Input:
Solve the equations:
5x + 6y = 49/4
3x + 9y = 87/4

Output:
5x + 6y = 49/4
3x + 9y = 87/4

Using elimination
3*(5x + 6y = 49/4)
5*(3x + 9y = 87/4)
15x + 18y = 147/4
15x + 45y = 435/4
Subtract equations
-27y = -72
y = -72/-27
y = 8/3

Substitute y
5x + 6(8/3) = 49/4
5x = -15/4
x = -15/4/5
x = -3/4


Input: Solve x^3 - 7/4x^2 - 17/16x - 9/64 = 0

Output:
x^3 - 7/4x^2 - 17/16x - 9/64 = 0
(x - 9/4)(x - -1/4)(x - -1/4) = 0
x - 9/4 = 0
x - -1/4 = 0
x - -1/4 = 0
x = 9/4
x = -1/4
x = -1/4


Input: Solve the equation 9x - 19 = 0

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


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

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


Input: Compute the solution of x^3 + 197/168x^2 - 1/4x - 1/21 = 0

Output:
x^3 + 197/168x^2 - 1/4x - 1/21 = 0
(x - -1/8)(x - -4/3)(x - 2/7) = 0
x - -1/8 = 0
x - -4/3 = 0
x - 2/7 = 0
x = -1/8
x = -4/3
x = 2/7


Input:
Solve the system:
4x + 5y = -2/5
1x + 10y = -141/10

Output:
4x + 5y = -2/5
1x + 10y = -141/10

Using elimination
1*(4x + 5y = -2/5)
4*(1x + 10y = -141/10)
4x + 5y = -2/5
4x + 40y = -282/5
Subtract equations
-35y = 56
y = 56/-35
y = -8/5

Substitute y
4x + 5(-8/5) = -2/5
4x = 38/5
x = 38/5/4
x = 19/10


Input:
Solve the equations:
7x + 3y = 16/5
1x + 9y = 88/5

Output:
7x + 3y = 16/5
1x + 9y = 88/5

Using elimination
1*(7x + 3y = 16/5)
7*(1x + 9y = 88/5)
7x + 3y = 16/5
7x + 63y = 616/5
Subtract equations
-60y = -120
y = -120/-60
y = 2

Substitute y
7x + 3(2) = 16/5
7x = -14/5
x = -14/5/7
x = -2/5


Input:
Find x and y such that
7x + 3y = -1
9x + 5y = -25/7

Output:
7x + 3y = -1
9x + 5y = -25/7

Using elimination
9*(7x + 3y = -1)
7*(9x + 5y = -25/7)
63x + 27y = -9
63x + 35y = -25
Subtract equations
-8y = 16
y = 16/-8
y = -2

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


Input:
Solve simultaneously:
9x + 2y = -194/5
2x + 1y = -47/5

Output:
9x + 2y = -194/5
2x + 1y = -47/5

Using elimination
2*(9x + 2y = -194/5)
9*(2x + 1y = -47/5)
18x + 4y = -388/5
18x + 9y = -423/5
Subtract equations
-5y = 7
y = 7/-5
y = -7/5

Substitute y
9x + 2(-7/5) = -194/5
9x = -36
x = -36/9
x = -4


Input: Find x for 6x - 54/5 = 0

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


Input: Compute the solution of x^3 + 1/8x^2 - 1/4x - 1/32 = 0

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


Input: Find x for x^3 - 62/7x^2 + 47/7x + 8/7 = 0

Output:
x^3 - 62/7x^2 + 47/7x + 8/7 = 0
(x - -1/7)(x - 1)(x - 8) = 0
x - -1/7 = 0
x - 1 = 0
x - 8 = 0
x = -1/7
x = 1
x = 8


Input: Determine x in x^3 + 1487/180x^2 + 67/3x + 3553/180 = 0

Output:
x^3 + 1487/180x^2 + 67/3x + 3553/180 = 0
(x - -17/5)(x - -11/4)(x - -19/9) = 0
x - -17/5 = 0
x - -11/4 = 0
x - -19/9 = 0
x = -17/5
x = -11/4
x = -19/9


Input: Compute the solution of 3x - 9/5 = 0

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


Input: What value of x satisfies x^3 - 117/8x^2 - 653/8x - 57/2 = 0

Output:
x^3 - 117/8x^2 - 653/8x - 57/2 = 0
(x - -3/8)(x - 19)(x - -4) = 0
x - -3/8 = 0
x - 19 = 0
x - -4 = 0
x = -3/8
x = 19
x = -4


Input: Find x for x^3 - 144/35x^2 - 149/35x - 6/7 = 0

Output:
x^3 - 144/35x^2 - 149/35x - 6/7 = 0
(x - -2/7)(x - 5)(x - -3/5) = 0
x - -2/7 = 0
x - 5 = 0
x - -3/5 = 0
x = -2/7
x = 5
x = -3/5


Input: Find x for x^3 - 1853/315x^2 + 1199/105x - 2299/315 = 0

Output:
x^3 - 1853/315x^2 + 1199/105x - 2299/315 = 0
(x - 19/9)(x - 11/7)(x - 11/5) = 0
x - 19/9 = 0
x - 11/7 = 0
x - 11/5 = 0
x = 19/9
x = 11/7
x = 11/5


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: Compute the solution of x^3 - 197/180x^2 - 5/12x + 5/18 = 0

Output:
x^3 - 197/180x^2 - 5/12x + 5/18 = 0
(x - -5/9)(x - 5/4)(x - 2/5) = 0
x - -5/9 = 0
x - 5/4 = 0
x - 2/5 = 0
x = -5/9
x = 5/4
x = 2/5


Input: Find x for x^2 + 9/2x + 45/16 = 0

Output:
x^2 + 9/2x + 45/16 = 0
(x - -15/4)(x - -3/4) = 0
x - -15/4 = 0  or  x - -3/4 = 0
x = -15/4
x = -3/4


Input: What value of x satisfies 9x - 27/4 = 0

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


Input: Solve the equation x^3 - 23/3x^2 + 22/3x + 16 = 0

Output:
x^3 - 23/3x^2 + 22/3x + 16 = 0
(x - 6)(x - -1)(x - 8/3) = 0
x - 6 = 0
x - -1 = 0
x - 8/3 = 0
x = 6
x = -1
x = 8/3


Input: What value of x satisfies x^2 - 34/9x + 280/81 = 0

Output:
x^2 - 34/9x + 280/81 = 0
(x - 20/9)(x - 14/9) = 0
x - 20/9 = 0  or  x - 14/9 = 0
x = 20/9
x = 14/9


Input: What value of x satisfies x^3 - 29/5x^2 - 86/5x - 16/5 = 0

Output:
x^3 - 29/5x^2 - 86/5x - 16/5 = 0
(x - -2)(x - 8)(x - -1/5) = 0
x - -2 = 0
x - 8 = 0
x - -1/5 = 0
x = -2
x = 8
x = -1/5


Input: Find x in x^3 + 859/90x^2 + 89/18x + 2/5 = 0

Output:
x^3 + 859/90x^2 + 89/18x + 2/5 = 0
(x - -9)(x - -4/9)(x - -1/10) = 0
x - -9 = 0
x - -4/9 = 0
x - -1/10 = 0
x = -9
x = -4/9
x = -1/10


Input: Find the solution to x^2 + 57/8x + 7/8 = 0

Output:
x^2 + 57/8x + 7/8 = 0
(x - -1/8)(x - -7) = 0
x - -1/8 = 0  or  x - -7 = 0
x = -1/8
x = -7


Input: Find x for 9x + 18 = 0

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


Input: Solve quickly: x^2 - 23x + 90 = 0

Output:
x^2 - 23x + 90 = 0
(x - 18)(x - 5) = 0
x - 18 = 0  or  x - 5 = 0
x = 18
x = 5


Input: Find the solution to x^3 - 91/5x^2 - 36x  = 0

Output:
x^3 - 91/5x^2 - 36x  = 0
(x - 0)(x - -9/5)(x - 20) = 0
x - 0 = 0
x - -9/5 = 0
x - 20 = 0
x = 0
x = -9/5
x = 20


Input: Solve quickly: x^3 - 403/84x^2 + 160/21x - 4 = 0

Output:
x^3 - 403/84x^2 + 160/21x - 4 = 0
(x - 12/7)(x - 4/3)(x - 7/4) = 0
x - 12/7 = 0
x - 4/3 = 0
x - 7/4 = 0
x = 12/7
x = 4/3
x = 7/4


Input:
Solve the system:
8x + 5y = -183/10
5x + 7y = -157/10

Output:
8x + 5y = -183/10
5x + 7y = -157/10

Using elimination
5*(8x + 5y = -183/10)
8*(5x + 7y = -157/10)
40x + 25y = -183/2
40x + 56y = -628/5
Subtract equations
-31y = 341/10
y = 341/10/-31
y = -11/10

Substitute y
8x + 5(-11/10) = -183/10
8x = -64/5
x = -64/5/8
x = -8/5


Input:
Solve the equations:
3x + 9y = 3/28
9x + 1y = 1153/28

Output:
3x + 9y = 3/28
9x + 1y = 1153/28

Using elimination
9*(3x + 9y = 3/28)
3*(9x + 1y = 1153/28)
27x + 81y = 27/28
27x + 3y = 3459/28
Subtract equations
78y = -858/7
y = -858/7/78
y = -11/7

Substitute y
3x + 9(-11/7) = 3/28
3x = 57/4
x = 57/4/3
x = 19/4


Input: Find x for x^2 + 97/45x - 26/5 = 0

Output:
x^2 + 97/45x - 26/5 = 0
(x - 13/9)(x - -18/5) = 0
x - 13/9 = 0  or  x - -18/5 = 0
x = 13/9
x = -18/5


Input:
Solve the system:
6x + 1y = 190/3
3x + 8y = 170/3

Output:
6x + 1y = 190/3
3x + 8y = 170/3

Using elimination
3*(6x + 1y = 190/3)
6*(3x + 8y = 170/3)
18x + 3y = 190
18x + 48y = 340
Subtract equations
-45y = -150
y = -150/-45
y = 10/3

Substitute y
6x + 1(10/3) = 190/3
6x = 60
x = 60/6
x = 10


Input: Solve quickly: 8x + 24 = 0

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


Input: Solve x^2 - 39/20x - 11/5 = 0

Output:
x^2 - 39/20x - 11/5 = 0
(x - -4/5)(x - 11/4) = 0
x - -4/5 = 0  or  x - 11/4 = 0
x = -4/5
x = 11/4


Input: Find x for x^2 - 21x + 80 = 0

Output:
x^2 - 21x + 80 = 0
(x - 5)(x - 16) = 0
x - 5 = 0  or  x - 16 = 0
x = 5
x = 16


Input: Solve quickly: x^2 - 1/14x - 45/7 = 0

Output:
x^2 - 1/14x - 45/7 = 0
(x - 18/7)(x - -5/2) = 0
x - 18/7 = 0  or  x - -5/2 = 0
x = 18/7
x = -5/2


Input: Find x for 7x + 21/4 = 0

Output:
7x + 21/4 = 0
7x = -21/4
x = -21/4 / 7
x = -3/4


Input: Determine x in x^3 - 11/90x^2 - 998/135x - 221/270 = 0

Output:
x^3 - 11/90x^2 - 998/135x - 221/270 = 0
(x - 17/6)(x - -1/9)(x - -13/5) = 0
x - 17/6 = 0
x - -1/9 = 0
x - -13/5 = 0
x = 17/6
x = -1/9
x = -13/5


Input: Solve x^2 - 25/14x - 25/14 = 0

Output:
x^2 - 25/14x - 25/14 = 0
(x - 5/2)(x - -5/7) = 0
x - 5/2 = 0  or  x - -5/7 = 0
x = 5/2
x = -5/7


Input: Solve x^2 - 13/6x - 119/6 = 0

Output:
x^2 - 13/6x - 119/6 = 0
(x - 17/3)(x - -7/2) = 0
x - 17/3 = 0  or  x - -7/2 = 0
x = 17/3
x = -7/2


Input: Find x for x^2 - 1x - 8/49 = 0

Output:
x^2 - 1x - 8/49 = 0
(x - -1/7)(x - 8/7) = 0
x - -1/7 = 0  or  x - 8/7 = 0
x = -1/7
x = 8/7


Input: Find the solution to 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: Solve the equation x^3 - 25/2x^2 + 374/9x - 160/9 = 0

Output:
x^3 - 25/2x^2 + 374/9x - 160/9 = 0
(x - 16/3)(x - 20/3)(x - 1/2) = 0
x - 16/3 = 0
x - 20/3 = 0
x - 1/2 = 0
x = 16/3
x = 20/3
x = 1/2


Input: Solve the equation x^2 - 27/4x + 9/2 = 0

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


Input: Determine x in x^3 + 86/15x^2 - 11/15x - 442/15 = 0

Output:
x^3 + 86/15x^2 - 11/15x - 442/15 = 0
(x - -17/5)(x - -13/3)(x - 2) = 0
x - -17/5 = 0
x - -13/3 = 0
x - 2 = 0
x = -17/5
x = -13/3
x = 2


Input:
Find x and y such that
6x + 1y = -68/5
2x + 5y = -116/5

Output:
6x + 1y = -68/5
2x + 5y = -116/5

Using elimination
2*(6x + 1y = -68/5)
6*(2x + 5y = -116/5)
12x + 2y = -136/5
12x + 30y = -696/5
Subtract equations
-28y = 112
y = 112/-28
y = -4

Substitute y
6x + 1(-4) = -68/5
6x = -48/5
x = -48/5/6
x = -8/5


Input: Determine x in x^3 + 1754/315x^2 + 1027/105x + 338/63 = 0

Output:
x^3 + 1754/315x^2 + 1027/105x + 338/63 = 0
(x - -13/5)(x - -13/7)(x - -10/9) = 0
x - -13/5 = 0
x - -13/7 = 0
x - -10/9 = 0
x = -13/5
x = -13/7
x = -10/9


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

Output:
2x - 38/7 = 0
2x = 38/7
x = 38/7 / 2
x = 19/7


Input:
Find x and y such that
8x + 4y = -44/3
5x + 3y = -28/3

Output:
8x + 4y = -44/3
5x + 3y = -28/3

Using elimination
5*(8x + 4y = -44/3)
8*(5x + 3y = -28/3)
40x + 20y = -220/3
40x + 24y = -224/3
Subtract equations
-4y = 4/3
y = 4/3/-4
y = -1/3

Substitute y
8x + 4(-1/3) = -44/3
8x = -40/3
x = -40/3/8
x = -5/3


Input: Find x in x^3 + 1/60x^2 - 659/120x + 21/5 = 0

Output:
x^3 + 1/60x^2 - 659/120x + 21/5 = 0
(x - 9/10)(x - 7/4)(x - -8/3) = 0
x - 9/10 = 0
x - 7/4 = 0
x - -8/3 = 0
x = 9/10
x = 7/4
x = -8/3


Input:
Solve the equations:
9x + 9y = 67/2
2x + 9y = 323/18

Output:
9x + 9y = 67/2
2x + 9y = 323/18

Using elimination
2*(9x + 9y = 67/2)
9*(2x + 9y = 323/18)
18x + 18y = 67
18x + 81y = 323/2
Subtract equations
-63y = -189/2
y = -189/2/-63
y = 3/2

Substitute y
9x + 9(3/2) = 67/2
9x = 20
x = 20/9
x = 20/9


Input:
Find x and y such that
6x + 6y = 177/4
6x + 3y = 81/4

Output:
6x + 6y = 177/4
6x + 3y = 81/4

Using elimination
6*(6x + 6y = 177/4)
6*(6x + 3y = 81/4)
36x + 36y = 531/2
36x + 18y = 243/2
Subtract equations
18y = 144
y = 144/18
y = 8

Substitute y
6x + 6(8) = 177/4
6x = -15/4
x = -15/4/6
x = -5/8


Input:
Solve simultaneously:
5x + 6y = -296/15
1x + 9y = -563/30

Output:
5x + 6y = -296/15
1x + 9y = -563/30

Using elimination
1*(5x + 6y = -296/15)
5*(1x + 9y = -563/30)
5x + 6y = -296/15
5x + 45y = -563/6
Subtract equations
-39y = 741/10
y = 741/10/-39
y = -19/10

Substitute y
5x + 6(-19/10) = -296/15
5x = -25/3
x = -25/3/5
x = -5/3


Input: Solve 4x + 8 = 0

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


Input: Compute the solution of 10x + 26 = 0

Output:
10x + 26 = 0
10x = -26
x = -26 / 10
x = -13/5


Input:
Solve the system:
9x + 4y = 148/5
2x + 4y = 64/5

Output:
9x + 4y = 148/5
2x + 4y = 64/5

Using elimination
2*(9x + 4y = 148/5)
9*(2x + 4y = 64/5)
18x + 8y = 296/5
18x + 36y = 576/5
Subtract equations
-28y = -56
y = -56/-28
y = 2

Substitute y
9x + 4(2) = 148/5
9x = 108/5
x = 108/5/9
x = 12/5


Input: Solve x^3 + 41/4x^2 + 117/4x + 45/2 = 0

Output:
x^3 + 41/4x^2 + 117/4x + 45/2 = 0
(x - -3)(x - -6)(x - -5/4) = 0
x - -3 = 0
x - -6 = 0
x - -5/4 = 0
x = -3
x = -6
x = -5/4


Input: Find x in 10x - 40 = 0

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


Input: What value of x satisfies 8x - 20 = 0

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


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

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


Input: Compute the solution of x^2 + 5/7x - 104/49 = 0

Output:
x^2 + 5/7x - 104/49 = 0
(x - 8/7)(x - -13/7) = 0
x - 8/7 = 0  or  x - -13/7 = 0
x = 8/7
x = -13/7


Input: Solve x^2 - 33/8x + 65/16 = 0

Output:
x^2 - 33/8x + 65/16 = 0
(x - 13/8)(x - 5/2) = 0
x - 13/8 = 0  or  x - 5/2 = 0
x = 13/8
x = 5/2


Input: Solve quickly: x^2 - 22/15x - 133/15 = 0

Output:
x^2 - 22/15x - 133/15 = 0
(x - -7/3)(x - 19/5) = 0
x - -7/3 = 0  or  x - 19/5 = 0
x = -7/3
x = 19/5


