -4/5 = 0
x - 20/7 = 0
x - -5/2 = 0
x = -4/5
x = 20/7
x = -5/2


Input: Find the solution to x^3 + 4x^2 - 21/4x - 27/2 = 0

Output:
x^3 + 4x^2 - 21/4x - 27/2 = 0
(x - -9/2)(x - -3/2)(x - 2) = 0
x - -9/2 = 0
x - -3/2 = 0
x - 2 = 0
x = -9/2
x = -3/2
x = 2


Input: Find x in x^3 - 81/5x^2 + 68x - 60 = 0

Output:
x^3 - 81/5x^2 + 68x - 60 = 0
(x - 5)(x - 10)(x - 6/5) = 0
x - 5 = 0
x - 10 = 0
x - 6/5 = 0
x = 5
x = 10
x = 6/5


Input:
Find x and y such that
3x + 1y = 79/40
5x + 10y = 133/8

Output:
3x + 1y = 79/40
5x + 10y = 133/8

Using elimination
5*(3x + 1y = 79/40)
3*(5x + 10y = 133/8)
15x + 5y = 79/8
15x + 30y = 399/8
Subtract equations
-25y = -40
y = -40/-25
y = 8/5

Substitute y
3x + 1(8/5) = 79/40
3x = 3/8
x = 3/8/3
x = 1/8


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

Output:
4x + 13/2 = 0
4x = -13/2
x = -13/2 / 4
x = -13/8


Input:
Find x and y such that
10x + 2y = -68/5
8x + 5y = 0

Output:
10x + 2y = -68/5
8x + 5y = 0

Using elimination
8*(10x + 2y = -68/5)
10*(8x + 5y = 0)
80x + 16y = -544/5
80x + 50y = 0
Subtract equations
-34y = -544/5
y = -544/5/-34
y = 16/5

Substitute y
10x + 2(16/5) = -68/5
10x = -20
x = -20/10
x = -2


Input: Solve the equation x^3 - 11/2x^2 - 41/4x + 195/8 = 0

Output:
x^3 - 11/2x^2 - 41/4x + 195/8 = 0
(x - 3/2)(x - -5/2)(x - 13/2) = 0
x - 3/2 = 0
x - -5/2 = 0
x - 13/2 = 0
x = 3/2
x = -5/2
x = 13/2


Input:
Solve simultaneously:
3x + 8y = 753/40
5x + 8y = 743/40

Output:
3x + 8y = 753/40
5x + 8y = 743/40

Using elimination
5*(3x + 8y = 753/40)
3*(5x + 8y = 743/40)
15x + 40y = 753/8
15x + 24y = 2229/40
Subtract equations
16y = 192/5
y = 192/5/16
y = 12/5

Substitute y
3x + 8(12/5) = 753/40
3x = -3/8
x = -3/8/3
x = -1/8


Input: Solve quickly: 5x + 15/2 = 0

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


Input: Solve x^2 + 63/8x - 1 = 0

Output:
x^2 + 63/8x - 1 = 0
(x - -8)(x - 1/8) = 0
x - -8 = 0  or  x - 1/8 = 0
x = -8
x = 1/8


Input: Solve x^3 - 479/168x^2 - 205/84x + 475/56 = 0

Output:
x^3 - 479/168x^2 - 205/84x + 475/56 = 0
(x - 15/7)(x - -5/3)(x - 19/8) = 0
x - 15/7 = 0
x - -5/3 = 0
x - 19/8 = 0
x = 15/7
x = -5/3
x = 19/8


Input:
Solve the system:
10x + 7y = 8
8x + 5y = 32/5

Output:
10x + 7y = 8
8x + 5y = 32/5

Using elimination
8*(10x + 7y = 8)
10*(8x + 5y = 32/5)
80x + 56y = 64
80x + 50y = 64
Subtract equations
6y = 0
y = 0/6
y = 0

Substitute y
10x + 7(0) = 8
10x = 8
x = 8/10
x = 4/5


Input: Solve x^2 - 33/20x - 119/20 = 0

Output:
x^2 - 33/20x - 119/20 = 0
(x - -7/4)(x - 17/5) = 0
x - -7/4 = 0  or  x - 17/5 = 0
x = -7/4
x = 17/5


Input: Find the solution to x^3 - 131/10x^2 + 373/10x - 18/5 = 0

Output:
x^3 - 131/10x^2 + 373/10x - 18/5 = 0
(x - 1/10)(x - 4)(x - 9) = 0
x - 1/10 = 0
x - 4 = 0
x - 9 = 0
x = 1/10
x = 4
x = 9


Input: Determine x in x^2 + 107/30x + 19/15 = 0

Output:
x^2 + 107/30x + 19/15 = 0
(x - -2/5)(x - -19/6) = 0
x - -2/5 = 0  or  x - -19/6 = 0
x = -2/5
x = -19/6


Input: Solve x^3 - 67/20x^2 - 227/40x + 39/2 = 0

Output:
x^3 - 67/20x^2 - 227/40x + 39/2 = 0
(x - 5/2)(x - -12/5)(x - 13/4) = 0
x - 5/2 = 0
x - -12/5 = 0
x - 13/4 = 0
x = 5/2
x = -12/5
x = 13/4


Input: Determine x in x^2 + 7/10x  = 0

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


Input: Determine x in x^2 + 19/10x - 361/50 = 0

Output:
x^2 + 19/10x - 361/50 = 0
(x - 19/10)(x - -19/5) = 0
x - 19/10 = 0  or  x - -19/5 = 0
x = 19/10
x = -19/5


Input: What value of x satisfies 5x + 35/2 = 0

Output:
5x + 35/2 = 0
5x = -35/2
x = -35/2 / 5
x = -7/2


Input: Compute the solution of x^2 + 1/3x - 44/3 = 0

Output:
x^2 + 1/3x - 44/3 = 0
(x - -4)(x - 11/3) = 0
x - -4 = 0  or  x - 11/3 = 0
x = -4
x = 11/3


Input: What value of x satisfies x^2 - 120/7x - 400/7 = 0

Output:
x^2 - 120/7x - 400/7 = 0
(x - 20)(x - -20/7) = 0
x - 20 = 0  or  x - -20/7 = 0
x = 20
x = -20/7


Input:
Solve the system:
6x + 1y = -139/4
3x + 3y = -97/4

Output:
6x + 1y = -139/4
3x + 3y = -97/4

Using elimination
3*(6x + 1y = -139/4)
6*(3x + 3y = -97/4)
18x + 3y = -417/4
18x + 18y = -291/2
Subtract equations
-15y = 165/4
y = 165/4/-15
y = -11/4

Substitute y
6x + 1(-11/4) = -139/4
6x = -32
x = -32/6
x = -16/3


Input: Determine x in x^3 + 145/18x^2 + 52/9x - 169/6 = 0

Output:
x^3 + 145/18x^2 + 52/9x - 169/6 = 0
(x - 13/9)(x - -3)(x - -13/2) = 0
x - 13/9 = 0
x - -3 = 0
x - -13/2 = 0
x = 13/9
x = -3
x = -13/2


Input: Find the solution to x^2 + 43/24x - 209/48 = 0

Output:
x^2 + 43/24x - 209/48 = 0
(x - 11/8)(x - -19/6) = 0
x - 11/8 = 0  or  x - -19/6 = 0
x = 11/8
x = -19/6


Input: Compute the solution of 3x + 57/10 = 0

Output:
3x + 57/10 = 0
3x = -57/10
x = -57/10 / 3
x = -19/10


Input: Find x for x^2 + 23/6x + 11/3 = 0

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


Input: Find x in x^3 - 167/6x^2 + 423/2x - 1064/3 = 0

Output:
x^3 - 167/6x^2 + 423/2x - 1064/3 = 0
(x - 19/2)(x - 16)(x - 7/3) = 0
x - 19/2 = 0
x - 16 = 0
x - 7/3 = 0
x = 19/2
x = 16
x = 7/3


Input: Find x for x^2 + 111/35x + 88/35 = 0

Output:
x^2 + 111/35x + 88/35 = 0
(x - -8/5)(x - -11/7) = 0
x - -8/5 = 0  or  x - -11/7 = 0
x = -8/5
x = -11/7


Input: Solve x^2 + 10x + 21 = 0

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


Input: What value of x satisfies x^3 - 449/45x^2 - 1396/45x + 1216/15 = 0

Output:
x^3 - 449/45x^2 - 1396/45x + 1216/15 = 0
(x - -19/5)(x - 16/9)(x - 12) = 0
x - -19/5 = 0
x - 16/9 = 0
x - 12 = 0
x = -19/5
x = 16/9
x = 12


Input: Solve quickly: 10x - 17 = 0

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


Input: Find x in x^2 + 39/4x + 135/8 = 0

Output:
x^2 + 39/4x + 135/8 = 0
(x - -9/4)(x - -15/2) = 0
x - -9/4 = 0  or  x - -15/2 = 0
x = -9/4
x = -15/2


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

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


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

Output:
5x - 25/6 = 0
5x = 25/6
x = 25/6 / 5
x = 5/6


Input:
Solve the system:
4x + 8y = -206/5
10x + 8y = -37

Output:
4x + 8y = -206/5
10x + 8y = -37

Using elimination
10*(4x + 8y = -206/5)
4*(10x + 8y = -37)
40x + 80y = -412
40x + 32y = -148
Subtract equations
48y = -264
y = -264/48
y = -11/2

Substitute y
4x + 8(-11/2) = -206/5
4x = 14/5
x = 14/5/4
x = 7/10


Input: Find the solution to 5x + 80 = 0

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


Input:
Find x and y such that
8x + 9y = -144/7
1x + 1y = -16/7

Output:
8x + 9y = -144/7
1x + 1y = -16/7

Using elimination
1*(8x + 9y = -144/7)
8*(1x + 1y = -16/7)
8x + 9y = -144/7
8x + 8y = -128/7
Subtract equations
1y = -16/7
y = -16/7/1
y = -16/7

Substitute y
8x + 9(-16/7) = -144/7
8x = 0
x = 0/8
x = 0


Input: What value of x satisfies x^2 + 33/10x + 8/25 = 0

Output:
x^2 + 33/10x + 8/25 = 0
(x - -1/10)(x - -16/5) = 0
x - -1/10 = 0  or  x - -16/5 = 0
x = -1/10
x = -16/5


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

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


Input:
Solve the equations:
3x + 5y = 43/9
1x + 7y = 89/9

Output:
3x + 5y = 43/9
1x + 7y = 89/9

Using elimination
1*(3x + 5y = 43/9)
3*(1x + 7y = 89/9)
3x + 5y = 43/9
3x + 21y = 89/3
Subtract equations
-16y = -224/9
y = -224/9/-16
y = 14/9

Substitute y
3x + 5(14/9) = 43/9
3x = -3
x = -3/3
x = -1


Input:
Solve the equations:
1x + 6y = 339/8
3x + 1y = 331/24

Output:
1x + 6y = 339/8
3x + 1y = 331/24

Using elimination
3*(1x + 6y = 339/8)
1*(3x + 1y = 331/24)
3x + 18y = 1017/8
3x + 1y = 331/24
Subtract equations
17y = 340/3
y = 340/3/17
y = 20/3

Substitute y
1x + 6(20/3) = 339/8
1x = 19/8
x = 19/8/1
x = 19/8


Input: What value of x satisfies 3x - 17/2 = 0

Output:
3x - 17/2 = 0
3x = 17/2
x = 17/2 / 3
x = 17/6


Input: Find x for 4x - 8/3 = 0

Output:
4x - 8/3 = 0
4x = 8/3
x = 8/3 / 4
x = 2/3


Input: Solve quickly: x^3 + 29/5x^2 + 42/5x  = 0

Output:
x^3 + 29/5x^2 + 42/5x  = 0
(x - -14/5)(x - -3)(x - 0) = 0
x - -14/5 = 0
x - -3 = 0
x - 0 = 0
x = -14/5
x = -3
x = 0


Input:
Solve simultaneously:
4x + 7y = -58
8x + 1y = -142

Output:
4x + 7y = -58
8x + 1y = -142

Using elimination
8*(4x + 7y = -58)
4*(8x + 1y = -142)
32x + 56y = -464
32x + 4y = -568
Subtract equations
52y = 104
y = 104/52
y = 2