Input:
Solve simultaneously:
8x + 7y = 819/10
9x + 10y = 551/5

Output:
8x + 7y = 819/10
9x + 10y = 551/5

Using elimination
9*(8x + 7y = 819/10)
8*(9x + 10y = 551/5)
72x + 63y = 7371/10
72x + 80y = 4408/5
Subtract equations
-17y = -289/2
y = -289/2/-17
y = 17/2

Substitute y
8x + 7(17/2) = 819/10
8x = 112/5
x = 112/5/8
x = 14/5


Input: Solve the equation x^3 - 36/7x^2 + 53/7x - 24/7 = 0

Output:
x^3 - 36/7x^2 + 53/7x - 24/7 = 0
(x - 8/7)(x - 3)(x - 1) = 0
x - 8/7 = 0
x - 3 = 0
x - 1 = 0
x = 8/7
x = 3
x = 1


Input: Find x in x^2 - 44/9x + 17/3 = 0

Output:
x^2 - 44/9x + 17/3 = 0
(x - 17/9)(x - 3) = 0
x - 17/9 = 0  or  x - 3 = 0
x = 17/9
x = 3


Input: Solve 8x - 104/9 = 0

Output:
8x - 104/9 = 0
8x = 104/9
x = 104/9 / 8
x = 13/9


Input: Find x for x^3 - 26/15x^2 - 49/15x + 4 = 0

Output:
x^3 - 26/15x^2 - 49/15x + 4 = 0
(x - 12/5)(x - -5/3)(x - 1) = 0
x - 12/5 = 0
x - -5/3 = 0
x - 1 = 0
x = 12/5
x = -5/3
x = 1


Input:
Find x and y such that
3x + 6y = -12
10x + 10y = 20

Output:
3x + 6y = -12
10x + 10y = 20

Using elimination
10*(3x + 6y = -12)
3*(10x + 10y = 20)
30x + 60y = -120
30x + 30y = 60
Subtract equations
30y = -180
y = -180/30
y = -6

Substitute y
3x + 6(-6) = -12
3x = 24
x = 24/3
x = 8


Input:
Solve simultaneously:
6x + 5y = 65/14
8x + 9y = 5/14

Output:
6x + 5y = 65/14
8x + 9y = 5/14

Using elimination
8*(6x + 5y = 65/14)
6*(8x + 9y = 5/14)
48x + 40y = 260/7
48x + 54y = 15/7
Subtract equations
-14y = 35
y = 35/-14
y = -5/2

Substitute y
6x + 5(-5/2) = 65/14
6x = 120/7
x = 120/7/6
x = 20/7


Input:
Solve simultaneously:
5x + 5y = 145/12
3x + 8y = 367/12

Output:
5x + 5y = 145/12
3x + 8y = 367/12

Using elimination
3*(5x + 5y = 145/12)
5*(3x + 8y = 367/12)
15x + 15y = 145/4
15x + 40y = 1835/12
Subtract equations
-25y = -350/3
y = -350/3/-25
y = 14/3

Substitute y
5x + 5(14/3) = 145/12
5x = -45/4
x = -45/4/5
x = -9/4


Input: What value of x satisfies x^3 + 31/2x^2  - 225/2 = 0

Output:
x^3 + 31/2x^2  - 225/2 = 0
(x - -3)(x - 5/2)(x - -15) = 0
x - -3 = 0
x - 5/2 = 0
x - -15 = 0
x = -3
x = 5/2
x = -15


Input:
Find x and y such that
1x + 6y = 17/5
10x + 3y = -65/2

Output:
1x + 6y = 17/5
10x + 3y = -65/2

Using elimination
10*(1x + 6y = 17/5)
1*(10x + 3y = -65/2)
10x + 60y = 34
10x + 3y = -65/2
Subtract equations
57y = 133/2
y = 133/2/57
y = 7/6

Substitute y
1x + 6(7/6) = 17/5
1x = -18/5
x = -18/5/1
x = -18/5


Input:
Solve the system:
2x + 4y = 57/2
8x + 1y = 777/8

Output:
2x + 4y = 57/2
8x + 1y = 777/8

Using elimination
8*(2x + 4y = 57/2)
2*(8x + 1y = 777/8)
16x + 32y = 228
16x + 2y = 777/4
Subtract equations
30y = 135/4
y = 135/4/30
y = 9/8

Substitute y
2x + 4(9/8) = 57/2
2x = 24
x = 24/2
x = 12


Input:
Solve the system:
7x + 8y = -73/2
1x + 5y = 5/2

Output:
7x + 8y = -73/2
1x + 5y = 5/2

Using elimination
1*(7x + 8y = -73/2)
7*(1x + 5y = 5/2)
7x + 8y = -73/2
7x + 35y = 35/2
Subtract equations
-27y = -54
y = -54/-27
y = 2

Substitute y
7x + 8(2) = -73/2
7x = -105/2
x = -105/2/7
x = -15/2


Input:
Solve the system:
3x + 8y = -259/10
3x + 10y = -67/2

Output:
3x + 8y = -259/10
3x + 10y = -67/2

Using elimination
3*(3x + 8y = -259/10)
3*(3x + 10y = -67/2)
9x + 24y = -777/10
9x + 30y = -201/2
Subtract equations
-6y = 114/5
y = 114/5/-6
y = -19/5

Substitute y
3x + 8(-19/5) = -259/10
3x = 9/2
x = 9/2/3
x = 3/2


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

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


Input: Solve quickly: x^2 + 29/42x - 130/21 = 0

Output:
x^2 + 29/42x - 130/21 = 0
(x - 13/6)(x - -20/7) = 0
x - 13/6 = 0  or  x - -20/7 = 0
x = 13/6
x = -20/7


Input: Solve quickly: x^3 + 10x^2 - 619/4x + 1235/4 = 0

Output:
x^3 + 10x^2 - 619/4x + 1235/4 = 0
(x - 5/2)(x - -19)(x - 13/2) = 0
x - 5/2 = 0
x - -19 = 0
x - 13/2 = 0
x = 5/2
x = -19
x = 13/2


Input: What value of x satisfies 2x + 13 = 0

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


Input: Solve 3x + 57/8 = 0

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


Input: Find x for x^2 - 97/6x + 8/3 = 0

Output:
x^2 - 97/6x + 8/3 = 0
(x - 1/6)(x - 16) = 0
x - 1/6 = 0  or  x - 16 = 0
x = 1/6
x = 16


Input: Find the solution to x^2 + 13/9x - 10/9 = 0

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


Input: Solve the equation 3x + 14 = 0

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


Input:
Solve the equations:
5x + 10y = -55
7x + 5y = -127/2

Output:
5x + 10y = -55
7x + 5y = -127/2

Using elimination
7*(5x + 10y = -55)
5*(7x + 5y = -127/2)
35x + 70y = -385
35x + 25y = -635/2
Subtract equations
45y = -135/2
y = -135/2/45
y = -3/2

Substitute y
5x + 10(-3/2) = -55
5x = -40
x = -40/5
x = -8


Input: Solve quickly: x^2 + 5/9x - 50/27 = 0

Output:
x^2 + 5/9x - 50/27 = 0
(x - 10/9)(x - -5/3) = 0
x - 10/9 = 0  or  x - -5/3 = 0
x = 10/9
x = -5/3


Input: Determine x in x^3 - 123/28x^2 + 729/196x + 243/98 = 0

Output:
x^3 - 123/28x^2 + 729/196x + 243/98 = 0
(x - 18/7)(x - -3/7)(x - 9/4) = 0
x - 18/7 = 0
x - -3/7 = 0
x - 9/4 = 0
x = 18/7
x = -3/7
x = 9/4


Input:
Find x and y such that
6x + 10y = 0
5x + 8y = 1

Output:
6x + 10y = 0
5x + 8y = 1

Using elimination
5*(6x + 10y = 0)
6*(5x + 8y = 1)
30x + 50y = 0
30x + 48y = 6
Subtract equations
2y = -6
y = -6/2
y = -3

Substitute y
6x + 10(-3) = 0
6x = 30
x = 30/6
x = 5


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

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


Input: What value of x satisfies x^2 + 98/15x + 19/15 = 0

Output:
x^2 + 98/15x + 19/15 = 0
(x - -19/3)(x - -1/5) = 0
x - -19/3 = 0  or  x - -1/5 = 0
x = -19/3
x = -1/5


Input: Solve the equation x^3 - 131/60x^2 - 157/20x - 119/30 = 0

Output:
x^3 - 131/60x^2 - 157/20x - 119/30 = 0
(x - 17/4)(x - -7/5)(x - -2/3) = 0
x - 17/4 = 0
x - -7/5 = 0
x - -2/3 = 0
x = 17/4
x = -7/5
x = -2/3


Input: Solve quickly: 8x - 20 = 0

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


Input:
Solve the equations:
1x + 9y = -137/6
8x + 4y = -38/3

Output:
1x + 9y = -137/6
8x + 4y = -38/3

Using elimination
8*(1x + 9y = -137/6)
1*(8x + 4y = -38/3)
8x + 72y = -548/3
8x + 4y = -38/3
Subtract equations
68y = -170
y = -170/68
y = -5/2

Substitute y
1x + 9(-5/2) = -137/6
1x = -1/3
x = -1/3/1
x = -1/3


Input: Solve 3x + 36/7 = 0

Output:
3x + 36/7 = 0
3x = -36/7
x = -36/7 / 3
x = -12/7


Input: Find the solution to 7x + 70/9 = 0

Output:
7x + 70/9 = 0
7x = -70/9
x = -70/9 / 7
x = -10/9


Input: What value of x satisfies 5x - 45/8 = 0

Output:
5x - 45/8 = 0
5x = 45/8
x = 45/8 / 5
x = 9/8


Input: Compute the solution of x^3 + 169/24x^2 + 203/16x + 45/8 = 0

Output:
x^3 + 169/24x^2 + 203/16x + 45/8 = 0
(x - -2/3)(x - -15/8)(x - -9/2) = 0
x - -2/3 = 0
x - -15/8 = 0
x - -9/2 = 0
x = -2/3
x = -15/8
x = -9/2


Input:
Find x and y such that
6x + 5y = -38/5
3x + 2y = -14/5

Output:
6x + 5y = -38/5
3x + 2y = -14/5

Using elimination
3*(6x + 5y = -38/5)
6*(3x + 2y = -14/5)
18x + 15y = -114/5
18x + 12y = -84/5
Subtract equations
3y = -6
y = -6/3
y = -2

Substitute y
6x + 5(-2) = -38/5
6x = 12/5
x = 12/5/6
x = 2/5


Input: Solve the equation 5x - 55/8 = 0

Output:
5x - 55/8 = 0
5x = 55/8
x = 55/8 / 5
x = 11/8


Input: Find x for x^2 + 11/14x - 15/14 = 0

Output:
x^2 + 11/14x - 15/14 = 0
(x - 5/7)(x - -3/2) = 0
x - 5/7 = 0  or  x - -3/2 = 0
x = 5/7
x = -3/2


Input: Find the solution to x^3 + 172/105x^2 - 44/15x - 48/35 = 0

Output:
x^3 + 172/105x^2 - 44/15x - 48/35 = 0
(x - -2/5)(x - 4/3)(x - -18/7) = 0
x - -2/5 = 0
x - 4/3 = 0
x - -18/7 = 0
x = -2/5
x = 4/3
x = -18/7


Input: Find x in x^3 - 267/40x^2 + 491/40x - 63/10 = 0

Output:
x^3 - 267/40x^2 + 491/40x - 63/10 = 0
(x - 7/8)(x - 4)(x - 9/5) = 0
x - 7/8 = 0
x - 4 = 0
x - 9/5 = 0
x = 7/8
x = 4
x = 9/5


Input: Find x for x^3 - 61/84x^2 - 261/56x + 195/56 = 0

Output:
x^3 - 61/84x^2 - 261/56x + 195/56 = 0
(x - 15/7)(x - 3/4)(x - -13/6) = 0
x - 15/7 = 0
x - 3/4 = 0
x - -13/6 = 0
x = 15/7
x = 3/4
x = -13/6


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

Output:
x^2 - 11/2x - 3 = 0
(x - 6)(x - -1/2) = 0
x - 6 = 0  or  x - -1/2 = 0
x = 6
x = -1/2


Input: Solve the equation x^3 + 791/180x^2 + 2009/360x + 17/10 = 0

Output:
x^3 + 791/180x^2 + 2009/360x + 17/10 = 0
(x - -17/10)(x - -4/9)(x - -9/4) = 0
x - -17/10 = 0
x - -4/9 = 0
x - -9/4 = 0
x = -17/10
x = -4/9
x = -9/4


Input: Compute the solution of x^3 - 1/40x^2 - 1381/160x - 1547/160 = 0

Output:
x^3 - 1/40x^2 - 1381/160x - 1547/160 = 0
(x - -7/4)(x - 17/5)(x - -13/8) = 0
x - -7/4 = 0
x - 17/5 = 0
x - -13/8 = 0
x = -7/4
x = 17/5
x = -13/8


Input: Solve 5x - 10 = 0

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


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

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


Input: Determine x in x^2 - 74/15x + 91/15 = 0

Output:
x^2 - 74/15x + 91/15 = 0
(x - 13/5)(x - 7/3) = 0
x - 13/5 = 0  or  x - 7/3 = 0
x = 13/5
x = 7/3


Input: Find x in x^3 - 29/14x^2 - 2x + 30/7 = 0

Output:
x^3 - 29/14x^2 - 2x + 30/7 = 0
(x - -10/7)(x - 3/2)(x - 2) = 0
x - -10/7 = 0
x - 3/2 = 0
x - 2 = 0
x = -10/7
x = 3/2
x = 2


Input: Determine x in x^2 - 121/10x + 6/5 = 0

Output:
x^2 - 121/10x + 6/5 = 0
(x - 1/10)(x - 12) = 0
x - 1/10 = 0  or  x - 12 = 0
x = 1/10
x = 12


Input:
Solve the equations:
3x + 6y = 197/6
9x + 9y = 157/2

Output:
3x + 6y = 197/6
9x + 9y = 157/2

Using elimination
9*(3x + 6y = 197/6)
3*(9x + 9y = 157/2)
27x + 54y = 591/2
27x + 27y = 471/2
Subtract equations
27y = 60
y = 60/27
y = 20/9

Substitute y
3x + 6(20/9) = 197/6
3x = 39/2
x = 39/2/3
x = 13/2


Input: Solve quickly: 3x + 6 = 0

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


Input: Solve the equation x^2 + 7/2x - 39/2 = 0

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


Input:
Solve simultaneously:
2x + 3y = -9/10
8x + 5y = -71/10

Output:
2x + 3y = -9/10
8x + 5y = -71/10

Using elimination
8*(2x + 3y = -9/10)
2*(8x + 5y = -71/10)
16x + 24y = -36/5
16x + 10y = -71/5
Subtract equations
14y = 7
y = 7/14
y = 1/2

Substitute y
2x + 3(1/2) = -9/10
2x = -12/5
x = -12/5/2
x = -6/5


Input:
Solve the equations:
5x + 4y = 532/9
7x + 10y = 736/9

Output:
5x + 4y = 532/9
7x + 10y = 736/9

Using elimination
7*(5x + 4y = 532/9)
5*(7x + 10y = 736/9)
35x + 28y = 3724/9
35x + 50y = 3680/9
Subtract equations
-22y = 44/9
y = 44/9/-22
y = -2/9

Substitute y
5x + 4(-2/9) = 532/9
5x = 60
x = 60/5
x = 12


Input: Solve the equation x^2 - 26x + 144 = 0

Output:
x^2 - 26x + 144 = 0
(x - 8)(x - 18) = 0
x - 8 = 0  or  x - 18 = 0
x = 8
x = 18


Input: What value of x satisfies x^3 + 71/4x^2 + 549/8x - 495/8 = 0

Output:
x^3 + 71/4x^2 + 549/8x - 495/8 = 0
(x - -15/2)(x - -11)(x - 3/4) = 0
x - -15/2 = 0
x - -11 = 0
x - 3/4 = 0
x = -15/2
x = -11
x = 3/4


Input: Find x for 4x + 2 = 0

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


Input: Solve 6x - 21/2 = 0

Output:
6x - 21/2 = 0
6x = 21/2
x = 21/2 / 6
x = 7/4


Input: Solve quickly: 8x + 56/5 = 0

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


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

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


Input: Compute the solution of x^2 + 2/5x - 7/5 = 0

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


Input: Find x in x^2 + 13/4x - 45/8 = 0

Output:
x^2 + 13/4x - 45/8 = 0
(x - 5/4)(x - -9/2) = 0
x - 5/4 = 0  or  x - -9/2 = 0
x = 5/4
x = -9/2


Input:
Find x and y such that
5x + 2y = 10
1x + 1y = 2

Output:
5x + 2y = 10
1x + 1y = 2

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

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


Input: Solve the equation x^3 + 223/20x^2 + 133/4x + 147/5 = 0

Output:
x^3 + 223/20x^2 + 133/4x + 147/5 = 0
(x - -12/5)(x - -7)(x - -7/4) = 0
x - -12/5 = 0
x - -7 = 0
x - -7/4 = 0
x = -12/5
x = -7
x = -7/4


Input: Compute the solution of x^3 - 297/28x^2 - 1317/28x - 13/2 = 0

Output:
x^3 - 297/28x^2 - 1317/28x - 13/2 = 0
(x - -13/4)(x - -1/7)(x - 14) = 0
x - -13/4 = 0
x - -1/7 = 0
x - 14 = 0
x = -13/4
x = -1/7
x = 14


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

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


Input: Solve x^2 + 8/9x - 17/9 = 0

Output:
x^2 + 8/9x - 17/9 = 0
(x - 1)(x - -17/9) = 0
x - 1 = 0  or  x - -17/9 = 0
x = 1
x = -17/9


Input: Solve 2x - 12 = 0

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


Input: What value of x satisfies x^2 + 23/12x - 95/3 = 0

Output:
x^2 + 23/12x - 95/3 = 0
(x - 19/4)(x - -20/3) = 0
x - 19/4 = 0  or  x - -20/3 = 0
x = 19/4
x = -20/3


Input:
Solve the equations:
3x + 10y = 49
5x + 10y = 175/3

Output:
3x + 10y = 49
5x + 10y = 175/3

Using elimination
5*(3x + 10y = 49)
3*(5x + 10y = 175/3)
15x + 50y = 245
15x + 30y = 175
Subtract equations
20y = 70
y = 70/20
y = 7/2

Substitute y
3x + 10(7/2) = 49
3x = 14
x = 14/3
x = 14/3


Input: Solve x^3 - 13/6x^2 - 25/6x + 25/3 = 0

Output:
x^3 - 13/6x^2 - 25/6x + 25/3 = 0
(x - -2)(x - 5/3)(x - 5/2) = 0
x - -2 = 0
x - 5/3 = 0
x - 5/2 = 0
x = -2
x = 5/3
x = 5/2


Input:
Solve the system:
10x + 3y = -199/6
7x + 5y = -61/6

Output:
10x + 3y = -199/6
7x + 5y = -61/6

Using elimination
7*(10x + 3y = -199/6)
10*(7x + 5y = -61/6)
70x + 21y = -1393/6
70x + 50y = -305/3
Subtract equations
-29y = -261/2
y = -261/2/-29
y = 9/2

Substitute y
10x + 3(9/2) = -199/6
10x = -140/3
x = -140/3/10
x = -14/3


Input:
Find x and y such that
3x + 3y = -10
5x + 6y = -37/2

Output:
3x + 3y = -10
5x + 6y = -37/2

Using elimination
5*(3x + 3y = -10)
3*(5x + 6y = -37/2)
15x + 15y = -50
15x + 18y = -111/2
Subtract equations
-3y = 11/2
y = 11/2/-3
y = -11/6

Substitute y
3x + 3(-11/6) = -10
3x = -9/2
x = -9/2/3
x = -3/2


Input:
Find x and y such that
10x + 4y = 36
6x + 9y = 174/5

Output:
10x + 4y = 36
6x + 9y = 174/5

Using elimination
6*(10x + 4y = 36)
10*(6x + 9y = 174/5)
60x + 24y = 216
60x + 90y = 348
Subtract equations
-66y = -132
y = -132/-66
y = 2

Substitute y
10x + 4(2) = 36
10x = 28
x = 28/10
x = 14/5


Input: Find x in x^3 + 43/6x^2 - 73/18x - 532/9 = 0

Output:
x^3 + 43/6x^2 - 73/18x - 532/9 = 0
(x - -19/3)(x - 8/3)(x - -7/2) = 0
x - -19/3 = 0
x - 8/3 = 0
x - -7/2 = 0
x = -19/3
x = 8/3
x = -7/2


Input: Solve the equation x^3 - 33/7x^2 - 103/7x - 9 = 0

Output:
x^3 - 33/7x^2 - 103/7x - 9 = 0
(x - 7)(x - -1)(x - -9/7) = 0
x - 7 = 0
x - -1 = 0
x - -9/7 = 0
x = 7
x = -1
x = -9/7


Input:
Solve simultaneously:
2x + 4y = -27/2
4x + 10y = -29

Output:
2x + 4y = -27/2
4x + 10y = -29

Using elimination
4*(2x + 4y = -27/2)
2*(4x + 10y = -29)
8x + 16y = -54
8x + 20y = -58
Subtract equations
-4y = 4
y = 4/-4
y = -1

Substitute y
2x + 4(-1) = -27/2
2x = -19/2
x = -19/2/2
x = -19/4


Input:
Solve simultaneously:
6x + 4y = -54/7
9x + 4y = -81/7

Output:
6x + 4y = -54/7
9x + 4y = -81/7

Using elimination
9*(6x + 4y = -54/7)
6*(9x + 4y = -81/7)
54x + 36y = -486/7
54x + 24y = -486/7
Subtract equations
12y = 0
y = 0/12
y = 0

Substitute y
6x + 4(0) = -54/7
6x = -54/7
x = -54/7/6
x = -9/7


Input:
Solve the system:
3x + 10y = 39/2
3x + 7y = 111/8

Output:
3x + 10y = 39/2
3x + 7y = 111/8

Using elimination
3*(3x + 10y = 39/2)
3*(3x + 7y = 111/8)
9x + 30y = 117/2
9x + 21y = 333/8
Subtract equations
9y = 135/8
y = 135/8/9
y = 15/8

Substitute y
3x + 10(15/8) = 39/2
3x = 3/4
x = 3/4/3
x = 1/4


Input: Find x in 9x - 54 = 0

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


Input: Determine x in x^3 + 821/140x^2 + 603/70x + 18/7 = 0

Output:
x^3 + 821/140x^2 + 603/70x + 18/7 = 0
(x - -12/7)(x - -2/5)(x - -15/4) = 0
x - -12/7 = 0
x - -2/5 = 0
x - -15/4 = 0
x = -12/7
x = -2/5
x = -15/4


Input: Solve quickly: x^3 - 247/90x^2 - 52/9x + 136/45 = 0

Output:
x^3 - 247/90x^2 - 52/9x + 136/45 = 0
(x - -17/10)(x - 4/9)(x - 4) = 0
x - -17/10 = 0
x - 4/9 = 0
x - 4 = 0
x = -17/10
x = 4/9
x = 4


Input: Find x for 10x + 40 = 0

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


Input:
Solve simultaneously:
5x + 7y = 143/12
6x + 1y = -39/4

Output:
5x + 7y = 143/12
6x + 1y = -39/4

Using elimination
6*(5x + 7y = 143/12)
5*(6x + 1y = -39/4)
30x + 42y = 143/2
30x + 5y = -195/4
Subtract equations
37y = 481/4
y = 481/4/37
y = 13/4

Substitute y
5x + 7(13/4) = 143/12
5x = -65/6
x = -65/6/5
x = -13/6


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

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


Input: Find the solution to x^3 - 209/70x^2 - 513/70x + 81/35 = 0

Output:
x^3 - 209/70x^2 - 513/70x + 81/35 = 0
(x - 9/2)(x - -9/5)(x - 2/7) = 0
x - 9/2 = 0
x - -9/5 = 0
x - 2/7 = 0
x = 9/2
x = -9/5
x = 2/7


Input:
Find x and y such that
9x + 9y = -63/4
4x + 9y = -23/4

Output:
9x + 9y = -63/4
4x + 9y = -23/4

Using elimination
4*(9x + 9y = -63/4)
9*(4x + 9y = -23/4)
36x + 36y = -63
36x + 81y = -207/4
Subtract equations
-45y = -45/4
y = -45/4/-45
y = 1/4

Substitute y
9x + 9(1/4) = -63/4
9x = -18
x = -18/9
x = -2


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

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


Input: Compute the solution of x^3 - 61/18x^2 + 55/18x - 34/81 = 0

Output:
x^3 - 61/18x^2 + 55/18x - 34/81 = 0
(x - 17/9)(x - 1/6)(x - 4/3) = 0
x - 17/9 = 0
x - 1/6 = 0
x - 4/3 = 0
x = 17/9
x = 1/6
x = 4/3


Input:
Solve simultaneously:
7x + 3y = -297/5
5x + 8y = -177/5

Output:
7x + 3y = -297/5
5x + 8y = -177/5

Using elimination
5*(7x + 3y = -297/5)
7*(5x + 8y = -177/5)
35x + 15y = -297
35x + 56y = -1239/5
Subtract equations
-41y = -246/5
y = -246/5/-41
y = 6/5

Substitute y
7x + 3(6/5) = -297/5
7x = -63
x = -63/7
x = -9


Input: Compute the solution of 7x + 14 = 0

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


Input:
Find x and y such that
5x + 4y = 19
2x + 2y = 42/5

Output:
5x + 4y = 19
2x + 2y = 42/5

Using elimination
2*(5x + 4y = 19)
5*(2x + 2y = 42/5)
10x + 8y = 38
10x + 10y = 42
Subtract equations
-2y = -4
y = -4/-2
y = 2

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


Input:
Find x and y such that
1x + 2y = 34/35
10x + 1y = -103/7

Output:
1x + 2y = 34/35
10x + 1y = -103/7

Using elimination
10*(1x + 2y = 34/35)
1*(10x + 1y = -103/7)
10x + 20y = 68/7
10x + 1y = -103/7
Subtract equations
19y = 171/7
y = 171/7/19
y = 9/7

Substitute y
1x + 2(9/7) = 34/35
1x = -8/5
x = -8/5/1
x = -8/5


Input:
Find x and y such that
3x + 5y = 155/6
2x + 6y = 77/3

Output:
3x + 5y = 155/6
2x + 6y = 77/3

Using elimination
2*(3x + 5y = 155/6)
3*(2x + 6y = 77/3)
6x + 10y = 155/3
6x + 18y = 77
Subtract equations
-8y = -76/3
y = -76/3/-8
y = 19/6

Substitute y
3x + 5(19/6) = 155/6
3x = 10
x = 10/3
x = 10/3


Input:
Solve the equations:
2x + 8y = 21/5
9x + 8y = -28/5

Output:
2x + 8y = 21/5
9x + 8y = -28/5

Using elimination
9*(2x + 8y = 21/5)
2*(9x + 8y = -28/5)
18x + 72y = 189/5
18x + 16y = -56/5
Subtract equations
56y = 49
y = 49/56
y = 7/8

Substitute y
2x + 8(7/8) = 21/5
2x = -14/5
x = -14/5/2
x = -7/5


Input: Solve 2x + 9/5 = 0

Output:
2x + 9/5 = 0
2x = -9/5
x = -9/5 / 2
x = -9/10


Input: Find the solution to x^2 - 41/5x - 247/20 = 0

Output:
x^2 - 41/5x - 247/20 = 0
(x - -13/10)(x - 19/2) = 0
x - -13/10 = 0  or  x - 19/2 = 0
x = -13/10
x = 19/2


Input: Solve quickly: x^3 - 165/28x^2 + 233/28x - 15/14 = 0

Output:
x^3 - 165/28x^2 + 233/28x - 15/14 = 0
(x - 2)(x - 15/4)(x - 1/7) = 0
x - 2 = 0
x - 15/4 = 0
x - 1/7 = 0
x = 2
x = 15/4
x = 1/7


Input: Solve 2x - 2 = 0

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


Input: Find x in 1x - 19/10 = 0

Output:
1x - 19/10 = 0
1x = 19/10
x = 19/10 / 1
x = 19/10


Input: What value of x satisfies 10x - 70/3 = 0

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


Input:
Find x and y such that
3x + 9y = 9/4
7x + 6y = 93/2

Output:
3x + 9y = 9/4
7x + 6y = 93/2

Using elimination
7*(3x + 9y = 9/4)
3*(7x + 6y = 93/2)
21x + 63y = 63/4
21x + 18y = 279/2
Subtract equations
45y = -495/4
y = -495/4/45
y = -11/4

Substitute y
3x + 9(-11/4) = 9/4
3x = 27
x = 27/3
x = 9


Input: Solve x^2 - 76/45x - 1/5 = 0

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


Input: What value of x satisfies x^3 - 12x^2 + 20x + 96 = 0

Output:
x^3 - 12x^2 + 20x + 96 = 0
(x - -2)(x - 6)(x - 8) = 0
x - -2 = 0
x - 6 = 0
x - 8 = 0
x = -2
x = 6
x = 8


Input: Find x for x^2 - 7x + 10 = 0

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


Input: Determine x in 6x + 4 = 0

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


Input: Solve the equation x^2 + 207/40x + 209/40 = 0

Output:
x^2 + 207/40x + 209/40 = 0
(x - -11/8)(x - -19/5) = 0
x - -11/8 = 0  or  x - -19/5 = 0
x = -11/8
x = -19/5


Input: Find x for x^2 + 9x + 65/4 = 0

Output:
x^2 + 9x + 65/4 = 0
(x - -13/2)(x - -5/2) = 0
x - -13/2 = 0  or  x - -5/2 = 0
x = -13/2
x = -5/2


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

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


Input: Find x for x^2 - 63/10x + 22/5 = 0

Output:
x^2 - 63/10x + 22/5 = 0
(x - 11/2)(x - 4/5) = 0
x - 11/2 = 0  or  x - 4/5 = 0
x = 11/2
x = 4/5


Input: Find the solution to x^2 - 7x + 104/9 = 0

Output:
x^2 - 7x + 104/9 = 0
(x - 8/3)(x - 13/3) = 0
x - 8/3 = 0  or  x - 13/3 = 0
x = 8/3
x = 13/3


Input:
Solve the equations:
8x + 3y = 24
2x + 3y = 51/4

Output:
8x + 3y = 24
2x + 3y = 51/4

Using elimination
2*(8x + 3y = 24)
8*(2x + 3y = 51/4)
16x + 6y = 48
16x + 24y = 102
Subtract equations
-18y = -54
y = -54/-18
y = 3

Substitute y
8x + 3(3) = 24
8x = 15
x = 15/8
x = 15/8


Input:
Solve the equations:
4x + 8y = 299/2
5x + 8y = 1191/8

Output:
4x + 8y = 299/2
5x + 8y = 1191/8

Using elimination
5*(4x + 8y = 299/2)
4*(5x + 8y = 1191/8)
20x + 40y = 1495/2
20x + 32y = 1191/2
Subtract equations
8y = 152
y = 152/8
y = 19

Substitute y
4x + 8(19) = 299/2
4x = -5/2
x = -5/2/4
x = -5/8


Input: Solve x^3 - 35/6x^2 - 11x + 455/6 = 0

Output:
x^3 - 35/6x^2 - 11x + 455/6 = 0
(x - -7/2)(x - 5)(x - 13/3) = 0
x - -7/2 = 0
x - 5 = 0
x - 13/3 = 0
x = -7/2
x = 5
x = 13/3


Input: Solve the equation x^3 + 261/56x^2 + 801/112x + 405/112 = 0

Output:
x^3 + 261/56x^2 + 801/112x + 405/112 = 0
(x - -15/8)(x - -9/7)(x - -3/2) = 0
x - -15/8 = 0
x - -9/7 = 0
x - -3/2 = 0
x = -15/8
x = -9/7
x = -3/2


Input: What value of x satisfies 9x - 36 = 0

Output:
9x - 36 = 0
9x = 36
x = 36 / 9
x = 4


Input: Find x in 2x  = 0

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


Input:
Solve simultaneously:
10x + 5y = -35/3
10x + 4y = -37/3

Output:
10x + 5y = -35/3
10x + 4y = -37/3

Using elimination
10*(10x + 5y = -35/3)
10*(10x + 4y = -37/3)
100x + 50y = -350/3
100x + 40y = -370/3
Subtract equations
10y = 20/3
y = 20/3/10
y = 2/3

Substitute y
10x + 5(2/3) = -35/3
10x = -15
x = -15/10
x = -3/2


Input: Solve x^2 + 4x - 64/9 = 0

Output:
x^2 + 4x - 64/9 = 0
(x - -16/3)(x - 4/3) = 0
x - -16/3 = 0  or  x - 4/3 = 0
x = -16/3
x = 4/3


Input: What value of x satisfies x^2 - 27x + 182 = 0

Output:
x^2 - 27x + 182 = 0
(x - 14)(x - 13) = 0
x - 14 = 0  or  x - 13 = 0
x = 14
x = 13


Input:
Solve simultaneously:
4x + 8y = 34
10x + 4y = 31/3

Output:
4x + 8y = 34
10x + 4y = 31/3

Using elimination
10*(4x + 8y = 34)
4*(10x + 4y = 31/3)
40x + 80y = 340
40x + 16y = 124/3
Subtract equations
64y = 896/3
y = 896/3/64
y = 14/3

Substitute y
4x + 8(14/3) = 34
4x = -10/3
x = -10/3/4
x = -5/6


Input:
Solve the system:
4x + 4y = 8
2x + 1y = 3

Output:
4x + 4y = 8
2x + 1y = 3

Using elimination
2*(4x + 4y = 8)
4*(2x + 1y = 3)
8x + 8y = 16
8x + 4y = 12
Subtract equations
4y = 4
y = 4/4
y = 1

Substitute y
4x + 4(1) = 8
4x = 4
x = 4/4
x = 1


Input: Solve 7x - 133/9 = 0

Output:
7x - 133/9 = 0
7x = 133/9
x = 133/9 / 7
x = 19/9


Input: Solve x^3 + 181/42x^2 + 347/126x - 85/21 = 0

Output:
x^3 + 181/42x^2 + 347/126x - 85/21 = 0
(x - 2/3)(x - -17/6)(x - -15/7) = 0
x - 2/3 = 0
x - -17/6 = 0
x - -15/7 = 0
x = 2/3
x = -17/6
x = -15/7


Input: Find x for x^3 - 23/30x^2 - 733/150x - 12/25 = 0

Output:
x^3 - 23/30x^2 - 733/150x - 12/25 = 0
(x - -9/5)(x - -1/10)(x - 8/3) = 0
x - -9/5 = 0
x - -1/10 = 0
x - 8/3 = 0
x = -9/5
x = -1/10
x = 8/3


Input: Find the solution to x^3 + 14/5x^2 - 8/45x - 64/45 = 0

Output:
x^3 + 14/5x^2 - 8/45x - 64/45 = 0
(x - 2/3)(x - -4/5)(x - -8/3) = 0
x - 2/3 = 0
x - -4/5 = 0
x - -8/3 = 0
x = 2/3
x = -4/5
x = -8/3


Input: Find x in x^2 - 7/2x - 15/2 = 0

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


Input: Compute the solution of x^3 + 5/8x^2 - 51/32x - 27/64 = 0

Output:
x^3 + 5/8x^2 - 51/32x - 27/64 = 0
(x - 9/8)(x - -1/4)(x - -3/2) = 0
x - 9/8 = 0
x - -1/4 = 0
x - -3/2 = 0
x = 9/8
x = -1/4
x = -3/2


Input:
Solve simultaneously:
1x + 9y = -102/7
5x + 3y = 162/7

Output:
1x + 9y = -102/7
5x + 3y = 162/7

Using elimination
5*(1x + 9y = -102/7)
1*(5x + 3y = 162/7)
5x + 45y = -510/7
5x + 3y = 162/7
Subtract equations
42y = -96
y = -96/42
y = -16/7

Substitute y
1x + 9(-16/7) = -102/7
1x = 6
x = 6/1
x = 6


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: Compute the solution of 10x  = 0