Substitute y
4x + 7(2) = -58
4x = -72
x = -72/4
x = -18


Input: Compute the solution of x^2 + 7/6x - 1/2 = 0

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


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

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


Input:
Solve the system:
6x + 5y = 29/5
7x + 7y = 63/10

Output:
6x + 5y = 29/5
7x + 7y = 63/10

Using elimination
7*(6x + 5y = 29/5)
6*(7x + 7y = 63/10)
42x + 35y = 203/5
42x + 42y = 189/5
Subtract equations
-7y = 14/5
y = 14/5/-7
y = -2/5

Substitute y
6x + 5(-2/5) = 29/5
6x = 39/5
x = 39/5/6
x = 13/10


Input: Find x in x^3 + 5/2x^2 - 303/16x + 99/8 = 0

Output:
x^3 + 5/2x^2 - 303/16x + 99/8 = 0
(x - -6)(x - 11/4)(x - 3/4) = 0
x - -6 = 0
x - 11/4 = 0
x - 3/4 = 0
x = -6
x = 11/4
x = 3/4


Input: Compute the solution of x^2 - 7/18x - 95/18 = 0

Output:
x^2 - 7/18x - 95/18 = 0
(x - -19/9)(x - 5/2) = 0
x - -19/9 = 0  or  x - 5/2 = 0
x = -19/9
x = 5/2


Input:
Find x and y such that
4x + 1y = 3/2
3x + 2y = -3/4

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

Using elimination
3*(4x + 1y = 3/2)
4*(3x + 2y = -3/4)
12x + 3y = 9/2
12x + 8y = -3
Subtract equations
-5y = 15/2
y = 15/2/-5
y = -3/2

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


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

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


Input: Solve the equation x^2 - 39/8x - 169/16 = 0

Output:
x^2 - 39/8x - 169/16 = 0
(x - 13/2)(x - -13/8) = 0
x - 13/2 = 0  or  x - -13/8 = 0
x = 13/2
x = -13/8


Input: Solve quickly: x^3 + 277/120x^2 + 89/60x + 11/40 = 0

Output:
x^3 + 277/120x^2 + 89/60x + 11/40 = 0
(x - -11/8)(x - -1/3)(x - -3/5) = 0
x - -11/8 = 0
x - -1/3 = 0
x - -3/5 = 0
x = -11/8
x = -1/3
x = -3/5


Input: Solve x^3 + 23/3x^2 - 142/3x + 56 = 0

Output:
x^3 + 23/3x^2 - 142/3x + 56 = 0
(x - 7/3)(x - 2)(x - -12) = 0
x - 7/3 = 0
x - 2 = 0
x - -12 = 0
x = 7/3
x = 2
x = -12


Input: Find x for 2x + 32 = 0

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


Input: Find x in x^3 + 56/45x^2 - 13/9x - 4/5 = 0

Output:
x^3 + 56/45x^2 - 13/9x - 4/5 = 0
(x - -9/5)(x - -4/9)(x - 1) = 0
x - -9/5 = 0
x - -4/9 = 0
x - 1 = 0
x = -9/5
x = -4/9
x = 1


Input:
Solve simultaneously:
2x + 2y = 19/4
6x + 9y = 147/8

Output:
2x + 2y = 19/4
6x + 9y = 147/8

Using elimination
6*(2x + 2y = 19/4)
2*(6x + 9y = 147/8)
12x + 12y = 57/2
12x + 18y = 147/4
Subtract equations
-6y = -33/4
y = -33/4/-6
y = 11/8

Substitute y
2x + 2(11/8) = 19/4
2x = 2
x = 2/2
x = 1


Input: Find x for 3x - 9/4 = 0

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


Input: What value of x satisfies 7x - 112/3 = 0

Output:
7x - 112/3 = 0
7x = 112/3
x = 112/3 / 7
x = 16/3


Input:
Solve the equations:
5x + 1y = -374/63
9x + 1y = -82/7

Output:
5x + 1y = -374/63
9x + 1y = -82/7

Using elimination
9*(5x + 1y = -374/63)
5*(9x + 1y = -82/7)
45x + 9y = -374/7
45x + 5y = -410/7
Subtract equations
4y = 36/7
y = 36/7/4
y = 9/7

Substitute y
5x + 1(9/7) = -374/63
5x = -65/9
x = -65/9/5
x = -13/9


Input: Determine x in 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: What value of x satisfies x^3 + 1063/180x^2 + 679/60x + 637/90 = 0

Output:
x^3 + 1063/180x^2 + 679/60x + 637/90 = 0
(x - -7/4)(x - -13/5)(x - -14/9) = 0
x - -7/4 = 0
x - -13/5 = 0
x - -14/9 = 0
x = -7/4
x = -13/5
x = -14/9


Input: Determine x in x^2 + 67/5x - 24 = 0

Output:
x^2 + 67/5x - 24 = 0
(x - 8/5)(x - -15) = 0
x - 8/5 = 0  or  x - -15 = 0
x = 8/5
x = -15


Input: Solve the equation 8x - 6 = 0

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


Input: What value of x satisfies x^3 + 59/6x^2 + 57/2x + 77/3 = 0

Output:
x^3 + 59/6x^2 + 57/2x + 77/3 = 0
(x - -11/2)(x - -7/3)(x - -2) = 0
x - -11/2 = 0
x - -7/3 = 0
x - -2 = 0
x = -11/2
x = -7/3
x = -2


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

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


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

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


Input: Determine x in 4x - 4 = 0

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


Input: Determine x in x^2 + 45/7x - 4 = 0

Output:
x^2 + 45/7x - 4 = 0
(x - -7)(x - 4/7) = 0
x - -7 = 0  or  x - 4/7 = 0
x = -7
x = 4/7


Input: What value of x satisfies x^3 - 35/3x^2 + 326/9x - 520/27 = 0

Output:
x^3 - 35/3x^2 + 326/9x - 520/27 = 0
(x - 2/3)(x - 20/3)(x - 13/3) = 0
x - 2/3 = 0
x - 20/3 = 0
x - 13/3 = 0
x = 2/3
x = 20/3
x = 13/3


Input: Determine x in x^2 - 21/8x - 11/2 = 0

Output:
x^2 - 21/8x - 11/2 = 0
(x - 4)(x - -11/8) = 0
x - 4 = 0  or  x - -11/8 = 0
x = 4
x = -11/8


Input: Determine x in 8x - 8 = 0

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


Input: Determine x in x^2 - 11/3x  = 0

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


Input: What value of x satisfies x^3 - 40/9x^2 + 197/108x + 140/27 = 0

Output:
x^3 - 40/9x^2 + 197/108x + 140/27 = 0
(x - 7/2)(x - -5/6)(x - 16/9) = 0
x - 7/2 = 0
x - -5/6 = 0
x - 16/9 = 0
x = 7/2
x = -5/6
x = 16/9


Input: Determine x in x^3 - 25/2x^2 + 51x - 135/2 = 0

Output:
x^3 - 25/2x^2 + 51x - 135/2 = 0
(x - 9/2)(x - 5)(x - 3) = 0
x - 9/2 = 0
x - 5 = 0
x - 3 = 0
x = 9/2
x = 5
x = 3


Input:
Solve the system:
4x + 8y = -151/3
9x + 10y = -719/12

Output:
4x + 8y = -151/3
9x + 10y = -719/12

Using elimination
9*(4x + 8y = -151/3)
4*(9x + 10y = -719/12)
36x + 72y = -453
36x + 40y = -719/3
Subtract equations
32y = -640/3
y = -640/3/32
y = -20/3

Substitute y
4x + 8(-20/3) = -151/3
4x = 3
x = 3/4
x = 3/4


Input: Compute the solution of x^2 + 73/9x - 170/9 = 0

Output:
x^2 + 73/9x - 170/9 = 0
(x - 17/9)(x - -10) = 0
x - 17/9 = 0  or  x - -10 = 0
x = 17/9
x = -10


Input: Find x for 9x + 72/5 = 0

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


Input: Find x in x^2 - 149/24x + 65/8 = 0

Output:
x^2 - 149/24x + 65/8 = 0
(x - 15/8)(x - 13/3) = 0
x - 15/8 = 0  or  x - 13/3 = 0
x = 15/8
x = 13/3


Input: Solve the equation 4x + 32/9 = 0

Output:
4x + 32/9 = 0
4x = -32/9
x = -32/9 / 4
x = -8/9


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

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


Input: Solve x^3 - 7/6x^2 - 13/18x + 1/3 = 0

Output:
x^3 - 7/6x^2 - 13/18x + 1/3 = 0
(x - -2/3)(x - 3/2)(x - 1/3) = 0
x - -2/3 = 0
x - 3/2 = 0
x - 1/3 = 0
x = -2/3
x = 3/2
x = 1/3


Input:
Solve the system:
3x + 5y = 76/7
3x + 9y = 120/7

Output:
3x + 5y = 76/7
3x + 9y = 120/7

Using elimination
3*(3x + 5y = 76/7)
3*(3x + 9y = 120/7)
9x + 15y = 228/7
9x + 27y = 360/7
Subtract equations
-12y = -132/7
y = -132/7/-12
y = 11/7

Substitute y
3x + 5(11/7) = 76/7
3x = 3
x = 3/3
x = 1


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

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


Input: Compute the solution of 4x - 8/5 = 0

Output:
4x - 8/5 = 0
4x = 8/5
x = 8/5 / 4
x = 2/5


Input: Compute the solution of x^3 - 181/360x^2 - 229/120x + 11/45 = 0

Output:
x^3 - 181/360x^2 - 229/120x + 11/45 = 0
(x - 1/8)(x - 8/5)(x - -11/9) = 0
x - 1/8 = 0
x - 8/5 = 0
x - -11/9 = 0
x = 1/8
x = 8/5
x = -11/9


Input: Find the solution to x^2 - 3/5x - 8/5 = 0

Output:
x^2 - 3/5x - 8/5 = 0
(x - -1)(x - 8/5) = 0
x - -1 = 0  or  x - 8/5 = 0
x = -1
x = 8/5


Input: Solve the equation 6x + 20 = 0

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


Input:
Solve the equations:
1x + 3y = -41/4
2x + 4y = -25

Output:
1x + 3y = -41/4
2x + 4y = -25

Using elimination
2*(1x + 3y = -41/4)
1*(2x + 4y = -25)
2x + 6y = -41/2
2x + 4y = -25
Subtract equations
2y = 9/2
y = 9/2/2
y = 9/4

Substitute y
1x + 3(9/4) = -41/4
1x = -17
x = -17/1
x = -17


Input:
Solve simultaneously:
1x + 9y = 321/7
10x + 5y = 235/7

Output:
1x + 9y = 321/7
10x + 5y = 235/7

Using elimination
10*(1x + 9y = 321/7)
1*(10x + 5y = 235/7)
10x + 90y = 3210/7
10x + 5y = 235/7
Subtract equations
85y = 425
y = 425/85
y = 5

Substitute y
1x + 9(5) = 321/7
1x = 6/7
x = 6/7/1
x = 6/7


Input: Find x in 9x - 45/2 = 0

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


Input:
Find x and y such that
2x + 6y = 34
2x + 9y = 49

Output:
2x + 6y = 34
2x + 9y = 49

Using elimination
2*(2x + 6y = 34)
2*(2x + 9y = 49)
4x + 12y = 68
4x + 18y = 98
Subtract equations
-6y = -30
y = -30/-6
y = 5

Substitute y
2x + 6(5) = 34
2x = 4
x = 4/2
x = 2


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

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


Input: Find x for x^3 - 197/90x^2 - 2/15x + 119/90 = 0

Output:
x^3 - 197/90x^2 - 2/15x + 119/90 = 0
(x - 17/9)(x - -7/10)(x - 1) = 0
x - 17/9 = 0
x - -7/10 = 0
x - 1 = 0
x = 17/9
x = -7/10
x = 1


Input: Determine x in x^2 - 5/56x - 25/56 = 0

Output:
x^2 - 5/56x - 25/56 = 0
(x - -5/8)(x - 5/7) = 0
x - -5/8 = 0  or  x - 5/7 = 0
x = -5/8
x = 5/7


Input: Find x in 6x - 36 = 0

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


Input: Solve x^3 - 731/70x^2 + 933/70x - 108/35 = 0

Output:
x^3 - 731/70x^2 + 933/70x - 108/35 = 0
(x - 8/7)(x - 9)(x - 3/10) = 0
x - 8/7 = 0
x - 9 = 0
x - 3/10 = 0
x = 8/7
x = 9
x = 3/10