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


Input: Determine x in x^3 - 14/3x^2 - 5x + 50/3 = 0

Output:
x^3 - 14/3x^2 - 5x + 50/3 = 0
(x - 5)(x - 5/3)(x - -2) = 0
x - 5 = 0
x - 5/3 = 0
x - -2 = 0
x = 5
x = 5/3
x = -2


Input: What value of x satisfies x^3 + 56/15x^2 - 63/5x + 6 = 0

Output:
x^3 + 56/15x^2 - 63/5x + 6 = 0
(x - -6)(x - 3/5)(x - 5/3) = 0
x - -6 = 0
x - 3/5 = 0
x - 5/3 = 0
x = -6
x = 3/5
x = 5/3


Input: Solve the equation x^2 - 23/10x + 33/25 = 0

Output:
x^2 - 23/10x + 33/25 = 0
(x - 6/5)(x - 11/10) = 0
x - 6/5 = 0  or  x - 11/10 = 0
x = 6/5
x = 11/10


Input: Compute the solution of 9x + 90/7 = 0

Output:
9x + 90/7 = 0
9x = -90/7
x = -90/7 / 9
x = -10/7


Input: Compute the solution of 5x - 35 = 0

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


Input: Find x in x^3 + 553/24x^2 + 1273/16x + 2527/48 = 0

Output:
x^3 + 553/24x^2 + 1273/16x + 2527/48 = 0
(x - -19)(x - -19/6)(x - -7/8) = 0
x - -19 = 0
x - -19/6 = 0
x - -7/8 = 0
x = -19
x = -19/6
x = -7/8


Input: Solve 1x - 3/10 = 0

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


Input: Solve quickly: x^3 - 79/4x^2 + 223/2x - 140 = 0

Output:
x^3 - 79/4x^2 + 223/2x - 140 = 0
(x - 7/4)(x - 10)(x - 8) = 0
x - 7/4 = 0
x - 10 = 0
x - 8 = 0
x = 7/4
x = 10
x = 8


Input: Find x in x^3 - 619/210x^2 + 79/42x + 2/5 = 0

Output:
x^3 - 619/210x^2 + 79/42x + 2/5 = 0
(x - 7/5)(x - -1/6)(x - 12/7) = 0
x - 7/5 = 0
x - -1/6 = 0
x - 12/7 = 0
x = 7/5
x = -1/6
x = 12/7


Input:
Find x and y such that
8x + 8y = 168
6x + 10y = 134

Output:
8x + 8y = 168
6x + 10y = 134

Using elimination
6*(8x + 8y = 168)
8*(6x + 10y = 134)
48x + 48y = 1008
48x + 80y = 1072
Subtract equations
-32y = -64
y = -64/-32
y = 2

Substitute y
8x + 8(2) = 168
8x = 152
x = 152/8
x = 19


Input: Find x for 10x + 40 = 0

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


Input: Solve the equation 9x + 153/4 = 0

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


Input: What value of x satisfies 9x + 27/8 = 0

Output:
9x + 27/8 = 0
9x = -27/8
x = -27/8 / 9
x = -3/8


Input: Find the solution to x^3 + 245/24x^2 + 679/24x + 95/4 = 0

Output:
x^3 + 245/24x^2 + 679/24x + 95/4 = 0
(x - -19/3)(x - -2)(x - -15/8) = 0
x - -19/3 = 0
x - -2 = 0
x - -15/8 = 0
x = -19/3
x = -2
x = -15/8


Input: Solve the equation x^3 - 53/252x^2 - 131/126x + 10/21 = 0

Output:
x^3 - 53/252x^2 - 131/126x + 10/21 = 0
(x - 4/7)(x - 3/4)(x - -10/9) = 0
x - 4/7 = 0
x - 3/4 = 0
x - -10/9 = 0
x = 4/7
x = 3/4
x = -10/9


Input:
Solve the equations:
4x + 10y = 108/5
10x + 9y = 22

Output:
4x + 10y = 108/5
10x + 9y = 22

Using elimination
10*(4x + 10y = 108/5)
4*(10x + 9y = 22)
40x + 100y = 216
40x + 36y = 88
Subtract equations
64y = 128
y = 128/64
y = 2

Substitute y
4x + 10(2) = 108/5
4x = 8/5
x = 8/5/4
x = 2/5


Input: What value of x satisfies x^2 + 123/35x + 108/35 = 0

Output:
x^2 + 123/35x + 108/35 = 0
(x - -12/7)(x - -9/5) = 0
x - -12/7 = 0  or  x - -9/5 = 0
x = -12/7
x = -9/5


Input:
Solve simultaneously:
3x + 1y = 15/2
5x + 4y = -5

Output:
3x + 1y = 15/2
5x + 4y = -5

Using elimination
5*(3x + 1y = 15/2)
3*(5x + 4y = -5)
15x + 5y = 75/2
15x + 12y = -15
Subtract equations
-7y = 105/2
y = 105/2/-7
y = -15/2

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


Input: Compute the solution of 8x - 64/5 = 0

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


Input: Solve quickly: x^3 + 224/15x^2 - 263/15x - 112/15 = 0

Output:
x^3 + 224/15x^2 - 263/15x - 112/15 = 0
(x - 7/5)(x - -1/3)(x - -16) = 0
x - 7/5 = 0
x - -1/3 = 0
x - -16 = 0
x = 7/5
x = -1/3
x = -16


Input: Find x in x^3 - 34/9x^2 - 25/3x + 100/9 = 0

Output:
x^3 - 34/9x^2 - 25/3x + 100/9 = 0
(x - -20/9)(x - 5)(x - 1) = 0
x - -20/9 = 0
x - 5 = 0
x - 1 = 0
x = -20/9
x = 5
x = 1


Input:
Solve the system:
2x + 10y = 10
8x + 7y = 499/10

Output:
2x + 10y = 10
8x + 7y = 499/10

Using elimination
8*(2x + 10y = 10)
2*(8x + 7y = 499/10)
16x + 80y = 80
16x + 14y = 499/5
Subtract equations
66y = -99/5
y = -99/5/66
y = -3/10

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


Input: Solve x^3 - 23/4x^2 + 9/2x + 45/4 = 0

Output:
x^3 - 23/4x^2 + 9/2x + 45/4 = 0
(x - -1)(x - 15/4)(x - 3) = 0
x - -1 = 0
x - 15/4 = 0
x - 3 = 0
x = -1
x = 15/4
x = 3


Input: Solve 5x + 55/3 = 0

Output:
5x + 55/3 = 0
5x = -55/3
x = -55/3 / 5
x = -11/3


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

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


Input: Solve 4x + 76/7 = 0

Output:
4x + 76/7 = 0
4x = -76/7
x = -76/7 / 4
x = -19/7


Input: Find the solution to 10x - 90/7 = 0

Output:
10x - 90/7 = 0
10x = 90/7
x = 90/7 / 10
x = 9/7


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

Output:
x^2 + 11/3x + 19/12 = 0
(x - -1/2)(x - -19/6) = 0
x - -1/2 = 0  or  x - -19/6 = 0
x = -1/2
x = -19/6


Input: Find the solution to 10x + 70/3 = 0

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


Input: Determine x in x^3 + 5/72x^2 - 29/48x - 7/36 = 0

Output:
x^3 + 5/72x^2 - 29/48x - 7/36 = 0
(x - -1/2)(x - 7/8)(x - -4/9) = 0
x - -1/2 = 0
x - 7/8 = 0
x - -4/9 = 0
x = -1/2
x = 7/8
x = -4/9


Input: Find x in x^3 + 767/280x^2 + 219/280x - 117/70 = 0

Output:
x^3 + 767/280x^2 + 219/280x - 117/70 = 0
(x - -13/8)(x - 3/5)(x - -12/7) = 0
x - -13/8 = 0
x - 3/5 = 0
x - -12/7 = 0
x = -13/8
x = 3/5
x = -12/7


Input: Solve the equation 2x + 12 = 0

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


Input:
Solve the system:
3x + 2y = -47/4
8x + 8y = -34

Output:
3x + 2y = -47/4
8x + 8y = -34

Using elimination
8*(3x + 2y = -47/4)
3*(8x + 8y = -34)
24x + 16y = -94
24x + 24y = -102
Subtract equations
-8y = 8
y = 8/-8
y = -1

Substitute y
3x + 2(-1) = -47/4
3x = -39/4
x = -39/4/3
x = -13/4


Input: Solve the equation x^2 + 164/9x - 320/9 = 0

Output:
x^2 + 164/9x - 320/9 = 0
(x - -20)(x - 16/9) = 0
x - -20 = 0  or  x - 16/9 = 0
x = -20
x = 16/9


Input: Solve the equation 7x - 126/5 = 0

Output:
7x - 126/5 = 0
7x = 126/5
x = 126/5 / 7
x = 18/5


Input: Solve the equation 7x - 7 = 0

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


Input: Find x for 3x + 57/7 = 0

Output:
3x + 57/7 = 0
3x = -57/7
x = -57/7 / 3
x = -19/7


Input: Determine x in 5x + 25/6 = 0

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


Input:
Solve simultaneously:
7x + 10y = 61/2
2x + 5y = 409/28

Output:
7x + 10y = 61/2
2x + 5y = 409/28

Using elimination
2*(7x + 10y = 61/2)
7*(2x + 5y = 409/28)
14x + 20y = 61
14x + 35y = 409/4
Subtract equations
-15y = -165/4
y = -165/4/-15
y = 11/4

Substitute y
7x + 10(11/4) = 61/2
7x = 3
x = 3/7
x = 3/7


Input: Solve quickly: x^2 + 37/4x + 85/4 = 0

Output:
x^2 + 37/4x + 85/4 = 0
(x - -5)(x - -17/4) = 0
x - -5 = 0  or  x - -17/4 = 0
x = -5
x = -17/4


Input:
Solve the equations:
2x + 9y = -141/28
8x + 7y = -16

Output:
2x + 9y = -141/28
8x + 7y = -16

Using elimination
8*(2x + 9y = -141/28)
2*(8x + 7y = -16)
16x + 72y = -282/7
16x + 14y = -32
Subtract equations
58y = -58/7
y = -58/7/58
y = -1/7

Substitute y
2x + 9(-1/7) = -141/28
2x = -15/4
x = -15/4/2
x = -15/8


Input: Solve quickly: x^3 + 25/14x^2 - 37/14x - 24/7 = 0

Output:
x^3 + 25/14x^2 - 37/14x - 24/7 = 0
(x - 3/2)(x - -1)(x - -16/7) = 0
x - 3/2 = 0
x - -1 = 0
x - -16/7 = 0
x = 3/2
x = -1
x = -16/7


Input: Find x for x^3 + 107/20x^2 - 389/20x + 14 = 0

Output:
x^3 + 107/20x^2 - 389/20x + 14 = 0
(x - -8)(x - 5/4)(x - 7/5) = 0
x - -8 = 0
x - 5/4 = 0
x - 7/5 = 0
x = -8
x = 5/4
x = 7/5


Input: Compute the solution of x^3 - 19/4x^2 + 395/64x - 323/256 = 0

Output:
x^3 - 19/4x^2 + 395/64x - 323/256 = 0
(x - 17/8)(x - 19/8)(x - 1/4) = 0
x - 17/8 = 0
x - 19/8 = 0
x - 1/4 = 0
x = 17/8
x = 19/8
x = 1/4


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

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


Input:
Find x and y such that
5x + 5y = -260/7
6x + 3y = -207/7

Output:
5x + 5y = -260/7
6x + 3y = -207/7

Using elimination
6*(5x + 5y = -260/7)
5*(6x + 3y = -207/7)
30x + 30y = -1560/7
30x + 15y = -1035/7
Subtract equations
15y = -75
y = -75/15
y = -5

Substitute y
5x + 5(-5) = -260/7
5x = -85/7
x = -85/7/5
x = -17/7


Input: What value of x satisfies x^2 - 23/8x - 285/32 = 0

Output:
x^2 - 23/8x - 285/32 = 0
(x - 19/4)(x - -15/8) = 0
x - 19/4 = 0  or  x - -15/8 = 0
x = 19/4
x = -15/8


Input: Compute the solution of x^3 + 3/2x^2 - 305/98x - 102/49 = 0

Output:
x^3 + 3/2x^2 - 305/98x - 102/49 = 0
(x - -4/7)(x - 3/2)(x - -17/7) = 0
x - -4/7 = 0
x - 3/2 = 0
x - -17/7 = 0
x = -4/7
x = 3/2
x = -17/7


Input: Solve the equation 3x - 21 = 0

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


Input:
Find x and y such that
2x + 10y = 167/7
2x + 2y = 27/7

Output:
2x + 10y = 167/7
2x + 2y = 27/7

Using elimination
2*(2x + 10y = 167/7)
2*(2x + 2y = 27/7)
4x + 20y = 334/7
4x + 4y = 54/7
Subtract equations
16y = 40
y = 40/16
y = 5/2

Substitute y
2x + 10(5/2) = 167/7
2x = -8/7
x = -8/7/2
x = -4/7


Input: Find x in 9x + 171/10 = 0

Output:
9x + 171/10 = 0
9x = -171/10
x = -171/10 / 9
x = -19/10


Input:
Find x and y such that
9x + 8y = 9/5
7x + 3y = -8/15

Output:
9x + 8y = 9/5
7x + 3y = -8/15

Using elimination
7*(9x + 8y = 9/5)
9*(7x + 3y = -8/15)
63x + 56y = 63/5
63x + 27y = -24/5
Subtract equations
29y = 87/5
y = 87/5/29
y = 3/5

Substitute y
9x + 8(3/5) = 9/5
9x = -3
x = -3/9
x = -1/3


Input:
Solve simultaneously:
4x + 2y = 282/35
6x + 2y = 338/35

Output:
4x + 2y = 282/35
6x + 2y = 338/35

Using elimination
6*(4x + 2y = 282/35)
4*(6x + 2y = 338/35)
24x + 12y = 1692/35
24x + 8y = 1352/35
Subtract equations
4y = 68/7
y = 68/7/4
y = 17/7

Substitute y
4x + 2(17/7) = 282/35
4x = 16/5
x = 16/5/4
x = 4/5


Input:
Solve simultaneously:
7x + 2y = 130/9
3x + 2y = 262/63

Output:
7x + 2y = 130/9
3x + 2y = 262/63

Using elimination
3*(7x + 2y = 130/9)
7*(3x + 2y = 262/63)
21x + 6y = 130/3
21x + 14y = 262/9
Subtract equations
-8y = 128/9
y = 128/9/-8
y = -16/9

Substitute y
7x + 2(-16/9) = 130/9
7x = 18
x = 18/7
x = 18/7


Input: Solve quickly: x^2 + 17/6x - 1/2 = 0

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


Input: Solve x^2 + 17/12x - 33/4 = 0

Output:
x^2 + 17/12x - 33/4 = 0
(x - -11/3)(x - 9/4) = 0
x - -11/3 = 0  or  x - 9/4 = 0
x = -11/3
x = 9/4


Input: Solve x^3 + 5/3x^2 - 33/4x - 51/4 = 0

Output:
x^3 + 5/3x^2 - 33/4x - 51/4 = 0
(x - -3)(x - -3/2)(x - 17/6) = 0
x - -3 = 0
x - -3/2 = 0
x - 17/6 = 0
x = -3
x = -3/2
x = 17/6


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

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


Input: Compute the solution of x^2 - 10/9x - 19/9 = 0

Output:
x^2 - 10/9x - 19/9 = 0
(x - 19/9)(x - -1) = 0
x - 19/9 = 0  or  x - -1 = 0
x = 19/9
x = -1


Input: What value of x satisfies x^3 + 197/30x^2 + 761/60x + 273/40 = 0

Output:
x^3 + 197/30x^2 + 761/60x + 273/40 = 0
(x - -7/2)(x - -13/6)(x - -9/10) = 0
x - -7/2 = 0
x - -13/6 = 0
x - -9/10 = 0
x = -7/2
x = -13/6
x = -9/10


Input: Solve the equation 4x - 7/2 = 0

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


Input: Find the solution to 1x + 10/3 = 0

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


Input:
Find x and y such that
7x + 5y = -191/4
7x + 6y = -51

Output:
7x + 5y = -191/4
7x + 6y = -51

Using elimination
7*(7x + 5y = -191/4)
7*(7x + 6y = -51)
49x + 35y = -1337/4
49x + 42y = -357
Subtract equations
-7y = 91/4
y = 91/4/-7
y = -13/4

Substitute y
7x + 5(-13/4) = -191/4
7x = -63/2
x = -63/2/7
x = -9/2


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

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


Input: Find x in x^3 + 17/9x^2 - 56/81x - 128/81 = 0

Output:
x^3 + 17/9x^2 - 56/81x - 128/81 = 0
(x - 8/9)(x - -16/9)(x - -1) = 0
x - 8/9 = 0
x - -16/9 = 0
x - -1 = 0
x = 8/9
x = -16/9
x = -1


Input: Find the solution to 1x + 15 = 0

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


Input:
Solve simultaneously:
8x + 5y = 667/28
6x + 9y = 831/28

Output:
8x + 5y = 667/28
6x + 9y = 831/28

Using elimination
6*(8x + 5y = 667/28)
8*(6x + 9y = 831/28)
48x + 30y = 2001/14
48x + 72y = 1662/7
Subtract equations
-42y = -189/2
y = -189/2/-42
y = 9/4

Substitute y
8x + 5(9/4) = 667/28
8x = 88/7
x = 88/7/8
x = 11/7


Input: Compute the solution of x^3 - 133/12x^2 + 203/8x - 17/3 = 0

Output:
x^3 - 133/12x^2 + 203/8x - 17/3 = 0
(x - 8)(x - 1/4)(x - 17/6) = 0
x - 8 = 0
x - 1/4 = 0
x - 17/6 = 0
x = 8
x = 1/4
x = 17/6


Input:
Find x and y such that
8x + 1y = -171/7
5x + 5y = -260/7

Output:
8x + 1y = -171/7
5x + 5y = -260/7

Using elimination
5*(8x + 1y = -171/7)
8*(5x + 5y = -260/7)
40x + 5y = -855/7
40x + 40y = -2080/7
Subtract equations
-35y = 175
y = 175/-35
y = -5

Substitute y
8x + 1(-5) = -171/7
8x = -136/7
x = -136/7/8
x = -17/7


Input:
Solve simultaneously:
6x + 5y = -24/5
5x + 10y = -4

Output:
6x + 5y = -24/5
5x + 10y = -4

Using elimination
5*(6x + 5y = -24/5)
6*(5x + 10y = -4)
30x + 25y = -24
30x + 60y = -24
Subtract equations
-35y = 0
y = 0/-35
y = 0

Substitute y
6x + 5(0) = -24/5
6x = -24/5
x = -24/5/6
x = -4/5


Input: Solve quickly: 4x - 68/9 = 0

Output:
4x - 68/9 = 0
4x = 68/9
x = 68/9 / 4
x = 17/9


Input:
Find x and y such that
3x + 2y = -38/5
7x + 10y = -38

Output:
3x + 2y = -38/5
7x + 10y = -38

Using elimination
7*(3x + 2y = -38/5)
3*(7x + 10y = -38)
21x + 14y = -266/5
21x + 30y = -114
Subtract equations
-16y = 304/5
y = 304/5/-16
y = -19/5

Substitute y
3x + 2(-19/5) = -38/5
3x = 0
x = 0/3
x = 0


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

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


Input: Determine x in x^3 - 73/4x^2 - 16x + 133/4 = 0

Output:
x^3 - 73/4x^2 - 16x + 133/4 = 0
(x - 19)(x - -7/4)(x - 1) = 0
x - 19 = 0
x - -7/4 = 0
x - 1 = 0
x = 19
x = -7/4
x = 1


Input:
Find x and y such that
5x + 2y = 131/5
3x + 1y = 78/5

Output:
5x + 2y = 131/5
3x + 1y = 78/5

Using elimination
3*(5x + 2y = 131/5)
5*(3x + 1y = 78/5)
15x + 6y = 393/5
15x + 5y = 78
Subtract equations
1y = 3/5
y = 3/5/1
y = 3/5

Substitute y
5x + 2(3/5) = 131/5
5x = 25
x = 25/5
x = 5


Input:
Find x and y such that
2x + 5y = 53/4
1x + 2y = 197/40

Output:
2x + 5y = 53/4
1x + 2y = 197/40

Using elimination
1*(2x + 5y = 53/4)
2*(1x + 2y = 197/40)
2x + 5y = 53/4
2x + 4y = 197/20
Subtract equations
1y = 17/5
y = 17/5/1
y = 17/5

Substitute y
2x + 5(17/5) = 53/4
2x = -15/4
x = -15/4/2
x = -15/8


Input:
Solve simultaneously:
6x + 7y = -497/5
8x + 2y = -186/5

Output:
6x + 7y = -497/5
8x + 2y = -186/5

Using elimination
8*(6x + 7y = -497/5)
6*(8x + 2y = -186/5)
48x + 56y = -3976/5
48x + 12y = -1116/5
Subtract equations
44y = -572
y = -572/44
y = -13

Substitute y
6x + 7(-13) = -497/5
6x = -42/5
x = -42/5/6
x = -7/5


Input: Solve the equation x^2 - 1/3x - 14/3 = 0

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


Input:
Find x and y such that
2x + 7y = 247/35
8x + 9y = 589/35

Output:
2x + 7y = 247/35
8x + 9y = 589/35

Using elimination
8*(2x + 7y = 247/35)
2*(8x + 9y = 589/35)
16x + 56y = 1976/35
16x + 18y = 1178/35
Subtract equations
38y = 114/5
y = 114/5/38
y = 3/5

Substitute y
2x + 7(3/5) = 247/35
2x = 20/7
x = 20/7/2
x = 10/7


Input: Solve quickly: 7x - 7/5 = 0

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


Input:
Solve the equations:
1x + 8y = 12
5x + 9y = -2

Output:
1x + 8y = 12
5x + 9y = -2

Using elimination
5*(1x + 8y = 12)
1*(5x + 9y = -2)
5x + 40y = 60
5x + 9y = -2
Subtract equations
31y = 62
y = 62/31
y = 2

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


Input: Find x in 9x + 99/8 = 0

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


Input:
Solve simultaneously:
3x + 6y = 93/7
5x + 7y = 17

Output:
3x + 6y = 93/7
5x + 7y = 17

Using elimination
5*(3x + 6y = 93/7)
3*(5x + 7y = 17)
15x + 30y = 465/7
15x + 21y = 51
Subtract equations
9y = 108/7
y = 108/7/9
y = 12/7

Substitute y
3x + 6(12/7) = 93/7
3x = 3
x = 3/3
x = 1


Input: Compute the solution of 8x - 26 = 0

Output:
8x - 26 = 0
8x = 26
x = 26 / 8
x = 13/4


Input: Solve quickly: x^2 + 151/72x + 77/72 = 0

Output:
x^2 + 151/72x + 77/72 = 0
(x - -11/9)(x - -7/8) = 0
x - -11/9 = 0  or  x - -7/8 = 0
x = -11/9
x = -7/8


Input: Find x for x^2 - 37/6x - 10/3 = 0

Output:
x^2 - 37/6x - 10/3 = 0
(x - -1/2)(x - 20/3) = 0
x - -1/2 = 0  or  x - 20/3 = 0
x = -1/2
x = 20/3


Input: Find x for x^3 - 27/4x^2 - 19x - 45/4 = 0

Output:
x^3 - 27/4x^2 - 19x - 45/4 = 0
(x - -5/4)(x - -1)(x - 9) = 0
x - -5/4 = 0
x - -1 = 0
x - 9 = 0
x = -5/4
x = -1
x = 9


Input:
Find x and y such that
8x + 10y = -346/3
9x + 6y = -128

Output:
8x + 10y = -346/3
9x + 6y = -128

Using elimination
9*(8x + 10y = -346/3)
8*(9x + 6y = -128)
72x + 90y = -1038
72x + 48y = -1024
Subtract equations
42y = -14
y = -14/42
y = -1/3

Substitute y
8x + 10(-1/3) = -346/3
8x = -112
x = -112/8
x = -14


Input: Solve quickly: x^2 - 81/70x - 13/70 = 0

Output:
x^2 - 81/70x - 13/70 = 0
(x - 13/10)(x - -1/7) = 0
x - 13/10 = 0  or  x - -1/7 = 0
x = 13/10
x = -1/7


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

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


Input:
Find x and y such that
9x + 6y = -123/5
3x + 9y = -174/5

Output:
9x + 6y = -123/5
3x + 9y = -174/5

Using elimination
3*(9x + 6y = -123/5)
9*(3x + 9y = -174/5)
27x + 18y = -369/5
27x + 81y = -1566/5
Subtract equations
-63y = 1197/5
y = 1197/5/-63
y = -19/5

Substitute y
9x + 6(-19/5) = -123/5
9x = -9/5
x = -9/5/9
x = -1/5


Input: Find x for x^3 - 943/315x^2 + 64/35x - 16/63 = 0

Output:
x^3 - 943/315x^2 + 64/35x - 16/63 = 0
(x - 1/5)(x - 4/7)(x - 20/9) = 0
x - 1/5 = 0
x - 4/7 = 0
x - 20/9 = 0
x = 1/5
x = 4/7
x = 20/9


Input: Find the solution to x^3 + 37/5x^2 + 99/20x - 117/20 = 0

Output:
x^3 + 37/5x^2 + 99/20x - 117/20 = 0
(x - 3/5)(x - -13/2)(x - -3/2) = 0
x - 3/5 = 0
x - -13/2 = 0
x - -3/2 = 0
x = 3/5
x = -13/2
x = -3/2


Input:
Solve the system:
9x + 6y = 62
8x + 2y = 112/3

Output:
9x + 6y = 62
8x + 2y = 112/3

Using elimination
8*(9x + 6y = 62)
9*(8x + 2y = 112/3)
72x + 48y = 496
72x + 18y = 336
Subtract equations
30y = 160
y = 160/30
y = 16/3

Substitute y
9x + 6(16/3) = 62
9x = 30
x = 30/9
x = 10/3


Input: Determine x in x^3 + 61/9x^2 - 86/9x + 16/9 = 0

Output:
x^3 + 61/9x^2 - 86/9x + 16/9 = 0
(x - -8)(x - 1)(x - 2/9) = 0
x - -8 = 0
x - 1 = 0
x - 2/9 = 0
x = -8
x = 1
x = 2/9


Input:
Solve the equations:
9x + 10y = -3
8x + 1y = 173/15

Output:
9x + 10y = -3
8x + 1y = 173/15

Using elimination
8*(9x + 10y = -3)
9*(8x + 1y = 173/15)
72x + 80y = -24
72x + 9y = 519/5
Subtract equations
71y = -639/5
y = -639/5/71
y = -9/5

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


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

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


Input: Find x in 10x - 12 = 0

Output:
10x - 12 = 0
10x = 12
x = 12 / 10
x = 6/5


Input: Determine x in x^3 - 83/35x^2 - 452/245x + 608/245 = 0

Output:
x^3 - 83/35x^2 - 452/245x + 608/245 = 0
(x - 19/7)(x - -8/7)(x - 4/5) = 0
x - 19/7 = 0
x - -8/7 = 0
x - 4/5 = 0
x = 19/7
x = -8/7
x = 4/5


Input:
Solve the equations:
4x + 3y = -11/9
5x + 7y = 1

Output:
4x + 3y = -11/9
5x + 7y = 1

Using elimination
5*(4x + 3y = -11/9)
4*(5x + 7y = 1)
20x + 15y = -55/9
20x + 28y = 4
Subtract equations
-13y = -91/9
y = -91/9/-13
y = 7/9

Substitute y
4x + 3(7/9) = -11/9
4x = -32/9
x = -32/9/4
x = -8/9


Input: Find x for x^3 - 27/10x^2 - 53/20x - 21/40 = 0

Output:
x^3 - 27/10x^2 - 53/20x - 21/40 = 0
(x - -3/10)(x - 7/2)(x - -1/2) = 0
x - -3/10 = 0
x - 7/2 = 0
x - -1/2 = 0
x = -3/10
x = 7/2
x = -1/2


Input: What value of x satisfies x^2  - 64/25 = 0

Output:
x^2  - 64/25 = 0
(x - 8/5)(x - -8/5) = 0
x - 8/5 = 0  or  x - -8/5 = 0
x = 8/5
x = -8/5


Input: Find x for 2x - 1/5 = 0

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


Input: Solve quickly: 1x - 3 = 0

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


Input:
Find x and y such that
2x + 7y = 61/5
3x + 10y = 71/4

Output:
2x + 7y = 61/5
3x + 10y = 71/4

Using elimination
3*(2x + 7y = 61/5)
2*(3x + 10y = 71/4)
6x + 21y = 183/5
6x + 20y = 71/2
Subtract equations
1y = 11/10
y = 11/10/1
y = 11/10

Substitute y
2x + 7(11/10) = 61/5
2x = 9/2
x = 9/2/2
x = 9/4


Input: Solve x^3 + 89/30x^2 + 19/15x - 3/2 = 0

Output:
x^3 + 89/30x^2 + 19/15x - 3/2 = 0
(x - -9/5)(x - -5/3)(x - 1/2) = 0
x - -9/5 = 0
x - -5/3 = 0
x - 1/2 = 0
x = -9/5
x = -5/3
x = 1/2


Input: Compute the solution of x^2 + 3x - 40 = 0

Output:
x^2 + 3x - 40 = 0
(x - -8)(x - 5) = 0
x - -8 = 0  or  x - 5 = 0
x = -8
x = 5


Input: Solve quickly: 8x + 128/3 = 0

Output:
8x + 128/3 = 0
8x = -128/3
x = -128/3 / 8
x = -16/3


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

Output:
x^2 - 2/5x - 3/25 = 0
(x - 3/5)(x - -1/5) = 0
x - 3/5 = 0  or  x - -1/5 = 0
x = 3/5
x = -1/5


Input:
Find x and y such that
1x + 5y = -161/8
9x + 6y = -201/8

Output:
1x + 5y = -161/8
9x + 6y = -201/8

Using elimination
9*(1x + 5y = -161/8)
1*(9x + 6y = -201/8)
9x + 45y = -1449/8
9x + 6y = -201/8
Subtract equations
39y = -156
y = -156/39
y = -4

Substitute y
1x + 5(-4) = -161/8
1x = -1/8
x = -1/8/1
x = -1/8


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

Output:
x^2 - 19/6x - 6 = 0
(x - 9/2)(x - -4/3) = 0
x - 9/2 = 0  or  x - -4/3 = 0
x = 9/2
x = -4/3


Input: Find x in x^2 - 47/18x + 5/18 = 0

Output:
x^2 - 47/18x + 5/18 = 0
(x - 1/9)(x - 5/2) = 0
x - 1/9 = 0  or  x - 5/2 = 0
x = 1/9
x = 5/2


Input: Find x for 6x - 3/4 = 0

Output:
6x - 3/4 = 0
6x = 3/4
x = 3/4 / 6
x = 1/8


Input: Solve quickly: 6x + 26 = 0

Output:
6x + 26 = 0
6x = -26
x = -26 / 6
x = -13/3


Input: Solve the equation x^2 - 73/45x + 22/45 = 0

Output:
x^2 - 73/45x + 22/45 = 0
(x - 2/5)(x - 11/9) = 0
x - 2/5 = 0  or  x - 11/9 = 0
x = 2/5
x = 11/9


Input:
Solve the system:
4x + 7y = -692/15
9x + 10y = -1097/15

Output:
4x + 7y = -692/15
9x + 10y = -1097/15

Using elimination
9*(4x + 7y = -692/15)
4*(9x + 10y = -1097/15)
36x + 63y = -2076/5
36x + 40y = -4388/15
Subtract equations
23y = -368/3
y = -368/3/23
y = -16/3

Substitute y
4x + 7(-16/3) = -692/15
4x = -44/5
x = -44/5/4
x = -11/5


Input: Find the solution to x^3 - 7/2x^2 + 189/64x - 171/256 = 0

Output:
x^3 - 7/2x^2 + 189/64x - 171/256 = 0
(x - 3/8)(x - 3/4)(x - 19/8) = 0
x - 3/8 = 0
x - 3/4 = 0
x - 19/8 = 0
x = 3/8
x = 3/4
x = 19/8


Input: Find the solution to x^3 - 125/7x^2 - 26/7x + 144/7 = 0

Output:
x^3 - 125/7x^2 - 26/7x + 144/7 = 0
(x - -8/7)(x - 1)(x - 18) = 0
x - -8/7 = 0
x - 1 = 0
x - 18 = 0
x = -8/7
x = 1
x = 18


Input: Solve quickly: x^3 - 160/9x^2 - 43/9x + 14 = 0

Output:
x^3 - 160/9x^2 - 43/9x + 14 = 0
(x - -1)(x - 7/9)(x - 18) = 0
x - -1 = 0
x - 7/9 = 0
x - 18 = 0
x = -1
x = 7/9
x = 18


Input: Compute the solution of x^2 - 62/45x + 7/15 = 0

Output:
x^2 - 62/45x + 7/15 = 0
(x - 3/5)(x - 7/9) = 0
x - 3/5 = 0  or  x - 7/9 = 0
x = 3/5
x = 7/9


Input: Solve quickly: 3x + 33/7 = 0

Output:
3x + 33/7 = 0
3x = -33/7
x = -33/7 / 3
x = -11/7


Input: Find x in x^3 - 73/12x^2 - 35/8x + 117/4 = 0

Output:
x^3 - 73/12x^2 - 35/8x + 117/4 = 0
(x - 6)(x - -13/6)(x - 9/4) = 0
x - 6 = 0
x - -13/6 = 0
x - 9/4 = 0
x = 6
x = -13/6
x = 9/4


Input: Find x in 5x + 45/4 = 0

Output:
5x + 45/4 = 0
5x = -45/4
x = -45/4 / 5
x = -9/4


Input: Compute the solution of x^3 + 33/5x^2 - 437/5x - 273/5 = 0

Output:
x^3 + 33/5x^2 - 437/5x - 273/5 = 0
(x - 7)(x - -13)(x - -3/5) = 0
x - 7 = 0
x - -13 = 0
x - -3/5 = 0
x = 7
x = -13
x = -3/5


Input: Find the solution to x^3 + 134/21x^2 - 289/147x - 20/49 = 0

Output:
x^3 + 134/21x^2 - 289/147x - 20/49 = 0
(x - -1/7)(x - 3/7)(x - -20/3) = 0
x - -1/7 = 0
x - 3/7 = 0
x - -20/3 = 0
x = -1/7
x = 3/7
x = -20/3


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

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


Input: Compute the solution of x^3 + 56/15x^2 + 191/75x - 42/25 = 0

Output:
x^3 + 56/15x^2 + 191/75x - 42/25 = 0
(x - 2/5)(x - -7/3)(x - -9/5) = 0
x - 2/5 = 0
x - -7/3 = 0
x - -9/5 = 0
x = 2/5
x = -7/3
x = -9/5


Input: Solve 6x + 24/5 = 0

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


Input: Solve 9x - 72 = 0

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


Input: Find the solution to 6x  = 0

Output:
6x  = 0
6x = 0
x = 0 / 6
x = 0


Input:
Find x and y such that
6x + 6y = 172/15
5x + 7y = 502/45

Output:
6x + 6y = 172/15
5x + 7y = 502/45

Using elimination
5*(6x + 6y = 172/15)
6*(5x + 7y = 502/45)
30x + 30y = 172/3
30x + 42y = 1004/15
Subtract equations
-12y = -48/5
y = -48/5/-12
y = 4/5

Substitute y
6x + 6(4/5) = 172/15
6x = 20/3
x = 20/3/6
x = 10/9


Input: Find x for x^2 + 13/10x  = 0

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


Input: Determine x in x^2 + 14x + 40 = 0

Output:
x^2 + 14x + 40 = 0
(x - -10)(x - -4) = 0
x - -10 = 0  or  x - -4 = 0
x = -10
x = -4


Input: Determine x in 5x + 10/7 = 0

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


Input: Determine x in 3x + 27/10 = 0

Output:
3x + 27/10 = 0
3x = -27/10
x = -27/10 / 3
x = -9/10


Input:
Find x and y such that
8x + 4y = 520/7
6x + 7y = 894/7

Output:
8x + 4y = 520/7
6x + 7y = 894/7

Using elimination
6*(8x + 4y = 520/7)
8*(6x + 7y = 894/7)
48x + 24y = 3120/7
48x + 56y = 7152/7
Subtract equations
-32y = -576
y = -576/-32
y = 18