Input: Solve the equation x^2 - 23x + 76 = 0

Output:
x^2 - 23x + 76 = 0
(x - 19)(x - 4) = 0
x - 19 = 0  or  x - 4 = 0
x = 19
x = 4


Input: Solve the equation x^3 - 869/36x^2 + 2963/36x + 85/9 = 0

Output:
x^3 - 869/36x^2 + 2963/36x + 85/9 = 0
(x - 20)(x - -1/9)(x - 17/4) = 0
x - 20 = 0
x - -1/9 = 0
x - 17/4 = 0
x = 20
x = -1/9
x = 17/4


Input: Solve quickly: 5x - 85/6 = 0

Output:
5x - 85/6 = 0
5x = 85/6
x = 85/6 / 5
x = 17/6


Input:
Solve the system:
5x + 5y = 225/14
10x + 5y = 415/14

Output:
5x + 5y = 225/14
10x + 5y = 415/14

Using elimination
10*(5x + 5y = 225/14)
5*(10x + 5y = 415/14)
50x + 50y = 1125/7
50x + 25y = 2075/14
Subtract equations
25y = 25/2
y = 25/2/25
y = 1/2

Substitute y
5x + 5(1/2) = 225/14
5x = 95/7
x = 95/7/5
x = 19/7


Input:
Solve simultaneously:
5x + 5y = -215/72
9x + 3y = -73/8

Output:
5x + 5y = -215/72
9x + 3y = -73/8

Using elimination
9*(5x + 5y = -215/72)
5*(9x + 3y = -73/8)
45x + 45y = -215/8
45x + 15y = -365/8
Subtract equations
30y = 75/4
y = 75/4/30
y = 5/8

Substitute y
5x + 5(5/8) = -215/72
5x = -55/9
x = -55/9/5
x = -11/9


Input: Find x in x^3 - 112/45x^2 - 221/45x + 152/15 = 0

Output:
x^3 - 112/45x^2 - 221/45x + 152/15 = 0
(x - 3)(x - 8/5)(x - -19/9) = 0
x - 3 = 0
x - 8/5 = 0
x - -19/9 = 0
x = 3
x = 8/5
x = -19/9


Input: Solve x^3 - 283/21x^2 + 380/21x - 32/7 = 0

Output:
x^3 - 283/21x^2 + 380/21x - 32/7 = 0
(x - 1/3)(x - 8/7)(x - 12) = 0
x - 1/3 = 0
x - 8/7 = 0
x - 12 = 0
x = 1/3
x = 8/7
x = 12


Input: What value of x satisfies x^2 + 53/30x + 4/15 = 0

Output:
x^2 + 53/30x + 4/15 = 0
(x - -8/5)(x - -1/6) = 0
x - -8/5 = 0  or  x - -1/6 = 0
x = -8/5
x = -1/6


Input: Solve quickly: x^3 + 3/2x^2 + 2/9x - 5/18 = 0

Output:
x^3 + 3/2x^2 + 2/9x - 5/18 = 0
(x - -1)(x - -5/6)(x - 1/3) = 0
x - -1 = 0
x - -5/6 = 0
x - 1/3 = 0
x = -1
x = -5/6
x = 1/3


Input:
Find x and y such that
8x + 8y = 432/5
4x + 7y = 381/5

Output:
8x + 8y = 432/5
4x + 7y = 381/5

Using elimination
4*(8x + 8y = 432/5)
8*(4x + 7y = 381/5)
32x + 32y = 1728/5
32x + 56y = 3048/5
Subtract equations
-24y = -264
y = -264/-24
y = 11

Substitute y
8x + 8(11) = 432/5
8x = -8/5
x = -8/5/8
x = -1/5


Input: Solve 2x - 1 = 0

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


Input: What value of x satisfies x^2 - 11/2x + 9/2 = 0

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


Input: Find x for x^2 - 26/15x - 17/3 = 0

Output:
x^2 - 26/15x - 17/3 = 0
(x - -5/3)(x - 17/5) = 0
x - -5/3 = 0  or  x - 17/5 = 0
x = -5/3
x = 17/5


Input:
Find x and y such that
3x + 2y = 43/20
1x + 9y = -513/40

Output:
3x + 2y = 43/20
1x + 9y = -513/40

Using elimination
1*(3x + 2y = 43/20)
3*(1x + 9y = -513/40)
3x + 2y = 43/20
3x + 27y = -1539/40
Subtract equations
-25y = 325/8
y = 325/8/-25
y = -13/8

Substitute y
3x + 2(-13/8) = 43/20
3x = 27/5
x = 27/5/3
x = 9/5


Input: Find the solution to 1x - 3 = 0

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


Input: What value of x satisfies x^2 - 29/8x + 13/4 = 0

Output:
x^2 - 29/8x + 13/4 = 0
(x - 2)(x - 13/8) = 0
x - 2 = 0  or  x - 13/8 = 0
x = 2
x = 13/8


Input: Find x for x^3 + 73/30x^2 + 9/5x + 11/30 = 0

Output:
x^3 + 73/30x^2 + 9/5x + 11/30 = 0
(x - -1/3)(x - -1)(x - -11/10) = 0
x - -1/3 = 0
x - -1 = 0
x - -11/10 = 0
x = -1/3
x = -1
x = -11/10


Input: Solve the equation 8x  = 0

Output:
8x  = 0
8x = 0
x = 0 / 8
x = 0


Input: Find x in x^3 - 61/15x^2 + 76/15x - 28/15 = 0

Output:
x^3 - 61/15x^2 + 76/15x - 28/15 = 0
(x - 7/5)(x - 2/3)(x - 2) = 0
x - 7/5 = 0
x - 2/3 = 0
x - 2 = 0
x = 7/5
x = 2/3
x = 2


Input:
Solve the equations:
6x + 8y = -622/21
3x + 2y = -241/21

Output:
6x + 8y = -622/21
3x + 2y = -241/21

Using elimination
3*(6x + 8y = -622/21)
6*(3x + 2y = -241/21)
18x + 24y = -622/7
18x + 12y = -482/7
Subtract equations
12y = -20
y = -20/12
y = -5/3

Substitute y
6x + 8(-5/3) = -622/21
6x = -114/7
x = -114/7/6
x = -19/7


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

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


Input: What value of x satisfies x^2 + 21/10x - 27/10 = 0

Output:
x^2 + 21/10x - 27/10 = 0
(x - 9/10)(x - -3) = 0
x - 9/10 = 0  or  x - -3 = 0
x = 9/10
x = -3


Input: Solve 9x - 45 = 0

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


Input:
Solve the system:
6x + 3y = 43
5x + 2y = 88/3

Output:
6x + 3y = 43
5x + 2y = 88/3

Using elimination
5*(6x + 3y = 43)
6*(5x + 2y = 88/3)
30x + 15y = 215
30x + 12y = 176
Subtract equations
3y = 39
y = 39/3
y = 13

Substitute y
6x + 3(13) = 43
6x = 4
x = 4/6
x = 2/3


Input:
Solve the equations:
10x + 2y = 9
2x + 4y = -63/5

Output:
10x + 2y = 9
2x + 4y = -63/5

Using elimination
2*(10x + 2y = 9)
10*(2x + 4y = -63/5)
20x + 4y = 18
20x + 40y = -126
Subtract equations
-36y = 144
y = 144/-36
y = -4

Substitute y
10x + 2(-4) = 9
10x = 17
x = 17/10
x = 17/10


Input: Find x in 10x - 20 = 0

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


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

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


Input:
Solve simultaneously:
5x + 2y = -53/15
4x + 6y = -49/15

Output:
5x + 2y = -53/15
4x + 6y = -49/15

Using elimination
4*(5x + 2y = -53/15)
5*(4x + 6y = -49/15)
20x + 8y = -212/15
20x + 30y = -49/3
Subtract equations
-22y = 11/5
y = 11/5/-22
y = -1/10

Substitute y
5x + 2(-1/10) = -53/15
5x = -10/3
x = -10/3/5
x = -2/3


Input: Find the solution to x^2 + 47/9x - 190/27 = 0

Output:
x^2 + 47/9x - 190/27 = 0
(x - -19/3)(x - 10/9) = 0
x - -19/3 = 0  or  x - 10/9 = 0
x = -19/3
x = 10/9


Input:
Find x and y such that
6x + 8y = 184/3
3x + 6y = 44

Output:
6x + 8y = 184/3
3x + 6y = 44

Using elimination
3*(6x + 8y = 184/3)
6*(3x + 6y = 44)
18x + 24y = 184
18x + 36y = 264
Subtract equations
-12y = -80
y = -80/-12
y = 20/3

Substitute y
6x + 8(20/3) = 184/3
6x = 8
x = 8/6
x = 4/3


Input: Solve quickly: x^3 + 113/7x^2 + 15x - 225/7 = 0

Output:
x^3 + 113/7x^2 + 15x - 225/7 = 0
(x - 1)(x - -15)(x - -15/7) = 0
x - 1 = 0
x - -15 = 0
x - -15/7 = 0
x = 1
x = -15
x = -15/7


Input: Find x for x^2 - 53/10x - 39/5 = 0

Output:
x^2 - 53/10x - 39/5 = 0
(x - -6/5)(x - 13/2) = 0
x - -6/5 = 0  or  x - 13/2 = 0
x = -6/5
x = 13/2


Input: Determine x in x^2 + 87/20x + 143/40 = 0

Output:
x^2 + 87/20x + 143/40 = 0
(x - -13/4)(x - -11/10) = 0
x - -13/4 = 0  or  x - -11/10 = 0
x = -13/4
x = -11/10


Input: Solve quickly: x^3 + 71/24x^2 + 163/96x - 5/8 = 0

Output:
x^3 + 71/24x^2 + 163/96x - 5/8 = 0
(x - 1/4)(x - -4/3)(x - -15/8) = 0
x - 1/4 = 0
x - -4/3 = 0
x - -15/8 = 0
x = 1/4
x = -4/3
x = -15/8


Input: Solve the equation x^3 - 25/6x^2 - 68/3x + 40 = 0

Output:
x^3 - 25/6x^2 - 68/3x + 40 = 0
(x - -4)(x - 3/2)(x - 20/3) = 0
x - -4 = 0
x - 3/2 = 0
x - 20/3 = 0
x = -4
x = 3/2
x = 20/3


Input: Find x in 1x + 12 = 0

Output:
1x + 12 = 0
1x = -12
x = -12 / 1
x = -12


Input:
Find x and y such that
7x + 7y = -49/5
8x + 6y = -47/5

Output:
7x + 7y = -49/5
8x + 6y = -47/5

Using elimination
8*(7x + 7y = -49/5)
7*(8x + 6y = -47/5)
56x + 56y = -392/5
56x + 42y = -329/5
Subtract equations
14y = -63/5
y = -63/5/14
y = -9/10

Substitute y
7x + 7(-9/10) = -49/5
7x = -7/2
x = -7/2/7
x = -1/2


Input: Find the solution to 4x + 32/3 = 0

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


Input: Solve quickly: x^2 + 52/9x + 169/27 = 0

Output:
x^2 + 52/9x + 169/27 = 0
(x - -13/3)(x - -13/9) = 0
x - -13/3 = 0  or  x - -13/9 = 0
x = -13/3
x = -13/9


Input: Find the solution to x^3 + 9/5x^2 - 38/5x + 24/5 = 0

Output:
x^3 + 9/5x^2 - 38/5x + 24/5 = 0
(x - 6/5)(x - -4)(x - 1) = 0
x - 6/5 = 0
x - -4 = 0
x - 1 = 0
x = 6/5
x = -4
x = 1


Input: What value of x satisfies 1x + 5/9 = 0

Output:
1x + 5/9 = 0
1x = -5/9
x = -5/9 / 1
x = -5/9


Input:
Find x and y such that
1x + 4y = 46/3
5x + 4y = 42

Output:
1x + 4y = 46/3
5x + 4y = 42

Using elimination
5*(1x + 4y = 46/3)
1*(5x + 4y = 42)
5x + 20y = 230/3
5x + 4y = 42
Subtract equations
16y = 104/3
y = 104/3/16
y = 13/6

Substitute y
1x + 4(13/6) = 46/3
1x = 20/3
x = 20/3/1
x = 20/3


Input: Solve quickly: x^2 + 35/3x + 304/9 = 0

Output:
x^2 + 35/3x + 304/9 = 0
(x - -19/3)(x - -16/3) = 0
x - -19/3 = 0  or  x - -16/3 = 0
x = -19/3
x = -16/3