Substitute y
8x + 4(18) = 520/7
8x = 16/7
x = 16/7/8
x = 2/7


Input: Solve quickly: x^2 - 67/15x - 44/3 = 0

Output:
x^2 - 67/15x - 44/3 = 0
(x - 20/3)(x - -11/5) = 0
x - 20/3 = 0  or  x - -11/5 = 0
x = 20/3
x = -11/5


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

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


Input: Compute the solution of x^2 - 41/14x + 15/7 = 0

Output:
x^2 - 41/14x + 15/7 = 0
(x - 3/2)(x - 10/7) = 0
x - 3/2 = 0  or  x - 10/7 = 0
x = 3/2
x = 10/7


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

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


Input: Find x in x^2 - 16/9x + 5/27 = 0

Output:
x^2 - 16/9x + 5/27 = 0
(x - 1/9)(x - 5/3) = 0
x - 1/9 = 0  or  x - 5/3 = 0
x = 1/9
x = 5/3


Input: Find x for 6x + 12/5 = 0

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


Input: Find x for 10x + 170/9 = 0

Output:
10x + 170/9 = 0
10x = -170/9
x = -170/9 / 10
x = -17/9


Input: Solve x^2 - 68/15x + 64/15 = 0

Output:
x^2 - 68/15x + 64/15 = 0
(x - 16/5)(x - 4/3) = 0
x - 16/5 = 0  or  x - 4/3 = 0
x = 16/5
x = 4/3


Input:
Solve the system:
3x + 8y = -54
4x + 8y = -72

Output:
3x + 8y = -54
4x + 8y = -72

Using elimination
4*(3x + 8y = -54)
3*(4x + 8y = -72)
12x + 32y = -216
12x + 24y = -216
Subtract equations
8y = 0
y = 0/8
y = 0

Substitute y
3x + 8(0) = -54
3x = -54
x = -54/3
x = -18


Input: Find x in 9x - 63/2 = 0

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


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

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


Input: Find the solution to x^3 - 27/2x^2 + 207/4x - 405/8 = 0

Output:
x^3 - 27/2x^2 + 207/4x - 405/8 = 0
(x - 3/2)(x - 15/2)(x - 9/2) = 0
x - 3/2 = 0
x - 15/2 = 0
x - 9/2 = 0
x = 3/2
x = 15/2
x = 9/2


Input:
Solve the system:
2x + 8y = -6
7x + 2y = -55/2

Output:
2x + 8y = -6
7x + 2y = -55/2

Using elimination
7*(2x + 8y = -6)
2*(7x + 2y = -55/2)
14x + 56y = -42
14x + 4y = -55
Subtract equations
52y = 13
y = 13/52
y = 1/4

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


Input:
Find x and y such that
3x + 1y = -71/5
2x + 8y = -634/5

Output:
3x + 1y = -71/5
2x + 8y = -634/5

Using elimination
2*(3x + 1y = -71/5)
3*(2x + 8y = -634/5)
6x + 2y = -142/5
6x + 24y = -1902/5
Subtract equations
-22y = 352
y = 352/-22
y = -16

Substitute y
3x + 1(-16) = -71/5
3x = 9/5
x = 9/5/3
x = 3/5


Input:
Solve the equations:
10x + 9y = -86
4x + 9y = -110

Output:
10x + 9y = -86
4x + 9y = -110

Using elimination
4*(10x + 9y = -86)
10*(4x + 9y = -110)
40x + 36y = -344
40x + 90y = -1100
Subtract equations
-54y = 756
y = 756/-54
y = -14

Substitute y
10x + 9(-14) = -86
10x = 40
x = 40/10
x = 4


Input: Determine x in 1x - 4 = 0

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


Input: Solve x^2 + 61/28x - 17/28 = 0

Output:
x^2 + 61/28x - 17/28 = 0
(x - 1/4)(x - -17/7) = 0
x - 1/4 = 0  or  x - -17/7 = 0
x = 1/4
x = -17/7


Input: Find x in 9x + 9 = 0

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


Input: Find x for x^2 + 39/10x + 27/10 = 0

Output:
x^2 + 39/10x + 27/10 = 0
(x - -9/10)(x - -3) = 0
x - -9/10 = 0  or  x - -3 = 0
x = -9/10
x = -3


Input: Solve x^3 + 83/9x^2 + 250/27x - 112/27 = 0

Output:
x^3 + 83/9x^2 + 250/27x - 112/27 = 0
(x - 1/3)(x - -14/9)(x - -8) = 0
x - 1/3 = 0
x - -14/9 = 0
x - -8 = 0
x = 1/3
x = -14/9
x = -8


Input: Solve the equation 2x - 5/4 = 0

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


Input: Solve quickly: x^3 - 7/15x^2 - 31/3x - 133/15 = 0

Output:
x^3 - 7/15x^2 - 31/3x - 133/15 = 0
(x - -1)(x - 19/5)(x - -7/3) = 0
x - -1 = 0
x - 19/5 = 0
x - -7/3 = 0
x = -1
x = 19/5
x = -7/3


Input:
Solve simultaneously:
7x + 3y = -1067/42
5x + 10y = -1375/42

Output:
7x + 3y = -1067/42
5x + 10y = -1375/42

Using elimination
5*(7x + 3y = -1067/42)
7*(5x + 10y = -1375/42)
35x + 15y = -5335/42
35x + 70y = -1375/6
Subtract equations
-55y = 715/7
y = 715/7/-55
y = -13/7

Substitute y
7x + 3(-13/7) = -1067/42
7x = -119/6
x = -119/6/7
x = -17/6


Input: Find x in 7x + 35 = 0

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


Input: Solve the equation 10x + 6 = 0

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


Input: Find x in x^3 - 35/36x^2 - 49/36x  = 0

Output:
x^3 - 35/36x^2 - 49/36x  = 0
(x - 0)(x - -7/9)(x - 7/4) = 0
x - 0 = 0
x - -7/9 = 0
x - 7/4 = 0
x = 0
x = -7/9
x = 7/4


Input: Compute the solution of x^3  - 64x  = 0

Output:
x^3  - 64x  = 0
(x - 0)(x - 8)(x - -8) = 0
x - 0 = 0
x - 8 = 0
x - -8 = 0
x = 0
x = 8
x = -8


Input: Solve x^2  - 16 = 0

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


Input:
Solve simultaneously:
7x + 2y = -55/3
2x + 1y = -14/3

Output:
7x + 2y = -55/3
2x + 1y = -14/3

Using elimination
2*(7x + 2y = -55/3)
7*(2x + 1y = -14/3)
14x + 4y = -110/3
14x + 7y = -98/3
Subtract equations
-3y = -4
y = -4/-3
y = 4/3

Substitute y
7x + 2(4/3) = -55/3
7x = -21
x = -21/7
x = -3


Input:
Solve the system:
2x + 9y = 49/9
9x + 4y = -12

Output:
2x + 9y = 49/9
9x + 4y = -12

Using elimination
9*(2x + 9y = 49/9)
2*(9x + 4y = -12)
18x + 81y = 49
18x + 8y = -24
Subtract equations
73y = 73
y = 73/73
y = 1

Substitute y
2x + 9(1) = 49/9
2x = -32/9
x = -32/9/2
x = -16/9


Input: Find x for x^3 - 1/2x^2 - 4x + 2 = 0

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


Input:
Solve the equations:
5x + 5y = -770/9
6x + 3y = -298/3

Output:
5x + 5y = -770/9
6x + 3y = -298/3

Using elimination
6*(5x + 5y = -770/9)
5*(6x + 3y = -298/3)
30x + 30y = -1540/3
30x + 15y = -1490/3
Subtract equations
15y = -50/3
y = -50/3/15
y = -10/9

Substitute y
5x + 5(-10/9) = -770/9
5x = -80
x = -80/5
x = -16


Input: Solve quickly: x^3 - 82/21x^2 + 229/84x + 55/28 = 0

Output:
x^3 - 82/21x^2 + 229/84x + 55/28 = 0
(x - 5/2)(x - 11/6)(x - -3/7) = 0
x - 5/2 = 0
x - 11/6 = 0
x - -3/7 = 0
x = 5/2
x = 11/6
x = -3/7


Input: Find the solution to x^2 + 4/15x - 7/3 = 0

Output:
x^2 + 4/15x - 7/3 = 0
(x - -5/3)(x - 7/5) = 0
x - -5/3 = 0  or  x - 7/5 = 0
x = -5/3
x = 7/5


Input: Solve quickly: 4x + 4 = 0

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


Input: Find x in x^3 - 229/30x^2 - 251/10x + 2261/15 = 0

Output:
x^3 - 229/30x^2 - 251/10x + 2261/15 = 0
(x - 19/5)(x - 17/2)(x - -14/3) = 0
x - 19/5 = 0
x - 17/2 = 0
x - -14/3 = 0
x = 19/5
x = 17/2
x = -14/3


Input: Solve x^2 + 121/35x + 78/35 = 0

Output:
x^2 + 121/35x + 78/35 = 0
(x - -6/7)(x - -13/5) = 0
x - -6/7 = 0  or  x - -13/5 = 0
x = -6/7
x = -13/5


Input: Find the solution to 10x - 9 = 0

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


Input: What value of x satisfies x^2 - 47/30x - 187/30 = 0

Output:
x^2 - 47/30x - 187/30 = 0
(x - 17/5)(x - -11/6) = 0
x - 17/5 = 0  or  x - -11/6 = 0
x = 17/5
x = -11/6


Input: Find the solution to x^3 + 32/35x^2 - 2031/700x - 459/175 = 0

Output:
x^3 + 32/35x^2 - 2031/700x - 459/175 = 0
(x - -9/10)(x - -12/7)(x - 17/10) = 0
x - -9/10 = 0
x - -12/7 = 0
x - 17/10 = 0
x = -9/10
x = -12/7
x = 17/10


Input:
Solve the system:
3x + 4y = 43/5
1x + 4y = -7/5

Output:
3x + 4y = 43/5
1x + 4y = -7/5

Using elimination
1*(3x + 4y = 43/5)
3*(1x + 4y = -7/5)
3x + 4y = 43/5
3x + 12y = -21/5
Subtract equations
-8y = 64/5
y = 64/5/-8
y = -8/5

Substitute y
3x + 4(-8/5) = 43/5
3x = 15
x = 15/3
x = 5


Input: Solve quickly: 3x + 3/8 = 0

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


Input: Solve quickly: x^2 + 55/8x - 9 = 0

Output:
x^2 + 55/8x - 9 = 0
(x - -8)(x - 9/8) = 0
x - -8 = 0  or  x - 9/8 = 0
x = -8
x = 9/8


Input: What value of x satisfies x^2 + 5/2x - 39/16 = 0

Output:
x^2 + 5/2x - 39/16 = 0
(x - -13/4)(x - 3/4) = 0
x - -13/4 = 0  or  x - 3/4 = 0
x = -13/4
x = 3/4


Input: Determine x in 6x - 3 = 0

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


Input: Determine x in x^2 + 226/45x + 209/45 = 0

Output:
x^2 + 226/45x + 209/45 = 0
(x - -11/9)(x - -19/5) = 0
x - -11/9 = 0  or  x - -19/5 = 0
x = -11/9
x = -19/5


Input: Compute the solution of x^3 - 11/10x^2 - 114/25x + 297/50 = 0

Output:
x^3 - 11/10x^2 - 114/25x + 297/50 = 0
(x - 9/5)(x - 3/2)(x - -11/5) = 0
x - 9/5 = 0
x - 3/2 = 0
x - -11/5 = 0
x = 9/5
x = 3/2
x = -11/5


Input: Find x for 5x - 55/3 = 0

Output:
5x - 55/3 = 0
5x = 55/3
x = 55/3 / 5
x = 11/3


Input: Find the solution to x^3 - 4/5x^2 - 73/100x + 11/25 = 0

Output:
x^3 - 4/5x^2 - 73/100x + 11/25 = 0
(x - 11/10)(x - 1/2)(x - -4/5) = 0
x - 11/10 = 0
x - 1/2 = 0
x - -4/5 = 0
x = 11/10
x = 1/2
x = -4/5


Input: Determine x in x^3 + 137/45x^2 + 124/45x + 32/45 = 0

Output:
x^3 + 137/45x^2 + 124/45x + 32/45 = 0
(x - -1)(x - -8/5)(x - -4/9) = 0
x - -1 = 0
x - -8/5 = 0
x - -4/9 = 0
x = -1
x = -8/5
x = -4/9


Input: Solve the equation x^3 + 34/21x^2 + 3/7x  = 0

Output:
x^3 + 34/21x^2 + 3/7x  = 0
(x - -1/3)(x - -9/7)(x - 0) = 0
x - -1/3 = 0
x - -9/7 = 0
x - 0 = 0
x = -1/3
x = -9/7
x = 0


Input: Solve x^3 + 15/4x^2 - 17/2x - 45/4 = 0

Output:
x^3 + 15/4x^2 - 17/2x - 45/4 = 0
(x - -5)(x - 9/4)(x - -1) = 0
x - -5 = 0
x - 9/4 = 0
x - -1 = 0
x = -5
x = 9/4
x = -1


Input: Compute the solution of x^2 - 9/2x + 5 = 0

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


Input: Solve the equation x^2 + 29/4x + 15/2 = 0

Output:
x^2 + 29/4x + 15/2 = 0
(x - -6)(x - -5/4) = 0
x - -6 = 0  or  x - -5/4 = 0
x = -6
x = -5/4


Input:
Find x and y such that
9x + 8y = 671/6
7x + 2y = 353/6

Output:
9x + 8y = 671/6
7x + 2y = 353/6

Using elimination
7*(9x + 8y = 671/6)
9*(7x + 2y = 353/6)
63x + 56y = 4697/6
63x + 18y = 1059/2
Subtract equations
38y = 760/3
y = 760/3/38
y = 20/3

Substitute y
9x + 8(20/3) = 671/6
9x = 117/2
x = 117/2/9
x = 13/2


Input: What value of x satisfies 4x + 28/3 = 0

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


Input:
Find x and y such that
8x + 2y = 109/15
1x + 5y = -43/6

Output:
8x + 2y = 109/15
1x + 5y = -43/6

Using elimination
1*(8x + 2y = 109/15)
8*(1x + 5y = -43/6)
8x + 2y = 109/15
8x + 40y = -172/3
Subtract equations
-38y = 323/5
y = 323/5/-38
y = -17/10

Substitute y
8x + 2(-17/10) = 109/15
8x = 32/3
x = 32/3/8
x = 4/3


Input: Solve x^2 - 41/5x + 42/5 = 0

Output:
x^2 - 41/5x + 42/5 = 0
(x - 7)(x - 6/5) = 0
x - 7 = 0  or  x - 6/5 = 0
x = 7
x = 6/5


Input: What value of x satisfies 4x + 18 = 0

Output:
4x + 18 = 0
4x = -18
x = -18 / 4
x = -9/2


Input:
Solve the system:
3x + 1y = 48/5
8x + 6y = 148/5

Output:
3x + 1y = 48/5
8x + 6y = 148/5

Using elimination
8*(3x + 1y = 48/5)
3*(8x + 6y = 148/5)
24x + 8y = 384/5
24x + 18y = 444/5
Subtract equations
-10y = -12
y = -12/-10
y = 6/5

Substitute y
3x + 1(6/5) = 48/5
3x = 42/5
x = 42/5/3
x = 14/5


Input: Solve x^2 + 55/28x - 68/7 = 0

Output:
x^2 + 55/28x - 68/7 = 0
(x - 16/7)(x - -17/4) = 0
x - 16/7 = 0  or  x - -17/4 = 0
x = 16/7
x = -17/4


Input:
Find x and y such that
2x + 8y = -49/5
8x + 4y = -56/5

Output:
2x + 8y = -49/5
8x + 4y = -56/5

Using elimination
8*(2x + 8y = -49/5)
2*(8x + 4y = -56/5)
16x + 64y = -392/5
16x + 8y = -112/5
Subtract equations
56y = -56
y = -56/56
y = -1

Substitute y
2x + 8(-1) = -49/5
2x = -9/5
x = -9/5/2
x = -9/10


Input:
Find x and y such that
5x + 1y = 80/3
7x + 8y = 244/3

Output:
5x + 1y = 80/3
7x + 8y = 244/3

Using elimination
7*(5x + 1y = 80/3)
5*(7x + 8y = 244/3)
35x + 7y = 560/3
35x + 40y = 1220/3
Subtract equations
-33y = -220
y = -220/-33
y = 20/3

Substitute y
5x + 1(20/3) = 80/3
5x = 20
x = 20/5
x = 4


Input:
Solve the system:
2x + 7y = -18
2x + 5y = -27/2

Output:
2x + 7y = -18
2x + 5y = -27/2

Using elimination
2*(2x + 7y = -18)
2*(2x + 5y = -27/2)
4x + 14y = -36
4x + 10y = -27
Subtract equations
4y = -9
y = -9/4
y = -9/4

Substitute y
2x + 7(-9/4) = -18
2x = -9/4
x = -9/4/2
x = -9/8


Input: Solve the equation x^3 - 191/84x^2 - 43/24x + 5/14 = 0

Output:
x^3 - 191/84x^2 - 43/24x + 5/14 = 0
(x - 20/7)(x - -3/4)(x - 1/6) = 0
x - 20/7 = 0
x - -3/4 = 0
x - 1/6 = 0
x = 20/7
x = -3/4
x = 1/6


Input: Find x for 10x + 5/4 = 0

Output:
10x + 5/4 = 0
10x = -5/4
x = -5/4 / 10
x = -1/8


Input:
Solve the system:
1x + 1y = -239/63
8x + 9y = -228/7

Output:
1x + 1y = -239/63
8x + 9y = -228/7

Using elimination
8*(1x + 1y = -239/63)
1*(8x + 9y = -228/7)
8x + 8y = -1912/63
8x + 9y = -228/7
Subtract equations
-1y = 20/9
y = 20/9/-1
y = -20/9

Substitute y
1x + 1(-20/9) = -239/63
1x = -11/7
x = -11/7/1
x = -11/7


Input:
Solve simultaneously:
4x + 6y = 146/3
5x + 3y = 203/6

Output:
4x + 6y = 146/3
5x + 3y = 203/6

Using elimination
5*(4x + 6y = 146/3)
4*(5x + 3y = 203/6)
20x + 30y = 730/3
20x + 12y = 406/3
Subtract equations
18y = 108
y = 108/18
y = 6