Input: Determine x in x^2 + 15/2x + 9 = 0

Output:
x^2 + 15/2x + 9 = 0
(x - -6)(x - -3/2) = 0
x - -6 = 0  or  x - -3/2 = 0
x = -6
x = -3/2


Input: Determine x in x^2 - 77/20x + 13/4 = 0

Output:
x^2 - 77/20x + 13/4 = 0
(x - 13/5)(x - 5/4) = 0
x - 13/5 = 0  or  x - 5/4 = 0
x = 13/5
x = 5/4


Input:
Solve the equations:
8x + 1y = -1205/8
8x + 6y = -575/4

Output:
8x + 1y = -1205/8
8x + 6y = -575/4

Using elimination
8*(8x + 1y = -1205/8)
8*(8x + 6y = -575/4)
64x + 8y = -1205
64x + 48y = -1150
Subtract equations
-40y = -55
y = -55/-40
y = 11/8

Substitute y
8x + 1(11/8) = -1205/8
8x = -152
x = -152/8
x = -19


Input: Find x for x^3 - 4x^2 - 433/36x + 187/9 = 0

Output:
x^3 - 4x^2 - 433/36x + 187/9 = 0
(x - 4/3)(x - -17/6)(x - 11/2) = 0
x - 4/3 = 0
x - -17/6 = 0
x - 11/2 = 0
x = 4/3
x = -17/6
x = 11/2


Input: Solve the equation x^2 + 1/2x - 3/50 = 0

Output:
x^2 + 1/2x - 3/50 = 0
(x - 1/10)(x - -3/5) = 0
x - 1/10 = 0  or  x - -3/5 = 0
x = 1/10
x = -3/5


Input: What value of x satisfies 8x + 64/3 = 0

Output:
8x + 64/3 = 0
8x = -64/3
x = -64/3 / 8
x = -8/3


Input:
Solve simultaneously:
7x + 3y = -499/8
2x + 5y = -353/4

Output:
7x + 3y = -499/8
2x + 5y = -353/4

Using elimination
2*(7x + 3y = -499/8)
7*(2x + 5y = -353/4)
14x + 6y = -499/4
14x + 35y = -2471/4
Subtract equations
-29y = 493
y = 493/-29
y = -17

Substitute y
7x + 3(-17) = -499/8
7x = -91/8
x = -91/8/7
x = -13/8


Input: Find x for x^2 + 137/28x + 19/28 = 0

Output:
x^2 + 137/28x + 19/28 = 0
(x - -1/7)(x - -19/4) = 0
x - -1/7 = 0  or  x - -19/4 = 0
x = -1/7
x = -19/4


Input:
Solve simultaneously:
3x + 2y = -35/2
7x + 5y = -85/2

Output:
3x + 2y = -35/2
7x + 5y = -85/2

Using elimination
7*(3x + 2y = -35/2)
3*(7x + 5y = -85/2)
21x + 14y = -245/2
21x + 15y = -255/2
Subtract equations
-1y = 5
y = 5/-1
y = -5

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


Input:
Solve the equations:
2x + 5y = -7/3
2x + 10y = 88/3

Output:
2x + 5y = -7/3
2x + 10y = 88/3

Using elimination
2*(2x + 5y = -7/3)
2*(2x + 10y = 88/3)
4x + 10y = -14/3
4x + 20y = 176/3
Subtract equations
-10y = -190/3
y = -190/3/-10
y = 19/3

Substitute y
2x + 5(19/3) = -7/3
2x = -34
x = -34/2
x = -17


Input: Solve the equation 7x + 133/4 = 0

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


Input: Solve the equation x^3 + 51/5x^2 + 11x + 9/5 = 0

Output:
x^3 + 51/5x^2 + 11x + 9/5 = 0
(x - -1/5)(x - -1)(x - -9) = 0
x - -1/5 = 0
x - -1 = 0
x - -9 = 0
x = -1/5
x = -1
x = -9


Input:
Solve the equations:
9x + 4y = -65/2
6x + 1y = -15

Output:
9x + 4y = -65/2
6x + 1y = -15

Using elimination
6*(9x + 4y = -65/2)
9*(6x + 1y = -15)
54x + 24y = -195
54x + 9y = -135
Subtract equations
15y = -60
y = -60/15
y = -4

Substitute y
9x + 4(-4) = -65/2
9x = -33/2
x = -33/2/9
x = -11/6


Input: Solve x^3 - 19/2x^2 + 37/2x - 7 = 0

Output:
x^3 - 19/2x^2 + 37/2x - 7 = 0
(x - 1/2)(x - 7)(x - 2) = 0
x - 1/2 = 0
x - 7 = 0
x - 2 = 0
x = 1/2
x = 7
x = 2


Input:
Solve the system:
9x + 2y = 401/10
4x + 8y = 82/5

Output:
9x + 2y = 401/10
4x + 8y = 82/5

Using elimination
4*(9x + 2y = 401/10)
9*(4x + 8y = 82/5)
36x + 8y = 802/5
36x + 72y = 738/5
Subtract equations
-64y = 64/5
y = 64/5/-64
y = -1/5

Substitute y
9x + 2(-1/5) = 401/10
9x = 81/2
x = 81/2/9
x = 9/2


Input:
Solve the system:
1x + 4y = 269/8
4x + 1y = 7

Output:
1x + 4y = 269/8
4x + 1y = 7

Using elimination
4*(1x + 4y = 269/8)
1*(4x + 1y = 7)
4x + 16y = 269/2
4x + 1y = 7
Subtract equations
15y = 255/2
y = 255/2/15
y = 17/2

Substitute y
1x + 4(17/2) = 269/8
1x = -3/8
x = -3/8/1
x = -3/8


Input: Find x for x^3 + 391/28x^2 + 479/14x + 495/28 = 0

Output:
x^3 + 391/28x^2 + 479/14x + 495/28 = 0
(x - -11)(x - -5/7)(x - -9/4) = 0
x - -11 = 0
x - -5/7 = 0
x - -9/4 = 0
x = -11
x = -5/7
x = -9/4


Input: Find the solution to x^3 + 21/4x^2 + 73/8x + 21/4 = 0

Output:
x^3 + 21/4x^2 + 73/8x + 21/4 = 0
(x - -7/4)(x - -3/2)(x - -2) = 0
x - -7/4 = 0
x - -3/2 = 0
x - -2 = 0
x = -7/4
x = -3/2
x = -2


Input: What value of x satisfies x^3 - 43/10x^2 + 201/50x - 9/25 = 0

Output:
x^3 - 43/10x^2 + 201/50x - 9/25 = 0
(x - 3)(x - 6/5)(x - 1/10) = 0
x - 3 = 0
x - 6/5 = 0
x - 1/10 = 0
x = 3
x = 6/5
x = 1/10


Input:
Solve simultaneously:
10x + 5y = -1
7x + 3y = -7/5

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

Using elimination
7*(10x + 5y = -1)
10*(7x + 3y = -7/5)
70x + 35y = -7
70x + 30y = -14
Subtract equations
5y = 7
y = 7/5
y = 7/5

Substitute y
10x + 5(7/5) = -1
10x = -8
x = -8/10
x = -4/5


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

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


Input: Find x for x^2 - 9x + 20 = 0

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


Input: Solve the equation x^2 - 4/3x - 32/3 = 0

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


Input:
Solve simultaneously:
1x + 9y = -95/4
5x + 1y = -79/4

Output:
1x + 9y = -95/4
5x + 1y = -79/4

Using elimination
5*(1x + 9y = -95/4)
1*(5x + 1y = -79/4)
5x + 45y = -475/4
5x + 1y = -79/4
Subtract equations
44y = -99
y = -99/44
y = -9/4

Substitute y
1x + 9(-9/4) = -95/4
1x = -7/2
x = -7/2/1
x = -7/2


Input:
Solve simultaneously:
4x + 9y = 247/5
8x + 4y = 242/5

Output:
4x + 9y = 247/5
8x + 4y = 242/5

Using elimination
8*(4x + 9y = 247/5)
4*(8x + 4y = 242/5)
32x + 72y = 1976/5
32x + 16y = 968/5
Subtract equations
56y = 1008/5
y = 1008/5/56
y = 18/5

Substitute y
4x + 9(18/5) = 247/5
4x = 17
x = 17/4
x = 17/4


Input: Find the solution to x^3 - 122/45x^2 - 244/45x + 8 = 0

Output:
x^3 - 122/45x^2 - 244/45x + 8 = 0
(x - 18/5)(x - 10/9)(x - -2) = 0
x - 18/5 = 0
x - 10/9 = 0
x - -2 = 0
x = 18/5
x = 10/9
x = -2


Input:
Find x and y such that
7x + 6y = -327/10
10x + 6y = -87/2

Output:
7x + 6y = -327/10
10x + 6y = -87/2

Using elimination
10*(7x + 6y = -327/10)
7*(10x + 6y = -87/2)
70x + 60y = -327
70x + 42y = -609/2
Subtract equations
18y = -45/2
y = -45/2/18
y = -5/4

Substitute y
7x + 6(-5/4) = -327/10
7x = -126/5
x = -126/5/7
x = -18/5


Input:
Find x and y such that
9x + 8y = 156/35
2x + 4y = -132/35

Output:
9x + 8y = 156/35
2x + 4y = -132/35

Using elimination
2*(9x + 8y = 156/35)
9*(2x + 4y = -132/35)
18x + 16y = 312/35
18x + 36y = -1188/35
Subtract equations
-20y = 300/7
y = 300/7/-20
y = -15/7

Substitute y
9x + 8(-15/7) = 156/35
9x = 108/5
x = 108/5/9
x = 12/5


Input: Solve quickly: x^2 + 12x - 28 = 0

Output:
x^2 + 12x - 28 = 0
(x - -14)(x - 2) = 0
x - -14 = 0  or  x - 2 = 0
x = -14
x = 2


Input: Find x in 1x - 1 = 0

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


Input:
Solve simultaneously:
4x + 7y = -81/10
6x + 5y = -21/2

Output:
4x + 7y = -81/10
6x + 5y = -21/2

Using elimination
6*(4x + 7y = -81/10)
4*(6x + 5y = -21/2)
24x + 42y = -243/5
24x + 20y = -42
Subtract equations
22y = -33/5
y = -33/5/22
y = -3/10

Substitute y
4x + 7(-3/10) = -81/10
4x = -6
x = -6/4
x = -3/2


Input:
Find x and y such that
10x + 2y = 710/7
7x + 6y = 520/7

Output:
10x + 2y = 710/7
7x + 6y = 520/7

Using elimination
7*(10x + 2y = 710/7)
10*(7x + 6y = 520/7)
70x + 14y = 710
70x + 60y = 5200/7
Subtract equations
-46y = -230/7
y = -230/7/-46
y = 5/7

Substitute y
10x + 2(5/7) = 710/7
10x = 100
x = 100/10
x = 10


Input: Solve the equation x^3 - 15/2x^2 - 9x + 40 = 0

Output:
x^3 - 15/2x^2 - 9x + 40 = 0
(x - 2)(x - -5/2)(x - 8) = 0
x - 2 = 0
x - -5/2 = 0
x - 8 = 0
x = 2
x = -5/2
x = 8


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

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


Input: Find the solution to x^3 - 141/8x^2 - 109/16x + 9/8 = 0

Output:
x^3 - 141/8x^2 - 109/16x + 9/8 = 0
(x - -1/2)(x - 1/8)(x - 18) = 0
x - -1/2 = 0
x - 1/8 = 0
x - 18 = 0
x = -1/2
x = 1/8
x = 18


Input:
Find x and y such that
5x + 4y = -71/3
5x + 5y = -625/24

Output:
5x + 4y = -71/3
5x + 5y = -625/24

Using elimination
5*(5x + 4y = -71/3)
5*(5x + 5y = -625/24)
25x + 20y = -355/3
25x + 25y = -3125/24
Subtract equations
-5y = 95/8
y = 95/8/-5
y = -19/8

Substitute y
5x + 4(-19/8) = -71/3
5x = -85/6
x = -85/6/5
x = -17/6


Input:
Find x and y such that
2x + 8y = 158/63
5x + 7y = -242/63

Output:
2x + 8y = 158/63
5x + 7y = -242/63

Using elimination
5*(2x + 8y = 158/63)
2*(5x + 7y = -242/63)
10x + 40y = 790/63
10x + 14y = -484/63
Subtract equations
26y = 182/9
y = 182/9/26
y = 7/9