Substitute y
4x + 6(6) = 146/3
4x = 38/3
x = 38/3/4
x = 19/6


Input: Solve the equation 5x - 5 = 0

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


Input:
Solve the equations:
5x + 1y = 88/3
6x + 10y = 88/3

Output:
5x + 1y = 88/3
6x + 10y = 88/3

Using elimination
6*(5x + 1y = 88/3)
5*(6x + 10y = 88/3)
30x + 6y = 176
30x + 50y = 440/3
Subtract equations
-44y = 88/3
y = 88/3/-44
y = -2/3

Substitute y
5x + 1(-2/3) = 88/3
5x = 30
x = 30/5
x = 6


Input: Solve x^3 + 149/45x^2 - 61/12x + 6/5 = 0

Output:
x^3 + 149/45x^2 - 61/12x + 6/5 = 0
(x - 3/10)(x - -9/2)(x - 8/9) = 0
x - 3/10 = 0
x - -9/2 = 0
x - 8/9 = 0
x = 3/10
x = -9/2
x = 8/9


Input:
Solve the equations:
5x + 3y = -3/2
2x + 8y = -29/3

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

Using elimination
2*(5x + 3y = -3/2)
5*(2x + 8y = -29/3)
10x + 6y = -3
10x + 40y = -145/3
Subtract equations
-34y = 136/3
y = 136/3/-34
y = -4/3

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


Input: Solve quickly: 3x + 9 = 0

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


Input: Find x in 1x - 9/5 = 0

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


Input: Solve quickly: x^2 + 49/18x + 49/27 = 0

Output:
x^2 + 49/18x + 49/27 = 0
(x - -14/9)(x - -7/6) = 0
x - -14/9 = 0  or  x - -7/6 = 0
x = -14/9
x = -7/6


Input: Solve the equation 8x + 13 = 0

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


Input: Find x in x^2 + 37/6x - 13/6 = 0

Output:
x^2 + 37/6x - 13/6 = 0
(x - 1/3)(x - -13/2) = 0
x - 1/3 = 0  or  x - -13/2 = 0
x = 1/3
x = -13/2


Input: Compute the solution of x^3 + 17/3x^2 + 28/3x + 4 = 0

Output:
x^3 + 17/3x^2 + 28/3x + 4 = 0
(x - -3)(x - -2/3)(x - -2) = 0
x - -3 = 0
x - -2/3 = 0
x - -2 = 0
x = -3
x = -2/3
x = -2


Input:
Solve the equations:
8x + 7y = 114/5
7x + 6y = 199/10

Output:
8x + 7y = 114/5
7x + 6y = 199/10

Using elimination
7*(8x + 7y = 114/5)
8*(7x + 6y = 199/10)
56x + 49y = 798/5
56x + 48y = 796/5
Subtract equations
1y = 2/5
y = 2/5/1
y = 2/5

Substitute y
8x + 7(2/5) = 114/5
8x = 20
x = 20/8
x = 5/2


Input: Find x for x^3 + 21/4x^2 - 103/4x - 30 = 0

Output:
x^3 + 21/4x^2 - 103/4x - 30 = 0
(x - -8)(x - 15/4)(x - -1) = 0
x - -8 = 0
x - 15/4 = 0
x - -1 = 0
x = -8
x = 15/4
x = -1


Input: Solve the equation 2x + 4 = 0

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


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

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


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

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


Input: Find x in x^3 + 9/5x^2 - 3/100x - 17/50 = 0

Output:
x^3 + 9/5x^2 - 3/100x - 17/50 = 0
(x - -1/2)(x - -17/10)(x - 2/5) = 0
x - -1/2 = 0
x - -17/10 = 0
x - 2/5 = 0
x = -1/2
x = -17/10
x = 2/5


Input: Find x for 6x - 30 = 0

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


Input: Determine x in x^2 + 5/6x - 1/6 = 0

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


Input:
Solve the equations:
5x + 8y = -455/72
10x + 6y = -85/12

Output:
5x + 8y = -455/72
10x + 6y = -85/12

Using elimination
10*(5x + 8y = -455/72)
5*(10x + 6y = -85/12)
50x + 80y = -2275/36
50x + 30y = -425/12
Subtract equations
50y = -250/9
y = -250/9/50
y = -5/9

Substitute y
5x + 8(-5/9) = -455/72
5x = -15/8
x = -15/8/5
x = -3/8


Input:
Solve the equations:
7x + 6y = 39/4
9x + 1y = 419/12

Output:
7x + 6y = 39/4
9x + 1y = 419/12

Using elimination
9*(7x + 6y = 39/4)
7*(9x + 1y = 419/12)
63x + 54y = 351/4
63x + 7y = 2933/12
Subtract equations
47y = -470/3
y = -470/3/47
y = -10/3

Substitute y
7x + 6(-10/3) = 39/4
7x = 119/4
x = 119/4/7
x = 17/4


Input: Solve x^2 - 27/20x - 7/10 = 0

Output:
x^2 - 27/20x - 7/10 = 0
(x - -2/5)(x - 7/4) = 0
x - -2/5 = 0  or  x - 7/4 = 0
x = -2/5
x = 7/4


Input: What value of x satisfies 10x - 4 = 0

Output:
10x - 4 = 0
10x = 4
x = 4 / 10
x = 2/5


Input: Find the solution to x^2 + 11/21x - 2/21 = 0

Output:
x^2 + 11/21x - 2/21 = 0
(x - 1/7)(x - -2/3) = 0
x - 1/7 = 0  or  x - -2/3 = 0
x = 1/7
x = -2/3


Input: Solve the equation x^2 + 25/4x + 63/8 = 0

Output:
x^2 + 25/4x + 63/8 = 0
(x - -7/4)(x - -9/2) = 0
x - -7/4 = 0  or  x - -9/2 = 0
x = -7/4
x = -9/2


Input: Find the solution to x^3 + 97/45x^2 + 206/135x + 16/45 = 0

Output:
x^3 + 97/45x^2 + 206/135x + 16/45 = 0
(x - -3/5)(x - -2/3)(x - -8/9) = 0
x - -3/5 = 0
x - -2/3 = 0
x - -8/9 = 0
x = -3/5
x = -2/3
x = -8/9


Input: Compute the solution of x^2 - 5x - 6 = 0

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


Input: Find the solution to x^2 - 23/8x + 15/8 = 0

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


Input:
Solve the equations:
7x + 2y = -121/5
5x + 5y = -18

Output:
7x + 2y = -121/5
5x + 5y = -18

Using elimination
5*(7x + 2y = -121/5)
7*(5x + 5y = -18)
35x + 10y = -121
35x + 35y = -126
Subtract equations
-25y = 5
y = 5/-25
y = -1/5

Substitute y
7x + 2(-1/5) = -121/5
7x = -119/5
x = -119/5/7
x = -17/5


Input: Determine x in x^2 - 14/5x + 8/5 = 0

Output:
x^2 - 14/5x + 8/5 = 0
(x - 4/5)(x - 2) = 0
x - 4/5 = 0  or  x - 2 = 0
x = 4/5
x = 2


Input: Find x for 10x - 20 = 0

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


Input:
Find x and y such that
8x + 3y = 41/6
4x + 7y = 27/2

Output:
8x + 3y = 41/6
4x + 7y = 27/2

Using elimination
4*(8x + 3y = 41/6)
8*(4x + 7y = 27/2)
32x + 12y = 82/3
32x + 56y = 108
Subtract equations
-44y = -242/3
y = -242/3/-44
y = 11/6

Substitute y
8x + 3(11/6) = 41/6
8x = 4/3
x = 4/3/8
x = 1/6


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

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


Input: Find x for x^2 - 21/8x - 49/16 = 0

Output:
x^2 - 21/8x - 49/16 = 0
(x - 7/2)(x - -7/8) = 0
x - 7/2 = 0  or  x - -7/8 = 0
x = 7/2
x = -7/8


Input:
Find x and y such that
8x + 1y = -99/5
5x + 1y = -63/5

Output:
8x + 1y = -99/5
5x + 1y = -63/5

Using elimination
5*(8x + 1y = -99/5)
8*(5x + 1y = -63/5)
40x + 5y = -99
40x + 8y = -504/5
Subtract equations
-3y = 9/5
y = 9/5/-3
y = -3/5

Substitute y
8x + 1(-3/5) = -99/5
8x = -96/5
x = -96/5/8
x = -12/5


Input: Solve the equation 1x + 3/5 = 0

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


Input: Solve quickly: x^2 - 82/15x + 112/15 = 0

Output:
x^2 - 82/15x + 112/15 = 0
(x - 8/3)(x - 14/5) = 0
x - 8/3 = 0  or  x - 14/5 = 0
x = 8/3
x = 14/5


Input: What value of x satisfies x^3 + 493/140x^2 + 467/140x + 33/35 = 0

Output:
x^3 + 493/140x^2 + 467/140x + 33/35 = 0
(x - -4/7)(x - -11/5)(x - -3/4) = 0
x - -4/7 = 0
x - -11/5 = 0
x - -3/4 = 0
x = -4/7
x = -11/5
x = -3/4


Input: Solve x^3 + 212/15x^2 + 9/5x - 14/15 = 0

Output:
x^3 + 212/15x^2 + 9/5x - 14/15 = 0
(x - -1/3)(x - -14)(x - 1/5) = 0
x - -1/3 = 0
x - -14 = 0
x - 1/5 = 0
x = -1/3
x = -14
x = 1/5


Input: Solve the equation 7x - 77 = 0

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


Input: Determine x in 6x - 36/5 = 0

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


Input:
Solve the equations:
4x + 9y = 8
7x + 4y = -19/2

Output:
4x + 9y = 8
7x + 4y = -19/2

Using elimination
7*(4x + 9y = 8)
4*(7x + 4y = -19/2)
28x + 63y = 56
28x + 16y = -38
Subtract equations
47y = 94
y = 94/47
y = 2

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


Input:
Find x and y such that
7x + 9y = -115/8
10x + 9y = -1069/56

Output:
7x + 9y = -115/8
10x + 9y = -1069/56

Using elimination
10*(7x + 9y = -115/8)
7*(10x + 9y = -1069/56)
70x + 90y = -575/4
70x + 63y = -1069/8
Subtract equations
27y = -81/8
y = -81/8/27
y = -3/8

Substitute y
7x + 9(-3/8) = -115/8
7x = -11
x = -11/7
x = -11/7


Input: Compute the solution of x^2 - 5/6x - 13/2 = 0

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


Input: Solve the equation 8x + 28/3 = 0

Output:
8x + 28/3 = 0
8x = -28/3
x = -28/3 / 8
x = -7/6


Input: Determine x in x^3 - 53/12x^2 - 14/3x + 49/3 = 0

Output:
x^3 - 53/12x^2 - 14/3x + 49/3 = 0
(x - 14/3)(x - -2)(x - 7/4) = 0
x - 14/3 = 0
x - -2 = 0
x - 7/4 = 0
x = 14/3
x = -2
x = 7/4


Input: Solve x^2 - 44/3x - 60 = 0

Output:
x^2 - 44/3x - 60 = 0
(x - 18)(x - -10/3) = 0
x - 18 = 0  or  x - -10/3 = 0
x = 18
x = -10/3


Input: Determine x in 9x - 27 = 0

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


Input: Solve quickly: x^3 - 17/6x^2 - 11/6x + 7 = 0

Output:
x^3 - 17/6x^2 - 11/6x + 7 = 0
(x - -3/2)(x - 2)(x - 7/3) = 0
x - -3/2 = 0
x - 2 = 0
x - 7/3 = 0
x = -3/2
x = 2
x = 7/3


Input: Solve quickly: x^2 + 25/2x - 75/2 = 0

Output:
x^2 + 25/2x - 75/2 = 0
(x - 5/2)(x - -15) = 0
x - 5/2 = 0  or  x - -15 = 0
x = 5/2
x = -15


Input: Solve the equation x^2 + 13/5x - 63/20 = 0

Output:
x^2 + 13/5x - 63/20 = 0
(x - 9/10)(x - -7/2) = 0
x - 9/10 = 0  or  x - -7/2 = 0
x = 9/10
x = -7/2


Input: Compute the solution of x^3 - 10/7x^2 - 11/49x  = 0

Output:
x^3 - 10/7x^2 - 11/49x  = 0
(x - 0)(x - 11/7)(x - -1/7) = 0
x - 0 = 0
x - 11/7 = 0
x - -1/7 = 0
x = 0
x = 11/7
x = -1/7


Input:
Solve the system:
1x + 9y = 225/4
8x + 7y = 60

Output:
1x + 9y = 225/4
8x + 7y = 60

Using elimination
8*(1x + 9y = 225/4)
1*(8x + 7y = 60)
8x + 72y = 450
8x + 7y = 60
Subtract equations
65y = 390
y = 390/65
y = 6

Substitute y
1x + 9(6) = 225/4
1x = 9/4
x = 9/4/1
x = 9/4


Input:
Solve the system:
3x + 6y = 36/5
3x + 7y = 41/5

Output:
3x + 6y = 36/5
3x + 7y = 41/5

Using elimination
3*(3x + 6y = 36/5)
3*(3x + 7y = 41/5)
9x + 18y = 108/5
9x + 21y = 123/5
Subtract equations
-3y = -3
y = -3/-3
y = 1

Substitute y
3x + 6(1) = 36/5
3x = 6/5
x = 6/5/3
x = 2/5


Input:
Find x and y such that
3x + 7y = -15/2
10x + 1y = 185/6

Output:
3x + 7y = -15/2
10x + 1y = 185/6

Using elimination
10*(3x + 7y = -15/2)
3*(10x + 1y = 185/6)
30x + 70y = -75
30x + 3y = 185/2
Subtract equations
67y = -335/2
y = -335/2/67
y = -5/2

Substitute y
3x + 7(-5/2) = -15/2
3x = 10
x = 10/3
x = 10/3


Input:
Solve the equations:
1x + 8y = -97/10
4x + 5y = -37/10

Output:
1x + 8y = -97/10
4x + 5y = -37/10

Using elimination
4*(1x + 8y = -97/10)
1*(4x + 5y = -37/10)
4x + 32y = -194/5
4x + 5y = -37/10
Subtract equations
27y = -351/10
y = -351/10/27
y = -13/10

Substitute y
1x + 8(-13/10) = -97/10
1x = 7/10
x = 7/10/1
x = 7/10


Input: What value of x satisfies 2x - 36/5 = 0

Output:
2x - 36/5 = 0
2x = 36/5
x = 36/5 / 2
x = 18/5


Input:
Solve the system:
10x + 4y = 120
2x + 10y = 24

Output:
10x + 4y = 120
2x + 10y = 24

Using elimination
2*(10x + 4y = 120)
10*(2x + 10y = 24)
20x + 8y = 240
20x + 100y = 240
Subtract equations
-92y = 0
y = 0/-92
y = 0

Substitute y
10x + 4(0) = 120
10x = 120
x = 120/10
x = 12


Input:
Solve simultaneously:
5x + 4y = 137/5
5x + 6y = 143/5

Output:
5x + 4y = 137/5
5x + 6y = 143/5

Using elimination
5*(5x + 4y = 137/5)
5*(5x + 6y = 143/5)
25x + 20y = 137
25x + 30y = 143
Subtract equations
-10y = -6
y = -6/-10
y = 3/5

Substitute y
5x + 4(3/5) = 137/5
5x = 25
x = 25/5
x = 5


Input:
Find x and y such that
1x + 5y = -87/40
8x + 7y = -201/40

Output:
1x + 5y = -87/40
8x + 7y = -201/40

Using elimination
8*(1x + 5y = -87/40)
1*(8x + 7y = -201/40)
8x + 40y = -87/5
8x + 7y = -201/40
Subtract equations
33y = -99/8
y = -99/8/33
y = -3/8

Substitute y
1x + 5(-3/8) = -87/40
1x = -3/10
x = -3/10/1
x = -3/10


Input: Find x for 6x + 102/5 = 0

Output:
6x + 102/5 = 0
6x = -102/5
x = -102/5 / 6
x = -17/5


Input: Solve x^2 - 32/7x + 256/49 = 0

Output:
x^2 - 32/7x + 256/49 = 0
(x - 16/7)(x - 16/7) = 0
x - 16/7 = 0  or  x - 16/7 = 0
x = 16/7
x = 16/7


Input:
Solve simultaneously:
3x + 8y = 25/7
8x + 7y = -13

Output:
3x + 8y = 25/7
8x + 7y = -13

Using elimination
8*(3x + 8y = 25/7)
3*(8x + 7y = -13)
24x + 64y = 200/7
24x + 21y = -39
Subtract equations
43y = 473/7
y = 473/7/43
y = 11/7

Substitute y
3x + 8(11/7) = 25/7
3x = -9
x = -9/3
x = -3


Input:
Solve simultaneously:
6x + 1y = -146/5
5x + 4y = -517/15

Output:
6x + 1y = -146/5
5x + 4y = -517/15

Using elimination
5*(6x + 1y = -146/5)
6*(5x + 4y = -517/15)
30x + 5y = -146
30x + 24y = -1034/5
Subtract equations
-19y = 304/5
y = 304/5/-19
y = -16/5

Substitute y
6x + 1(-16/5) = -146/5
6x = -26
x = -26/6
x = -13/3


Input: Find the solution to x^3 - 9x^2 - 57x + 65 = 0

Output:
x^3 - 9x^2 - 57x + 65 = 0
(x - -5)(x - 13)(x - 1) = 0
x - -5 = 0
x - 13 = 0
x - 1 = 0
x = -5
x = 13
x = 1


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

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


Input:
Find x and y such that
9x + 8y = -111
2x + 3y = -43

Output:
9x + 8y = -111
2x + 3y = -43

Using elimination
2*(9x + 8y = -111)
9*(2x + 3y = -43)
18x + 16y = -222
18x + 27y = -387
Subtract equations
-11y = 165
y = 165/-11
y = -15