Substitute y
2x + 8(7/9) = 158/63
2x = -26/7
x = -26/7/2
x = -13/7


Input: Compute the solution of 10x - 14 = 0

Output:
10x - 14 = 0
10x = 14
x = 14 / 10
x = 7/5


Input: Solve quickly: 9x  = 0

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


Input:
Solve simultaneously:
9x + 6y = 375/2
7x + 6y = 299/2

Output:
9x + 6y = 375/2
7x + 6y = 299/2

Using elimination
7*(9x + 6y = 375/2)
9*(7x + 6y = 299/2)
63x + 42y = 2625/2
63x + 54y = 2691/2
Subtract equations
-12y = -33
y = -33/-12
y = 11/4

Substitute y
9x + 6(11/4) = 375/2
9x = 171
x = 171/9
x = 19


Input: What value of x satisfies 7x + 133/4 = 0

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


Input:
Find x and y such that
6x + 10y = -25/2
7x + 6y = -49/2

Output:
6x + 10y = -25/2
7x + 6y = -49/2

Using elimination
7*(6x + 10y = -25/2)
6*(7x + 6y = -49/2)
42x + 70y = -175/2
42x + 36y = -147
Subtract equations
34y = 119/2
y = 119/2/34
y = 7/4

Substitute y
6x + 10(7/4) = -25/2
6x = -30
x = -30/6
x = -5


Input: Solve x^3 - 77/15x^2 - 82/15x + 352/15 = 0

Output:
x^3 - 77/15x^2 - 82/15x + 352/15 = 0
(x - -11/5)(x - 2)(x - 16/3) = 0
x - -11/5 = 0
x - 2 = 0
x - 16/3 = 0
x = -11/5
x = 2
x = 16/3


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

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


Input: Find x in 2x - 4 = 0

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


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 equations:
7x + 3y = 157/4
7x + 6y = 181/4

Output:
7x + 3y = 157/4
7x + 6y = 181/4

Using elimination
7*(7x + 3y = 157/4)
7*(7x + 6y = 181/4)
49x + 21y = 1099/4
49x + 42y = 1267/4
Subtract equations
-21y = -42
y = -42/-21
y = 2

Substitute y
7x + 3(2) = 157/4
7x = 133/4
x = 133/4/7
x = 19/4


Input: Solve 10x + 50/3 = 0

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


Input: Determine x in x^3 + 627/35x^2 + 496/35x - 816/35 = 0

Output:
x^3 + 627/35x^2 + 496/35x - 816/35 = 0
(x - 4/5)(x - -12/7)(x - -17) = 0
x - 4/5 = 0
x - -12/7 = 0
x - -17 = 0
x = 4/5
x = -12/7
x = -17


Input:
Find x and y such that
9x + 7y = -249/5
4x + 9y = -93/5

Output:
9x + 7y = -249/5
4x + 9y = -93/5

Using elimination
4*(9x + 7y = -249/5)
9*(4x + 9y = -93/5)
36x + 28y = -996/5
36x + 81y = -837/5
Subtract equations
-53y = -159/5
y = -159/5/-53
y = 3/5

Substitute y
9x + 7(3/5) = -249/5
9x = -54
x = -54/9
x = -6


Input: Find x in x^2 + 11/2x + 6 = 0

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


Input: Solve x^2 - 7/40x - 1/2 = 0

Output:
x^2 - 7/40x - 1/2 = 0
(x - 4/5)(x - -5/8) = 0
x - 4/5 = 0  or  x - -5/8 = 0
x = 4/5
x = -5/8


Input: Solve quickly: 4x - 12 = 0

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


Input: Solve the equation 5x + 15/2 = 0

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


Input: Compute the solution of x^2 + 16/9x - 4/9 = 0

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


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

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


Input: Solve 1x - 5/3 = 0

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


Input: Solve the equation x^2 + 26/9x - 40/9 = 0

Output:
x^2 + 26/9x - 40/9 = 0
(x - 10/9)(x - -4) = 0
x - 10/9 = 0  or  x - -4 = 0
x = 10/9
x = -4


Input:
Solve simultaneously:
1x + 6y = -99/20
9x + 5y = -557/40

Output:
1x + 6y = -99/20
9x + 5y = -557/40

Using elimination
9*(1x + 6y = -99/20)
1*(9x + 5y = -557/40)
9x + 54y = -891/20
9x + 5y = -557/40
Subtract equations
49y = -245/8
y = -245/8/49
y = -5/8

Substitute y
1x + 6(-5/8) = -99/20
1x = -6/5
x = -6/5/1
x = -6/5


Input: Solve the equation 7x + 7 = 0

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


Input: Determine x in 1x + 18/7 = 0

Output:
1x + 18/7 = 0
1x = -18/7
x = -18/7 / 1
x = -18/7


Input: Find x in x^2 - 7/5x - 52/5 = 0

Output:
x^2 - 7/5x - 52/5 = 0
(x - -13/5)(x - 4) = 0
x - -13/5 = 0  or  x - 4 = 0
x = -13/5
x = 4


Input: Find the solution to x^2 - 13/7x - 24/7 = 0

Output:
x^2 - 13/7x - 24/7 = 0
(x - 3)(x - -8/7) = 0
x - 3 = 0  or  x - -8/7 = 0
x = 3
x = -8/7


Input: Compute the solution of x^3 - 26/35x^2 - 471/245x + 216/245 = 0

Output:
x^3 - 26/35x^2 - 471/245x + 216/245 = 0
(x - 8/5)(x - 3/7)(x - -9/7) = 0
x - 8/5 = 0
x - 3/7 = 0
x - -9/7 = 0
x = 8/5
x = 3/7
x = -9/7


Input: Solve x^3 + 389/140x^2 + 5/14x - 39/140 = 0

Output:
x^3 + 389/140x^2 + 5/14x - 39/140 = 0
(x - -3/7)(x - 1/4)(x - -13/5) = 0
x - -3/7 = 0
x - 1/4 = 0
x - -13/5 = 0
x = -3/7
x = 1/4
x = -13/5


Input:
Solve the system:
4x + 8y = -77/2
9x + 9y = -333/8

Output:
4x + 8y = -77/2
9x + 9y = -333/8

Using elimination
9*(4x + 8y = -77/2)
4*(9x + 9y = -333/8)
36x + 72y = -693/2
36x + 36y = -333/2
Subtract equations
36y = -180
y = -180/36
y = -5

Substitute y
4x + 8(-5) = -77/2
4x = 3/2
x = 3/2/4
x = 3/8


Input:
Find x and y such that
8x + 7y = -64/7
6x + 1y = -48/7

Output:
8x + 7y = -64/7
6x + 1y = -48/7

Using elimination
6*(8x + 7y = -64/7)
8*(6x + 1y = -48/7)
48x + 42y = -384/7
48x + 8y = -384/7
Subtract equations
34y = 0
y = 0/34
y = 0

Substitute y
8x + 7(0) = -64/7
8x = -64/7
x = -64/7/8
x = -8/7


Input: Solve x^2 + 9/20x - 91/40 = 0

Output:
x^2 + 9/20x - 91/40 = 0
(x - 13/10)(x - -7/4) = 0
x - 13/10 = 0  or  x - -7/4 = 0
x = 13/10
x = -7/4


Input: Solve x^3 + 34/7x^2 + 359/49x + 170/49 = 0

Output:
x^3 + 34/7x^2 + 359/49x + 170/49 = 0
(x - -10/7)(x - -17/7)(x - -1) = 0
x - -10/7 = 0
x - -17/7 = 0
x - -1 = 0
x = -10/7
x = -17/7
x = -1


Input: Solve x^3 + 37/12x^2 - 461/24x + 209/24 = 0

Output:
x^3 + 37/12x^2 - 461/24x + 209/24 = 0
(x - -19/3)(x - 11/4)(x - 1/2) = 0
x - -19/3 = 0
x - 11/4 = 0
x - 1/2 = 0
x = -19/3
x = 11/4
x = 1/2


Input:
Solve the equations:
10x + 7y = 227/6
1x + 6y = 67/3

Output:
10x + 7y = 227/6
1x + 6y = 67/3

Using elimination
1*(10x + 7y = 227/6)
10*(1x + 6y = 67/3)
10x + 7y = 227/6
10x + 60y = 670/3
Subtract equations
-53y = -371/2
y = -371/2/-53
y = 7/2

Substitute y
10x + 7(7/2) = 227/6
10x = 40/3
x = 40/3/10
x = 4/3


Input:
Solve the system:
9x + 8y = -87/2
1x + 10y = -39

Output:
9x + 8y = -87/2
1x + 10y = -39

Using elimination
1*(9x + 8y = -87/2)
9*(1x + 10y = -39)
9x + 8y = -87/2
9x + 90y = -351
Subtract equations
-82y = 615/2
y = 615/2/-82
y = -15/4

Substitute y
9x + 8(-15/4) = -87/2
9x = -27/2
x = -27/2/9
x = -3/2


Input:
Solve the equations:
4x + 3y = 335/14
2x + 5y = 437/14

Output:
4x + 3y = 335/14
2x + 5y = 437/14

Using elimination
2*(4x + 3y = 335/14)
4*(2x + 5y = 437/14)
8x + 6y = 335/7
8x + 20y = 874/7
Subtract equations
-14y = -77
y = -77/-14
y = 11/2

Substitute y
4x + 3(11/2) = 335/14
4x = 52/7
x = 52/7/4
x = 13/7


Input:
Solve the equations:
9x + 7y = 5
10x + 8y = 27/5

Output:
9x + 7y = 5
10x + 8y = 27/5

Using elimination
10*(9x + 7y = 5)
9*(10x + 8y = 27/5)
90x + 70y = 50
90x + 72y = 243/5
Subtract equations
-2y = 7/5
y = 7/5/-2
y = -7/10

Substitute y
9x + 7(-7/10) = 5
9x = 99/10
x = 99/10/9
x = 11/10


Input:
Solve the system:
3x + 1y = 165/56
6x + 3y = 153/28

Output:
3x + 1y = 165/56
6x + 3y = 153/28

Using elimination
6*(3x + 1y = 165/56)
3*(6x + 3y = 153/28)
18x + 6y = 495/28
18x + 9y = 459/28
Subtract equations
-3y = 9/7
y = 9/7/-3
y = -3/7

Substitute y
3x + 1(-3/7) = 165/56
3x = 27/8
x = 27/8/3
x = 9/8


Input: Determine x in 1x + 8/7 = 0

Output:
1x + 8/7 = 0
1x = -8/7
x = -8/7 / 1
x = -8/7


Input:
Solve the system:
2x + 1y = 15
2x + 5y = 87

Output:
2x + 1y = 15
2x + 5y = 87

Using elimination
2*(2x + 1y = 15)
2*(2x + 5y = 87)
4x + 2y = 30
4x + 10y = 174
Subtract equations
-8y = -144
y = -144/-8
y = 18

Substitute y
2x + 1(18) = 15
2x = -3
x = -3/2
x = -3/2


Input:
Solve simultaneously:
7x + 5y = 18/7
7x + 6y = 37/7

Output:
7x + 5y = 18/7
7x + 6y = 37/7

Using elimination
7*(7x + 5y = 18/7)
7*(7x + 6y = 37/7)
49x + 35y = 18
49x + 42y = 37
Subtract equations
-7y = -19
y = -19/-7
y = 19/7

Substitute y
7x + 5(19/7) = 18/7
7x = -11
x = -11/7
x = -11/7


Input:
Find x and y such that
9x + 10y = -265/8
8x + 6y = -127/5

Output:
9x + 10y = -265/8
8x + 6y = -127/5

Using elimination
8*(9x + 10y = -265/8)
9*(8x + 6y = -127/5)
72x + 80y = -265
72x + 54y = -1143/5
Subtract equations
26y = -182/5
y = -182/5/26
y = -7/5

Substitute y
9x + 10(-7/5) = -265/8
9x = -153/8
x = -153/8/9
x = -17/8


Input: What value of x satisfies x^3 + 34/5x^2 + 69/5x + 36/5 = 0

Output:
x^3 + 34/5x^2 + 69/5x + 36/5 = 0
(x - -4/5)(x - -3)(x - -3) = 0
x - -4/5 = 0
x - -3 = 0
x - -3 = 0
x = -4/5
x = -3
x = -3


Input:
Solve simultaneously:
8x + 7y = -467/35
10x + 5y = -101/7

Output:
8x + 7y = -467/35
10x + 5y = -101/7

Using elimination
10*(8x + 7y = -467/35)
8*(10x + 5y = -101/7)
80x + 70y = -934/7
80x + 40y = -808/7
Subtract equations
30y = -18
y = -18/30
y = -3/5

Substitute y
8x + 7(-3/5) = -467/35
8x = -64/7
x = -64/7/8
x = -8/7


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

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


Input: Determine x in x^3 - 395/72x^2 + 139/18x - 19/24 = 0

Output:
x^3 - 395/72x^2 + 139/18x - 19/24 = 0
(x - 3)(x - 1/9)(x - 19/8) = 0
x - 3 = 0
x - 1/9 = 0
x - 19/8 = 0
x = 3
x = 1/9
x = 19/8


Input: What value of x satisfies 10x - 130 = 0

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


Input: Solve x^2 - 47/20x + 21/20 = 0

Output:
x^2 - 47/20x + 21/20 = 0
(x - 7/4)(x - 3/5) = 0
x - 7/4 = 0  or  x - 3/5 = 0
x = 7/4
x = 3/5


Input: Solve 5x - 20 = 0

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


Input: Solve quickly: x^2 + 113/63x + 22/63 = 0

Output:
x^2 + 113/63x + 22/63 = 0
(x - -2/9)(x - -11/7) = 0
x - -2/9 = 0  or  x - -11/7 = 0
x = -2/9
x = -11/7


Input: Solve x^2 - 29/18x - 19/18 = 0

Output:
x^2 - 29/18x - 19/18 = 0
(x - 19/9)(x - -1/2) = 0
x - 19/9 = 0  or  x - -1/2 = 0
x = 19/9
x = -1/2


Input: Find the solution to 8x - 20 = 0

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


Input: Solve the equation x^3 - 41/24x^2 - 229/24x + 55/4 = 0

Output:
x^3 - 41/24x^2 - 229/24x + 55/4 = 0
(x - 11/8)(x - -3)(x - 10/3) = 0
x - 11/8 = 0
x - -3 = 0
x - 10/3 = 0
x = 11/8
x = -3
x = 10/3


Input: Solve 10x + 25 = 0

Output:
10x + 25 = 0
10x = -25
x = -25 / 10
x = -5/2


Input: Find the solution to x^3 - 251/10x^2 + 912/5x - 378 = 0

Output:
x^3 - 251/10x^2 + 912/5x - 378 = 0
(x - 15/2)(x - 14)(x - 18/5) = 0
x - 15/2 = 0
x - 14 = 0
x - 18/5 = 0
x = 15/2
x = 14
x = 18/5


Input: Find x for 4x + 8 = 0

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


Input: Solve the equation x^3 - 55/6x^2 - 39/2x - 22/3 = 0

Output:
x^3 - 55/6x^2 - 39/2x - 22/3 = 0
(x - 11)(x - -1/2)(x - -4/3) = 0
x - 11 = 0
x - -1/2 = 0
x - -4/3 = 0
x = 11
x = -1/2
x = -4/3


Input: Find x for x^2 + 43/5x + 17/20 = 0

Output:
x^2 + 43/5x + 17/20 = 0
(x - -17/2)(x - -1/10) = 0
x - -17/2 = 0  or  x - -1/10 = 0
x = -17/2
x = -1/10


Input:
Solve simultaneously:
4x + 9y = 65/12
2x + 3y = 19/12

Output:
4x + 9y = 65/12
2x + 3y = 19/12

Using elimination
2*(4x + 9y = 65/12)
4*(2x + 3y = 19/12)
8x + 18y = 65/6
8x + 12y = 19/3
Subtract equations
6y = 9/2
y = 9/2/6
y = 3/4

Substitute y
4x + 9(3/4) = 65/12
4x = -4/3
x = -4/3/4
x = -1/3


Input:
Solve the system:
1x + 3y = -10
6x + 3y = 75/2

Output:
1x + 3y = -10
6x + 3y = 75/2

Using elimination
6*(1x + 3y = -10)
1*(6x + 3y = 75/2)
6x + 18y = -60
6x + 3y = 75/2
Subtract equations
15y = -195/2
y = -195/2/15
y = -13/2

Substitute y
1x + 3(-13/2) = -10
1x = 19/2
x = 19/2/1
x = 19/2


Input:
Solve the equations:
5x + 5y = -375/28
7x + 6y = -29/2

Output:
5x + 5y = -375/28
7x + 6y = -29/2

Using elimination
7*(5x + 5y = -375/28)
5*(7x + 6y = -29/2)
35x + 35y = -375/4
35x + 30y = -145/2
Subtract equations
5y = -85/4
y = -85/4/5
y = -17/4

Substitute y
5x + 5(-17/4) = -375/28
5x = 55/7
x = 55/7/5
x = 11/7


Input: Solve quickly: 8x - 16/5 = 0

Output:
8x - 16/5 = 0
8x = 16/5
x = 16/5 / 8
x = 2/5


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

Output:
5x + 5/9 = 0
5x = -5/9
x = -5/9 / 5
x = -1/9


Input: Solve quickly: x^3 + 9/8x^2 - 7/4x  = 0

Output:
x^3 + 9/8x^2 - 7/4x  = 0
(x - 7/8)(x - -2)(x - 0) = 0
x - 7/8 = 0
x - -2 = 0
x - 0 = 0
x = 7/8
x = -2
x = 0


Input:
Find x and y such that
6x + 6y = 12/5
1x + 8y = 137/10

Output:
6x + 6y = 12/5
1x + 8y = 137/10

Using elimination
1*(6x + 6y = 12/5)
6*(1x + 8y = 137/10)
6x + 6y = 12/5
6x + 48y = 411/5
Subtract equations
-42y = -399/5
y = -399/5/-42
y = 19/10

Substitute y
6x + 6(19/10) = 12/5
6x = -9
x = -9/6
x = -3/2


Input: Find x in x^2 + 19/3x + 26/3 = 0

Output:
x^2 + 19/3x + 26/3 = 0
(x - -2)(x - -13/3) = 0
x - -2 = 0  or  x - -13/3 = 0
x = -2
x = -13/3


Input: What value of x satisfies x^3 + 473/42x^2 + 148/7x + 99/14 = 0

Output:
x^3 + 473/42x^2 + 148/7x + 99/14 = 0
(x - -3/7)(x - -9)(x - -11/6) = 0
x - -3/7 = 0
x - -9 = 0
x - -11/6 = 0
x = -3/7
x = -9
x = -11/6


Input:
Solve the system:
8x + 7y = 178/5
7x + 8y = 212/5

Output:
8x + 7y = 178/5
7x + 8y = 212/5

Using elimination
7*(8x + 7y = 178/5)
8*(7x + 8y = 212/5)
56x + 49y = 1246/5
56x + 64y = 1696/5
Subtract equations
-15y = -90
y = -90/-15
y = 6

Substitute y
8x + 7(6) = 178/5
8x = -32/5
x = -32/5/8
x = -4/5


Input:
Solve the system:
7x + 3y = 87/4
5x + 7y = 135/4

Output:
7x + 3y = 87/4
5x + 7y = 135/4

Using elimination
5*(7x + 3y = 87/4)
7*(5x + 7y = 135/4)
35x + 15y = 435/4
35x + 49y = 945/4
Subtract equations
-34y = -255/2
y = -255/2/-34
y = 15/4

Substitute y
7x + 3(15/4) = 87/4
7x = 21/2
x = 21/2/7
x = 3/2


Input: Determine x in 2x + 1 = 0

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


Input: Solve x^2 + 23/3x + 10 = 0

Output:
x^2 + 23/3x + 10 = 0
(x - -6)(x - -5/3) = 0
x - -6 = 0  or  x - -5/3 = 0
x = -6
x = -5/3


Input: Find the solution to x^2 + 185/24x + 38/3 = 0

Output:
x^2 + 185/24x + 38/3 = 0
(x - -19/8)(x - -16/3) = 0
x - -19/8 = 0  or  x - -16/3 = 0
x = -19/8
x = -16/3


Input: Solve x^2 + 64/9x + 95/9 = 0

Output:
x^2 + 64/9x + 95/9 = 0
(x - -19/9)(x - -5) = 0
x - -19/9 = 0  or  x - -5 = 0
x = -19/9
x = -5


Input:
Solve the equations:
2x + 9y = 4
9x + 9y = 113/2

Output:
2x + 9y = 4
9x + 9y = 113/2

Using elimination
9*(2x + 9y = 4)
2*(9x + 9y = 113/2)
18x + 81y = 36
18x + 18y = 113
Subtract equations
63y = -77
y = -77/63
y = -11/9

Substitute y
2x + 9(-11/9) = 4
2x = 15
x = 15/2
x = 15/2


Input:
Solve simultaneously:
4x + 3y = -93/7
8x + 10y = -170/7

Output:
4x + 3y = -93/7
8x + 10y = -170/7

Using elimination
8*(4x + 3y = -93/7)
4*(8x + 10y = -170/7)
32x + 24y = -744/7
32x + 40y = -680/7
Subtract equations
-16y = -64/7
y = -64/7/-16
y = 4/7

Substitute y
4x + 3(4/7) = -93/7
4x = -15
x = -15/4
x = -15/4


Input: Solve 8x - 52 = 0

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


Input: Compute the solution of x^2 + 29/40x + 3/40 = 0

Output:
x^2 + 29/40x + 3/40 = 0
(x - -3/5)(x - -1/8) = 0
x - -3/5 = 0  or  x - -1/8 = 0
x = -3/5
x = -1/8


Input: What value of x satisfies x^2 - 13/14x - 5/7 = 0

Output:
x^2 - 13/14x - 5/7 = 0
(x - -1/2)(x - 10/7) = 0
x - -1/2 = 0  or  x - 10/7 = 0
x = -1/2
x = 10/7


Input: Determine x in x^3 - 271/45x^2 - 214/45x + 88/3 = 0

Output:
x^3 - 271/45x^2 - 214/45x + 88/3 = 0
(x - -11/5)(x - 6)(x - 20/9) = 0
x - -11/5 = 0
x - 6 = 0
x - 20/9 = 0
x = -11/5
x = 6
x = 20/9


Input: Solve the equation x^2 + 44/9x + 17/3 = 0

Output:
x^2 + 44/9x + 17/3 = 0
(x - -3)(x - -17/9) = 0
x - -3 = 0  or  x - -17/9 = 0
x = -3
x = -17/9


Input: Find x in x^2 + 41/4x - 33/4 = 0

Output:
x^2 + 41/4x - 33/4 = 0
(x - 3/4)(x - -11) = 0
x - 3/4 = 0  or  x - -11 = 0
x = 3/4
x = -11


Input: Solve the equation x^2 + 41/56x - 117/56 = 0

Output:
x^2 + 41/56x - 117/56 = 0
(x - -13/7)(x - 9/8) = 0
x - -13/7 = 0  or  x - 9/8 = 0
x = -13/7
x = 9/8


Input: Find x for x^2 + 103/10x + 21 = 0

Output:
x^2 + 103/10x + 21 = 0
(x - -14/5)(x - -15/2) = 0
x - -14/5 = 0  or  x - -15/2 = 0
x = -14/5
x = -15/2


Input: Solve quickly: 6x - 3 = 0

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


Input: Find x for 8x  = 0

Output:
8x  = 0
8x = 0
x = 0 / 8
x = 0


Input: Find x in x^2 - 19/42x - 88/21 = 0

Output:
x^2 - 19/42x - 88/21 = 0
(x - -11/6)(x - 16/7) = 0
x - -11/6 = 0  or  x - 16/7 = 0
x = -11/6
x = 16/7


Input: Solve 3x + 21 = 0

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


Input: Find x for x^3 + 103/21x^2 + 20/3x + 12/7 = 0

Output:
x^3 + 103/21x^2 + 20/3x + 12/7 = 0
(x - -1/3)(x - -2)(x - -18/7) = 0
x - -1/3 = 0
x - -2 = 0
x - -18/7 = 0
x = -1/3
x = -2
x = -18/7


Input: Solve x^2 + 4x - 28/9 = 0

Output:
x^2 + 4x - 28/9 = 0
(x - 2/3)(x - -14/3) = 0
x - 2/3 = 0  or  x - -14/3 = 0
x = 2/3
x = -14/3


Input: Solve quickly: x^3 - 11/5x^2 - 38/5x + 8/5 = 0

Output:
x^3 - 11/5x^2 - 38/5x + 8/5 = 0
(x - -2)(x - 4)(x - 1/5) = 0
x - -2 = 0
x - 4 = 0
x - 1/5 = 0
x = -2
x = 4
x = 1/5