Substitute y
9x + 8(-15) = -111
9x = 9
x = 9/9
x = 1


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

Output:
1x - 7/2 = 0
1x = 7/2
x = 7/2 / 1
x = 7/2


Input: Find x for x^2 + 41/24x + 1/2 = 0

Output:
x^2 + 41/24x + 1/2 = 0
(x - -3/8)(x - -4/3) = 0
x - -3/8 = 0  or  x - -4/3 = 0
x = -3/8
x = -4/3


Input: Compute the solution of x^2 - 73/4x + 195/4 = 0

Output:
x^2 - 73/4x + 195/4 = 0
(x - 13/4)(x - 15) = 0
x - 13/4 = 0  or  x - 15 = 0
x = 13/4
x = 15


Input: Solve x^2 + 83/9x + 88/9 = 0

Output:
x^2 + 83/9x + 88/9 = 0
(x - -8)(x - -11/9) = 0
x - -8 = 0  or  x - -11/9 = 0
x = -8
x = -11/9


Input: What value of x satisfies x^3 + 128/7x^2 + 452/7x + 64 = 0

Output:
x^3 + 128/7x^2 + 452/7x + 64 = 0
(x - -2)(x - -14)(x - -16/7) = 0
x - -2 = 0
x - -14 = 0
x - -16/7 = 0
x = -2
x = -14
x = -16/7


Input:
Find x and y such that
3x + 9y = -117/5
3x + 1y = -133/5

Output:
3x + 9y = -117/5
3x + 1y = -133/5

Using elimination
3*(3x + 9y = -117/5)
3*(3x + 1y = -133/5)
9x + 27y = -351/5
9x + 3y = -399/5
Subtract equations
24y = 48/5
y = 48/5/24
y = 2/5

Substitute y
3x + 9(2/5) = -117/5
3x = -27
x = -27/3
x = -9


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

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


Input: Compute the solution of x^2 + 7/5x - 34/5 = 0

Output:
x^2 + 7/5x - 34/5 = 0
(x - -17/5)(x - 2) = 0
x - -17/5 = 0  or  x - 2 = 0
x = -17/5
x = 2


Input: Solve the equation 7x + 63/5 = 0

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


Input:
Find x and y such that
6x + 8y = 160
4x + 6y = 113

Output:
6x + 8y = 160
4x + 6y = 113

Using elimination
4*(6x + 8y = 160)
6*(4x + 6y = 113)
24x + 32y = 640
24x + 36y = 678
Subtract equations
-4y = -38
y = -38/-4
y = 19/2

Substitute y
6x + 8(19/2) = 160
6x = 84
x = 84/6
x = 14


Input:
Solve the system:
1x + 2y = 8
3x + 1y = 23/2

Output:
1x + 2y = 8
3x + 1y = 23/2

Using elimination
3*(1x + 2y = 8)
1*(3x + 1y = 23/2)
3x + 6y = 24
3x + 1y = 23/2
Subtract equations
5y = 25/2
y = 25/2/5
y = 5/2

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


Input: Determine x in x^3 - 183/70x^2 - 422/245x + 144/49 = 0

Output:
x^3 - 183/70x^2 - 422/245x + 144/49 = 0
(x - -8/7)(x - 20/7)(x - 9/10) = 0
x - -8/7 = 0
x - 20/7 = 0
x - 9/10 = 0
x = -8/7
x = 20/7
x = 9/10


Input: Find x in x^2 + 43/9x + 52/27 = 0

Output:
x^2 + 43/9x + 52/27 = 0
(x - -4/9)(x - -13/3) = 0
x - -4/9 = 0  or  x - -13/3 = 0
x = -4/9
x = -13/3


Input: Find x for x^2 + 23/21x - 10/21 = 0

Output:
x^2 + 23/21x - 10/21 = 0
(x - 1/3)(x - -10/7) = 0
x - 1/3 = 0  or  x - -10/7 = 0
x = 1/3
x = -10/7


Input: Solve the equation x^2 - 10x + 200/9 = 0

Output:
x^2 - 10x + 200/9 = 0
(x - 20/3)(x - 10/3) = 0
x - 20/3 = 0  or  x - 10/3 = 0
x = 20/3
x = 10/3


Input: Solve quickly: x^3 + 493/126x^2 - 25/42x - 650/63 = 0

Output:
x^3 + 493/126x^2 - 25/42x - 650/63 = 0
(x - -5/2)(x - 13/9)(x - -20/7) = 0
x - -5/2 = 0
x - 13/9 = 0
x - -20/7 = 0
x = -5/2
x = 13/9
x = -20/7


Input: Solve quickly: x^2 + 5/3x - 19/4 = 0

Output:
x^2 + 5/3x - 19/4 = 0
(x - -19/6)(x - 3/2) = 0
x - -19/6 = 0  or  x - 3/2 = 0
x = -19/6
x = 3/2


Input: Compute the solution of x^3 + 23/2x^2 - 2x - 165/2 = 0

Output:
x^3 + 23/2x^2 - 2x - 165/2 = 0
(x - 5/2)(x - -3)(x - -11) = 0
x - 5/2 = 0
x - -3 = 0
x - -11 = 0
x = 5/2
x = -3
x = -11


Input: Find the solution to 6x + 16 = 0

Output:
6x + 16 = 0
6x = -16
x = -16 / 6
x = -8/3


Input: Solve the equation 8x - 12/5 = 0

Output:
8x - 12/5 = 0
8x = 12/5
x = 12/5 / 8
x = 3/10


Input: Determine x in x^3 - 197/210x^2 - 79/70x + 22/105 = 0

Output:
x^3 - 197/210x^2 - 79/70x + 22/105 = 0
(x - -4/5)(x - 1/6)(x - 11/7) = 0
x - -4/5 = 0
x - 1/6 = 0
x - 11/7 = 0
x = -4/5
x = 1/6
x = 11/7


Input: Find x for 2x - 38/9 = 0

Output:
2x - 38/9 = 0
2x = 38/9
x = 38/9 / 2
x = 19/9


Input:
Solve the system:
2x + 1y = -1/2
8x + 8y = -14

Output:
2x + 1y = -1/2
8x + 8y = -14

Using elimination
8*(2x + 1y = -1/2)
2*(8x + 8y = -14)
16x + 8y = -4
16x + 16y = -28
Subtract equations
-8y = 24
y = 24/-8
y = -3

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


Input: Compute the solution of 7x + 42 = 0

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


Input: Find x for x^3 + 179/28x^2 + 93/8x + 45/7 = 0

Output:
x^3 + 179/28x^2 + 93/8x + 45/7 = 0
(x - -3/2)(x - -15/4)(x - -8/7) = 0
x - -3/2 = 0
x - -15/4 = 0
x - -8/7 = 0
x = -3/2
x = -15/4
x = -8/7


Input: Find the solution to x^3 + 1x^2 - 253/4x - 595/4 = 0

Output:
x^3 + 1x^2 - 253/4x - 595/4 = 0
(x - -5/2)(x - 17/2)(x - -7) = 0
x - -5/2 = 0
x - 17/2 = 0
x - -7 = 0
x = -5/2
x = 17/2
x = -7


Input:
Solve simultaneously:
5x + 6y = 4
10x + 4y = 28/3

Output:
5x + 6y = 4
10x + 4y = 28/3

Using elimination
10*(5x + 6y = 4)
5*(10x + 4y = 28/3)
50x + 60y = 40
50x + 20y = 140/3
Subtract equations
40y = -20/3
y = -20/3/40
y = -1/6

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


Input: Compute the solution of x^3 + 541/35x^2 - 328/35x - 384/35 = 0

Output:
x^3 + 541/35x^2 - 328/35x - 384/35 = 0
(x - -16)(x - 8/7)(x - -3/5) = 0
x - -16 = 0
x - 8/7 = 0
x - -3/5 = 0
x = -16
x = 8/7
x = -3/5


Input: Solve 8x + 24 = 0

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


Input:
Solve simultaneously:
5x + 3y = -32
4x + 4y = -208/5

Output:
5x + 3y = -32
4x + 4y = -208/5

Using elimination
4*(5x + 3y = -32)
5*(4x + 4y = -208/5)
20x + 12y = -128
20x + 20y = -208
Subtract equations
-8y = 80
y = 80/-8
y = -10

Substitute y
5x + 3(-10) = -32
5x = -2
x = -2/5
x = -2/5


Input: Find x in 7x - 112/3 = 0

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


Input: Determine x in x^3 + 367/56x^2 + 27/8x + 9/28 = 0

Output:
x^3 + 367/56x^2 + 27/8x + 9/28 = 0
(x - -6)(x - -1/8)(x - -3/7) = 0
x - -6 = 0
x - -1/8 = 0
x - -3/7 = 0
x = -6
x = -1/8
x = -3/7


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

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


Input: Compute the solution of x^2 + 67/70x + 3/35 = 0

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


Input: Find x for x^3 + 1/5x^2 - 33/20x + 9/20 = 0

Output:
x^3 + 1/5x^2 - 33/20x + 9/20 = 0
(x - 3/10)(x - 1)(x - -3/2) = 0
x - 3/10 = 0
x - 1 = 0
x - -3/2 = 0
x = 3/10
x = 1
x = -3/2


Input:
Solve simultaneously:
10x + 8y = 22
5x + 1y = -1

Output:
10x + 8y = 22
5x + 1y = -1

Using elimination
5*(10x + 8y = 22)
10*(5x + 1y = -1)
50x + 40y = 110
50x + 10y = -10
Subtract equations
30y = 120
y = 120/30
y = 4

Substitute y
10x + 8(4) = 22
10x = -10
x = -10/10
x = -1


Input:
Solve the system:
1x + 3y = -9/5
4x + 3y = -21/5

Output:
1x + 3y = -9/5
4x + 3y = -21/5

Using elimination
4*(1x + 3y = -9/5)
1*(4x + 3y = -21/5)
4x + 12y = -36/5
4x + 3y = -21/5
Subtract equations
9y = -3
y = -3/9
y = -1/3

Substitute y
1x + 3(-1/3) = -9/5
1x = -4/5
x = -4/5/1
x = -4/5


Input: Find x in 5x + 65 = 0

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


Input: Find the solution to 7x - 35/2 = 0

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


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

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


Input: Solve the equation x^2 - 13/5x + 6/5 = 0

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


Input: Determine x in x^2 + 191/9x + 380/9 = 0

Output:
x^2 + 191/9x + 380/9 = 0
(x - -20/9)(x - -19) = 0
x - -20/9 = 0  or  x - -19 = 0
x = -20/9
x = -19


Input: Find the solution to x^3 + 988/45x^2 + 2459/45x - 1292/45 = 0

Output:
x^3 + 988/45x^2 + 2459/45x - 1292/45 = 0
(x - 4/9)(x - -17/5)(x - -19) = 0
x - 4/9 = 0
x - -17/5 = 0
x - -19 = 0
x = 4/9
x = -17/5
x = -19


Input: What value of x satisfies x^3 - 149/120x^2 - 467/240x + 119/60 = 0

Output:
x^3 - 149/120x^2 - 467/240x + 119/60 = 0
(x - 17/10)(x - 7/8)(x - -4/3) = 0
x - 17/10 = 0
x - 7/8 = 0
x - -4/3 = 0
x = 17/10
x = 7/8
x = -4/3


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

Output:
x^2 - 5/6x - 2/3 = 0
(x - 4/3)(x - -1/2) = 0
x - 4/3 = 0  or  x - -1/2 = 0
x = 4/3
x = -1/2


Input: Find the solution to x^3  - 7x - 6 = 0

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


Input:
Find x and y such that
4x + 5y = 1/3
6x + 9y = 0

Output:
4x + 5y = 1/3
6x + 9y = 0

Using elimination
6*(4x + 5y = 1/3)
4*(6x + 9y = 0)
24x + 30y = 2
24x + 36y = 0
Subtract equations
-6y = 2
y = 2/-6
y = -1/3

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


Input: Determine x in x^2 + 74/45x + 13/45 = 0

Output:
x^2 + 74/45x + 13/45 = 0
(x - -13/9)(x - -1/5) = 0
x - -13/9 = 0  or  x - -1/5 = 0
x = -13/9
x = -1/5


Input: Find x in x^3 - 9/2x^2 - 3x + 20 = 0

Output:
x^3 - 9/2x^2 - 3x + 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: Find x for x^3 + 5/2x^2 - 261/2x - 198 = 0

Output:
x^3 + 5/2x^2 - 261/2x - 198 = 0
(x - -12)(x - 11)(x - -3/2) = 0
x - -12 = 0
x - 11 = 0
x - -3/2 = 0
x = -12
x = 11
x = -3/2


Input: Solve quickly: x^2 + 25/3x + 52/3 = 0

Output:
x^2 + 25/3x + 52/3 = 0
(x - -4)(x - -13/3) = 0
x - -4 = 0  or  x - -13/3 = 0
x = -4
x = -13/3


Input: Find x for 4x - 24/7 = 0

Output:
4x - 24/7 = 0
4x = 24/7
x = 24/7 / 4
x = 6/7


Input: What value of x satisfies 3x + 9/2 = 0

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


Input:
Solve the system:
6x + 9y = 21/20
4x + 5y = 1

Output:
6x + 9y = 21/20
4x + 5y = 1

Using elimination
4*(6x + 9y = 21/20)
6*(4x + 5y = 1)
24x + 36y = 21/5
24x + 30y = 6
Subtract equations
6y = -9/5
y = -9/5/6
y = -3/10

Substitute y
6x + 9(-3/10) = 21/20
6x = 15/4
x = 15/4/6
x = 5/8


Input:
Solve the system:
6x + 2y = -349/14
7x + 9y = -1321/28

Output:
6x + 2y = -349/14
7x + 9y = -1321/28

Using elimination
7*(6x + 2y = -349/14)
6*(7x + 9y = -1321/28)
42x + 14y = -349/2
42x + 54y = -3963/14
Subtract equations
-40y = 760/7
y = 760/7/-40
y = -19/7

Substitute y
6x + 2(-19/7) = -349/14
6x = -39/2
x = -39/2/6
x = -13/4


Input: Find x for x^2 + 15/2x  = 0

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


Input: Solve x^2 + 104/63x - 17/9 = 0

Output:
x^2 + 104/63x - 17/9 = 0
(x - 7/9)(x - -17/7) = 0
x - 7/9 = 0  or  x - -17/7 = 0
x = 7/9
x = -17/7


Input:
Solve simultaneously:
6x + 6y = 204/5
2x + 1y = 38/5

Output:
6x + 6y = 204/5
2x + 1y = 38/5

Using elimination
2*(6x + 6y = 204/5)
6*(2x + 1y = 38/5)
12x + 12y = 408/5
12x + 6y = 228/5
Subtract equations
6y = 36
y = 36/6
y = 6

Substitute y
6x + 6(6) = 204/5
6x = 24/5
x = 24/5/6
x = 4/5


Input: Solve the equation x^2 + 12/35x - 36/35 = 0

Output:
x^2 + 12/35x - 36/35 = 0
(x - -6/5)(x - 6/7) = 0
x - -6/5 = 0  or  x - 6/7 = 0
x = -6/5
x = 6/7


Input:
Find x and y such that
4x + 8y = -16/7
10x + 6y = 9/7

Output:
4x + 8y = -16/7
10x + 6y = 9/7

Using elimination
10*(4x + 8y = -16/7)
4*(10x + 6y = 9/7)
40x + 80y = -160/7
40x + 24y = 36/7
Subtract equations
56y = -28
y = -28/56
y = -1/2

Substitute y
4x + 8(-1/2) = -16/7
4x = 12/7
x = 12/7/4
x = 3/7


Input: Compute the solution of x^3 - 1091/360x^2 + 21/20x + 13/72 = 0

Output:
x^3 - 1091/360x^2 + 21/20x + 13/72 = 0
(x - 13/5)(x - 5/9)(x - -1/8) = 0
x - 13/5 = 0
x - 5/9 = 0
x - -1/8 = 0
x = 13/5
x = 5/9
x = -1/8


Input:
Solve the system:
5x + 4y = 43
6x + 5y = 52

Output:
5x + 4y = 43
6x + 5y = 52

Using elimination
6*(5x + 4y = 43)
5*(6x + 5y = 52)
30x + 24y = 258
30x + 25y = 260
Subtract equations
-1y = -2
y = -2/-1
y = 2

Substitute y
5x + 4(2) = 43
5x = 35
x = 35/5
x = 7


Input: What value of x satisfies x^3 - 89/63x^2 - 38/21x + 80/63 = 0

Output:
x^3 - 89/63x^2 - 38/21x + 80/63 = 0
(x - -8/7)(x - 5/9)(x - 2) = 0
x - -8/7 = 0
x - 5/9 = 0
x - 2 = 0
x = -8/7
x = 5/9
x = 2


Input: Find x in 5x + 10 = 0

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


Input: What value of x satisfies x^3 + 187/35x^2 + 28/5x + 32/35 = 0

Output:
x^3 + 187/35x^2 + 28/5x + 32/35 = 0
(x - -8/7)(x - -1/5)(x - -4) = 0
x - -8/7 = 0
x - -1/5 = 0
x - -4 = 0
x = -8/7
x = -1/5
x = -4


Input: Determine x in x^3 + 23/2x^2 - 15/2x - 18 = 0

Output:
x^3 + 23/2x^2 - 15/2x - 18 = 0
(x - -1)(x - 3/2)(x - -12) = 0
x - -1 = 0
x - 3/2 = 0
x - -12 = 0
x = -1
x = 3/2
x = -12


Input: Find x for x^3 + 6x^2 + 17/4x - 15/4 = 0

Output:
x^3 + 6x^2 + 17/4x - 15/4 = 0
(x - -5)(x - 1/2)(x - -3/2) = 0
x - -5 = 0
x - 1/2 = 0
x - -3/2 = 0
x = -5
x = 1/2
x = -3/2


Input: Solve quickly: 4x - 34 = 0

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


Input: What value of x satisfies x^2 - 68/9x + 209/27 = 0

Output:
x^2 - 68/9x + 209/27 = 0
(x - 11/9)(x - 19/3) = 0
x - 11/9 = 0  or  x - 19/3 = 0
x = 11/9
x = 19/3


Input: Solve quickly: 4x - 3 = 0

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


Input: Compute the solution of x^2 + 55/9x + 76/9 = 0

Output:
x^2 + 55/9x + 76/9 = 0
(x - -4)(x - -19/9) = 0
x - -4 = 0  or  x - -19/9 = 0
x = -4
x = -19/9