Input:
Solve the system:
8x + 6y = 64/9
10x + 7y = 80/9

Output:
8x + 6y = 64/9
10x + 7y = 80/9

Using elimination
10*(8x + 6y = 64/9)
8*(10x + 7y = 80/9)
80x + 60y = 640/9
80x + 56y = 640/9
Subtract equations
4y = 0
y = 0/4
y = 0

Substitute y
8x + 6(0) = 64/9
8x = 64/9
x = 64/9/8
x = 8/9


Input:
Find x and y such that
7x + 7y = 483/10
7x + 6y = 247/5

Output:
7x + 7y = 483/10
7x + 6y = 247/5

Using elimination
7*(7x + 7y = 483/10)
7*(7x + 6y = 247/5)
49x + 49y = 3381/10
49x + 42y = 1729/5
Subtract equations
7y = -77/10
y = -77/10/7
y = -11/10

Substitute y
7x + 7(-11/10) = 483/10
7x = 56
x = 56/7
x = 8


Input: Determine x in 7x - 2 = 0

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


Input: Solve 5x - 15/2 = 0

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


Input: Find the solution to x^2 - 12/7x - 64/7 = 0

Output:
x^2 - 12/7x - 64/7 = 0
(x - 4)(x - -16/7) = 0
x - 4 = 0  or  x - -16/7 = 0
x = 4
x = -16/7


Input:
Solve simultaneously:
5x + 10y = 33
4x + 6y = 104/5

Output:
5x + 10y = 33
4x + 6y = 104/5

Using elimination
4*(5x + 10y = 33)
5*(4x + 6y = 104/5)
20x + 40y = 132
20x + 30y = 104
Subtract equations
10y = 28
y = 28/10
y = 14/5

Substitute y
5x + 10(14/5) = 33
5x = 5
x = 5/5
x = 1


Input: Solve the equation 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: Determine x in x^2 + 17/8x - 15/16 = 0

Output:
x^2 + 17/8x - 15/16 = 0
(x - -5/2)(x - 3/8) = 0
x - -5/2 = 0  or  x - 3/8 = 0
x = -5/2
x = 3/8


Input:
Solve the system:
10x + 3y = -1/5
10x + 2y = 6/5

Output:
10x + 3y = -1/5
10x + 2y = 6/5

Using elimination
10*(10x + 3y = -1/5)
10*(10x + 2y = 6/5)
100x + 30y = -2
100x + 20y = 12
Subtract equations
10y = -14
y = -14/10
y = -7/5

Substitute y
10x + 3(-7/5) = -1/5
10x = 4
x = 4/10
x = 2/5


Input: Solve x^2 + 101/45x + 52/45 = 0

Output:
x^2 + 101/45x + 52/45 = 0
(x - -13/9)(x - -4/5) = 0
x - -13/9 = 0  or  x - -4/5 = 0
x = -13/9
x = -4/5


Input: Find the solution to x^3 + 145/56x^2 - 41/28x - 171/56 = 0

Output:
x^3 + 145/56x^2 - 41/28x - 171/56 = 0
(x - -19/7)(x - 9/8)(x - -1) = 0
x - -19/7 = 0
x - 9/8 = 0
x - -1 = 0
x = -19/7
x = 9/8
x = -1


Input: Solve the equation x^3 - 131/10x^2 - 1401/50x - 36/5 = 0

Output:
x^3 - 131/10x^2 - 1401/50x - 36/5 = 0
(x - -3/10)(x - -8/5)(x - 15) = 0
x - -3/10 = 0
x - -8/5 = 0
x - 15 = 0
x = -3/10
x = -8/5
x = 15


Input: Determine x in x^3 - 41/18x^2 - 10/27x + 50/27 = 0

Output:
x^3 - 41/18x^2 - 10/27x + 50/27 = 0
(x - -5/6)(x - 10/9)(x - 2) = 0
x - -5/6 = 0
x - 10/9 = 0
x - 2 = 0
x = -5/6
x = 10/9
x = 2


Input: Find x for x^2 + 3/4x - 85/4 = 0

Output:
x^2 + 3/4x - 85/4 = 0
(x - -5)(x - 17/4) = 0
x - -5 = 0  or  x - 17/4 = 0
x = -5
x = 17/4


Input: Solve quickly: 4x + 17 = 0

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


Input: Find x for x^3 + 2x^2 - 11/4x - 15/4 = 0

Output:
x^3 + 2x^2 - 11/4x - 15/4 = 0
(x - 3/2)(x - -1)(x - -5/2) = 0
x - 3/2 = 0
x - -1 = 0
x - -5/2 = 0
x = 3/2
x = -1
x = -5/2


Input:
Solve the equations:
1x + 7y = 23/5
10x + 1y = -23

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

Using elimination
10*(1x + 7y = 23/5)
1*(10x + 1y = -23)
10x + 70y = 46
10x + 1y = -23
Subtract equations
69y = 69
y = 69/69
y = 1

Substitute y
1x + 7(1) = 23/5
1x = -12/5
x = -12/5/1
x = -12/5


Input:
Solve simultaneously:
10x + 4y = -44
5x + 10y = -40

Output:
10x + 4y = -44
5x + 10y = -40

Using elimination
5*(10x + 4y = -44)
10*(5x + 10y = -40)
50x + 20y = -220
50x + 100y = -400
Subtract equations
-80y = 180
y = 180/-80
y = -9/4

Substitute y
10x + 4(-9/4) = -44
10x = -35
x = -35/10
x = -7/2


Input: Find the solution to 2x - 17/5 = 0

Output:
2x - 17/5 = 0
2x = 17/5
x = 17/5 / 2
x = 17/10


Input:
Solve the equations:
10x + 7y = -739/30
7x + 5y = -52/3

Output:
10x + 7y = -739/30
7x + 5y = -52/3

Using elimination
7*(10x + 7y = -739/30)
10*(7x + 5y = -52/3)
70x + 49y = -5173/30
70x + 50y = -520/3
Subtract equations
-1y = 9/10
y = 9/10/-1
y = -9/10

Substitute y
10x + 7(-9/10) = -739/30
10x = -55/3
x = -55/3/10
x = -11/6


Input: What value of x satisfies x^2 - 117/14x + 110/7 = 0

Output:
x^2 - 117/14x + 110/7 = 0
(x - 20/7)(x - 11/2) = 0
x - 20/7 = 0  or  x - 11/2 = 0
x = 20/7
x = 11/2


Input: Determine x in x^2 - 37/30x - 14/5 = 0

Output:
x^2 - 37/30x - 14/5 = 0
(x - -7/6)(x - 12/5) = 0
x - -7/6 = 0  or  x - 12/5 = 0
x = -7/6
x = 12/5


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

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


Input: Find x for x^2 - 137/24x + 143/24 = 0

Output:
x^2 - 137/24x + 143/24 = 0
(x - 11/8)(x - 13/3) = 0
x - 11/8 = 0  or  x - 13/3 = 0
x = 11/8
x = 13/3


Input:
Find x and y such that
9x + 6y = 57/5
7x + 8y = 203/15

Output:
9x + 6y = 57/5
7x + 8y = 203/15

Using elimination
7*(9x + 6y = 57/5)
9*(7x + 8y = 203/15)
63x + 42y = 399/5
63x + 72y = 609/5
Subtract equations
-30y = -42
y = -42/-30
y = 7/5

Substitute y
9x + 6(7/5) = 57/5
9x = 3
x = 3/9
x = 1/3


Input: Find x for x^2 - 62/5x - 112/5 = 0

Output:
x^2 - 62/5x - 112/5 = 0
(x - -8/5)(x - 14) = 0
x - -8/5 = 0  or  x - 14 = 0
x = -8/5
x = 14


Input:
Find x and y such that
4x + 6y = 47/2
10x + 9y = 169/4

Output:
4x + 6y = 47/2
10x + 9y = 169/4

Using elimination
10*(4x + 6y = 47/2)
4*(10x + 9y = 169/4)
40x + 60y = 235
40x + 36y = 169
Subtract equations
24y = 66
y = 66/24
y = 11/4

Substitute y
4x + 6(11/4) = 47/2
4x = 7
x = 7/4
x = 7/4


Input: Compute the solution of x^2 - 8/3x - 11/3 = 0

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


Input: What value of x satisfies x^2 - 52/9x - 95/27 = 0

Output:
x^2 - 52/9x - 95/27 = 0
(x - -5/9)(x - 19/3) = 0
x - -5/9 = 0  or  x - 19/3 = 0
x = -5/9
x = 19/3


Input: Find x in 4x - 64 = 0

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


Input: Determine x in x^3 + 8/5x^2 - 11/5x - 14/5 = 0

Output:
x^3 + 8/5x^2 - 11/5x - 14/5 = 0
(x - -1)(x - -2)(x - 7/5) = 0
x - -1 = 0
x - -2 = 0
x - 7/5 = 0
x = -1
x = -2
x = 7/5


Input: Solve the equation x^3 + 1/5x^2 - 152/25x + 84/25 = 0

Output:
x^3 + 1/5x^2 - 152/25x + 84/25 = 0
(x - 2)(x - -14/5)(x - 3/5) = 0
x - 2 = 0
x - -14/5 = 0
x - 3/5 = 0
x = 2
x = -14/5
x = 3/5


Input: Find x for x^3 + 27/4x^2 + 1669/162x + 1235/324 = 0

Output:
x^3 + 27/4x^2 + 1669/162x + 1235/324 = 0
(x - -5/9)(x - -13/9)(x - -19/4) = 0
x - -5/9 = 0
x - -13/9 = 0
x - -19/4 = 0
x = -5/9
x = -13/9
x = -19/4


Input: Compute the solution of 1x + 14/3 = 0

Output:
1x + 14/3 = 0
1x = -14/3
x = -14/3 / 1
x = -14/3


Input: Solve the equation 8x + 24 = 0

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


Input: Solve quickly: x^3 + 8x^2 - 67/9x - 910/9 = 0

Output:
x^3 + 8x^2 - 67/9x - 910/9 = 0
(x - 10/3)(x - -7)(x - -13/3) = 0
x - 10/3 = 0
x - -7 = 0
x - -13/3 = 0
x = 10/3
x = -7
x = -13/3


Input: Find the solution to 7x - 35 = 0

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


Input: Solve x^2 + 115/24x - 25/2 = 0

Output:
x^2 + 115/24x - 25/2 = 0
(x - -20/3)(x - 15/8) = 0
x - -20/3 = 0  or  x - 15/8 = 0
x = -20/3
x = 15/8


Input: Determine x in 10x - 160/3 = 0

Output:
10x - 160/3 = 0
10x = 160/3
x = 160/3 / 10
x = 16/3


Input: Solve the equation x^2 + 20/7x + 64/49 = 0

Output:
x^2 + 20/7x + 64/49 = 0
(x - -16/7)(x - -4/7) = 0
x - -16/7 = 0  or  x - -4/7 = 0
x = -16/7
x = -4/7


Input: What value of x satisfies 2x + 12/5 = 0

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


Input:
Find x and y such that
4x + 1y = -44/3
6x + 7y = -187/6

Output:
4x + 1y = -44/3
6x + 7y = -187/6

Using elimination
6*(4x + 1y = -44/3)
4*(6x + 7y = -187/6)
24x + 6y = -88
24x + 28y = -374/3
Subtract equations
-22y = 110/3
y = 110/3/-22
y = -5/3

Substitute y
4x + 1(-5/3) = -44/3
4x = -13
x = -13/4
x = -13/4


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

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

Using elimination
1*(6x + 9y = -3)
6*(1x + 2y = -1/9)
6x + 9y = -3
6x + 12y = -2/3
Subtract equations
-3y = -7/3
y = -7/3/-3
y = 7/9

Substitute y
6x + 9(7/9) = -3
6x = -10
x = -10/6
x = -5/3


Input: Determine x in x^2 + 1/28x - 209/28 = 0

Output:
x^2 + 1/28x - 209/28 = 0
(x - -11/4)(x - 19/7) = 0
x - -11/4 = 0  or  x - 19/7 = 0
x = -11/4
x = 19/7


Input: What value of x satisfies x^3 - 43/3x^2 - 119/12x - 5/4 = 0

Output:
x^3 - 43/3x^2 - 119/12x - 5/4 = 0
(x - -1/6)(x - 15)(x - -1/2) = 0
x - -1/6 = 0
x - 15 = 0
x - -1/2 = 0
x = -1/6
x = 15
x = -1/2


Input:
Solve simultaneously:
9x + 10y = 105/4
1x + 9y = 59/4

Output:
9x + 10y = 105/4
1x + 9y = 59/4

Using elimination
1*(9x + 10y = 105/4)
9*(1x + 9y = 59/4)
9x + 10y = 105/4
9x + 81y = 531/4
Subtract equations
-71y = -213/2
y = -213/2/-71
y = 3/2

Substitute y
9x + 10(3/2) = 105/4
9x = 45/4
x = 45/4/9
x = 5/4


Input: Solve quickly: 1x + 13/10 = 0

Output:
1x + 13/10 = 0
1x = -13/10
x = -13/10 / 1
x = -13/10


Input: Find x in x^2 + 32/3x + 15 = 0

Output:
x^2 + 32/3x + 15 = 0
(x - -5/3)(x - -9) = 0
x - -5/3 = 0  or  x - -9 = 0
x = -5/3
x = -9


Input:
Find x and y such that
4x + 1y = 64/3
10x + 1y = 115/3

Output:
4x + 1y = 64/3
10x + 1y = 115/3

Using elimination
10*(4x + 1y = 64/3)
4*(10x + 1y = 115/3)
40x + 10y = 640/3
40x + 4y = 460/3
Subtract equations
6y = 60
y = 60/6
y = 10

Substitute y
4x + 1(10) = 64/3
4x = 34/3
x = 34/3/4
x = 17/6


Input: Find x for 8x - 4 = 0

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


Input:
Solve the system:
8x + 5y = -167/4
6x + 2y = -30

Output:
8x + 5y = -167/4
6x + 2y = -30

Using elimination
6*(8x + 5y = -167/4)
8*(6x + 2y = -30)
48x + 30y = -501/2
48x + 16y = -240
Subtract equations
14y = -21/2
y = -21/2/14
y = -3/4

Substitute y
8x + 5(-3/4) = -167/4
8x = -38
x = -38/8
x = -19/4


Input: Find x for 10x - 50 = 0

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


Input: Find x for x^3 - 3x^2 - 1/25x + 99/25 = 0

Output:
x^3 - 3x^2 - 1/25x + 99/25 = 0
(x - 11/5)(x - 9/5)(x - -1) = 0
x - 11/5 = 0
x - 9/5 = 0
x - -1 = 0
x = 11/5
x = 9/5
x = -1


Input: What value of x satisfies x^3 + 2/3x^2 - 144/25x - 96/25 = 0

Output:
x^3 + 2/3x^2 - 144/25x - 96/25 = 0
(x - 12/5)(x - -2/3)(x - -12/5) = 0
x - 12/5 = 0
x - -2/3 = 0
x - -12/5 = 0
x = 12/5
x = -2/3
x = -12/5


Input: Solve quickly: x^3 + 85/24x^2 + 59/24x - 5/4 = 0

Output:
x^3 + 85/24x^2 + 59/24x - 5/4 = 0
(x - -15/8)(x - -2)(x - 1/3) = 0
x - -15/8 = 0
x - -2 = 0
x - 1/3 = 0
x = -15/8
x = -2
x = 1/3


Input: Solve the equation x^2 - 7/8x  = 0

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


Input: Find x for x^3 - 11/8x^2 - 2467/8x + 2907/4 = 0

Output:
x^3 - 11/8x^2 - 2467/8x + 2907/4 = 0
(x - 19/8)(x - -18)(x - 17) = 0
x - 19/8 = 0
x - -18 = 0
x - 17 = 0
x = 19/8
x = -18
x = 17


Input: Determine x in x^2 + 43/8x + 15/8 = 0

Output:
x^2 + 43/8x + 15/8 = 0
(x - -3/8)(x - -5) = 0
x - -3/8 = 0  or  x - -5 = 0
x = -3/8
x = -5


Input: Determine x in 8x - 76 = 0

Output:
8x - 76 = 0
8x = 76
x = 76 / 8
x = 19/2


Input: Solve the equation x^2 - 92/45x + 13/15 = 0

Output:
x^2 - 92/45x + 13/15 = 0
(x - 3/5)(x - 13/9) = 0
x - 3/5 = 0  or  x - 13/9 = 0
x = 3/5
x = 13/9


Input: Find x for x^3 - 35/8x^2 + 203/36x - 19/9 = 0

Output:
x^3 - 35/8x^2 + 203/36x - 19/9 = 0
(x - 4/3)(x - 2/3)(x - 19/8) = 0
x - 4/3 = 0
x - 2/3 = 0
x - 19/8 = 0
x = 4/3
x = 2/3
x = 19/8


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

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


Input: Solve the equation 10x + 130/3 = 0

Output:
10x + 130/3 = 0
10x = -130/3
x = -130/3 / 10
x = -13/3


Input: What value of x satisfies x^3 - 313/30x^2 + 448/15x - 247/10 = 0

Output:
x^3 - 313/30x^2 + 448/15x - 247/10 = 0
(x - 13/5)(x - 3/2)(x - 19/3) = 0
x - 13/5 = 0
x - 3/2 = 0
x - 19/3 = 0
x = 13/5
x = 3/2
x = 19/3


Input: Find x in x^3 + 30x^2 + 209x - 240 = 0

Output:
x^3 + 30x^2 + 209x - 240 = 0
(x - 1)(x - -16)(x - -15) = 0
x - 1 = 0
x - -16 = 0
x - -15 = 0
x = 1
x = -16
x = -15


Input: Solve quickly: x^3 + 142/15x^2 + 57/5x - 8/3 = 0

Output:
x^3 + 142/15x^2 + 57/5x - 8/3 = 0
(x - -8)(x - -5/3)(x - 1/5) = 0
x - -8 = 0
x - -5/3 = 0
x - 1/5 = 0
x = -8
x = -5/3
x = 1/5


Input: Compute the solution of x^2 - 83/24x - 91/24 = 0

Output:
x^2 - 83/24x - 91/24 = 0
(x - 13/3)(x - -7/8) = 0
x - 13/3 = 0  or  x - -7/8 = 0
x = 13/3
x = -7/8


Input: Find x for x^3 + 43/28x^2 - 53/28x - 9/14 = 0

Output:
x^3 + 43/28x^2 - 53/28x - 9/14 = 0
(x - 1)(x - -2/7)(x - -9/4) = 0
x - 1 = 0
x - -2/7 = 0
x - -9/4 = 0
x = 1
x = -2/7
x = -9/4


Input: What value of x satisfies 10x + 19 = 0

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


Input: What value of x satisfies x^3 + 2/3x^2 - 365/9x + 238/9 = 0

Output:
x^3 + 2/3x^2 - 365/9x + 238/9 = 0
(x - 2/3)(x - 17/3)(x - -7) = 0
x - 2/3 = 0
x - 17/3 = 0
x - -7 = 0
x = 2/3
x = 17/3
x = -7


Input: Solve quickly: 3x - 39/5 = 0

Output:
3x - 39/5 = 0
3x = 39/5
x = 39/5 / 3
x = 13/5


Input: What value of x satisfies x^2 - 60/7x - 100/7 = 0

Output:
x^2 - 60/7x - 100/7 = 0
(x - 10)(x - -10/7) = 0
x - 10 = 0  or  x - -10/7 = 0
x = 10
x = -10/7


Input: Solve the equation x^2 - 13/6x - 55/3 = 0

Output:
x^2 - 13/6x - 55/3 = 0
(x - 11/2)(x - -10/3) = 0
x - 11/2 = 0  or  x - -10/3 = 0
x = 11/2
x = -10/3


Input: Determine x in x^3 + 97/10x^2 + 7/10x - 57/5 = 0

Output:
x^3 + 97/10x^2 + 7/10x - 57/5 = 0
(x - -6/5)(x - 1)(x - -19/2) = 0
x - -6/5 = 0
x - 1 = 0
x - -19/2 = 0
x = -6/5
x = 1
x = -19/2


Input:
Find x and y such that
6x + 7y = -629/30
6x + 6y = -89/5

Output:
6x + 7y = -629/30
6x + 6y = -89/5

Using elimination
6*(6x + 7y = -629/30)
6*(6x + 6y = -89/5)
36x + 42y = -629/5
36x + 36y = -534/5
Subtract equations
6y = -19
y = -19/6
y = -19/6

Substitute y
6x + 7(-19/6) = -629/30
6x = 6/5
x = 6/5/6
x = 1/5


Input:
Solve the system:
2x + 6y = 63/5
5x + 5y = 31/2

Output:
2x + 6y = 63/5
5x + 5y = 31/2

Using elimination
5*(2x + 6y = 63/5)
2*(5x + 5y = 31/2)
10x + 30y = 63
10x + 10y = 31
Subtract equations
20y = 32
y = 32/20
y = 8/5

Substitute y
2x + 6(8/5) = 63/5
2x = 3
x = 3/2
x = 3/2


Input: Compute the solution of x^3 + 7/12x^2 - 473/24x + 30 = 0

Output:
x^3 + 7/12x^2 - 473/24x + 30 = 0
(x - 9/4)(x - -16/3)(x - 5/2) = 0
x - 9/4 = 0
x - -16/3 = 0
x - 5/2 = 0
x = 9/4
x = -16/3
x = 5/2


Input: Find x for 5x - 2 = 0

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


Input: Solve x^2 + 14x + 45 = 0

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


Input:
Solve simultaneously:
1x + 4y = 118/15
7x + 6y = 147/5

Output:
1x + 4y = 118/15
7x + 6y = 147/5

Using elimination
7*(1x + 4y = 118/15)
1*(7x + 6y = 147/5)
7x + 28y = 826/15
7x + 6y = 147/5
Subtract equations
22y = 77/3
y = 77/3/22
y = 7/6

Substitute y
1x + 4(7/6) = 118/15
1x = 16/5
x = 16/5/1
x = 16/5


Input: Solve x^2 - 9/2x + 81/16 = 0

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


Input: What value of x satisfies 10x - 85/3 = 0

Output:
10x - 85/3 = 0
10x = 85/3
x = 85/3 / 10
x = 17/6


Input: Solve the equation 4x - 3 = 0

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


Input: Find x in x^2 - 1/18x - 13/6 = 0

Output:
x^2 - 1/18x - 13/6 = 0
(x - 3/2)(x - -13/9) = 0
x - 3/2 = 0  or  x - -13/9 = 0
x = 3/2
x = -13/9


Input: Solve x^3 + 113/15x^2 + 116/15x - 44/5 = 0

Output:
x^3 + 113/15x^2 + 116/15x - 44/5 = 0
(x - -11/5)(x - 2/3)(x - -6) = 0
x - -11/5 = 0
x - 2/3 = 0
x - -6 = 0
x = -11/5
x = 2/3
x = -6


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

Output:
x^2 + 14/3x - 8 = 0
(x - 4/3)(x - -6) = 0
x - 4/3 = 0  or  x - -6 = 0
x = 4/3
x = -6


Input: Solve quickly: 3x + 12 = 0

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


Input: Determine x in x^3 - 113/105x^2 - 268/35x - 36/7 = 0

Output:
x^3 - 113/105x^2 - 268/35x - 36/7 = 0
(x - -6/7)(x - 18/5)(x - -5/3) = 0
x - -6/7 = 0
x - 18/5 = 0
x - -5/3 = 0
x = -6/7
x = 18/5
x = -5/3


Input: Find x for 9x - 81/2 = 0

Output:
9x - 81/2 = 0
9x = 81/2
x = 81/2 / 9
x = 9/2


Input: Compute the solution of x^3 + 27/8x^2 + 3/2x - 5/2 = 0

Output:
x^3 + 27/8x^2 + 3/2x - 5/2 = 0
(x - -2)(x - 5/8)(x - -2) = 0
x - -2 = 0
x - 5/8 = 0
x - -2 = 0
x = -2
x = 5/8
x = -2


Input: Solve x^3 + 73/4x^2 + 491/8x + 105/4 = 0

Output:
x^3 + 73/4x^2 + 491/8x + 105/4 = 0
(x - -14)(x - -15/4)(x - -1/2) = 0
x - -14 = 0
x - -15/4 = 0
x - -1/2 = 0
x = -14
x = -15/4
x = -1/2


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

Output:
x^2 + 17/6x - 5/3 = 0
(x - -10/3)(x - 1/2) = 0
x - -10/3 = 0  or  x - 1/2 = 0
x = -10/3
x = 1/2