Input: Solve 3x - 5/3 = 0

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


Input: Solve quickly: x^2 + 4/5x - 12/5 = 0

Output:
x^2 + 4/5x - 12/5 = 0
(x - 6/5)(x - -2) = 0
x - 6/5 = 0  or  x - -2 = 0
x = 6/5
x = -2


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

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


Input:
Find x and y such that
5x + 2y = 41/3
3x + 10y = -5

Output:
5x + 2y = 41/3
3x + 10y = -5

Using elimination
3*(5x + 2y = 41/3)
5*(3x + 10y = -5)
15x + 6y = 41
15x + 50y = -25
Subtract equations
-44y = 66
y = 66/-44
y = -3/2

Substitute y
5x + 2(-3/2) = 41/3
5x = 50/3
x = 50/3/5
x = 10/3


Input: Determine x in x^3 - 241/70x^2 + 113/35x - 24/35 = 0

Output:
x^3 - 241/70x^2 + 113/35x - 24/35 = 0
(x - 2)(x - 8/7)(x - 3/10) = 0
x - 2 = 0
x - 8/7 = 0
x - 3/10 = 0
x = 2
x = 8/7
x = 3/10


Input: Solve x^2 + 97/6x + 247/6 = 0

Output:
x^2 + 97/6x + 247/6 = 0
(x - -19/6)(x - -13) = 0
x - -19/6 = 0  or  x - -13 = 0
x = -19/6
x = -13


Input: Find x in x^3 - 277/40x^2 + 91/16x + 1881/80 = 0

Output:
x^3 - 277/40x^2 + 91/16x + 1881/80 = 0
(x - -11/8)(x - 19/5)(x - 9/2) = 0
x - -11/8 = 0
x - 19/5 = 0
x - 9/2 = 0
x = -11/8
x = 19/5
x = 9/2


Input: Determine x in x^2 + 50/63x - 32/7 = 0

Output:
x^2 + 50/63x - 32/7 = 0
(x - -18/7)(x - 16/9) = 0
x - -18/7 = 0  or  x - 16/9 = 0
x = -18/7
x = 16/9


Input:
Find x and y such that
6x + 9y = -18
8x + 4y = -40/3

Output:
6x + 9y = -18
8x + 4y = -40/3

Using elimination
8*(6x + 9y = -18)
6*(8x + 4y = -40/3)
48x + 72y = -144
48x + 24y = -80
Subtract equations
48y = -64
y = -64/48
y = -4/3

Substitute y
6x + 9(-4/3) = -18
6x = -6
x = -6/6
x = -1


Input: Find the solution to x^3 - 7/12x^2 - 77/3x + 221/4 = 0

Output:
x^3 - 7/12x^2 - 77/3x + 221/4 = 0
(x - 13/4)(x - 3)(x - -17/3) = 0
x - 13/4 = 0
x - 3 = 0
x - -17/3 = 0
x = 13/4
x = 3
x = -17/3


Input: Compute the solution of 2x + 17/3 = 0

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


Input: Compute the solution of x^2 - 47/20x - 11/10 = 0

Output:
x^2 - 47/20x - 11/10 = 0
(x - -2/5)(x - 11/4) = 0
x - -2/5 = 0  or  x - 11/4 = 0
x = -2/5
x = 11/4


Input: Solve x^3 - 9x^2 + 74/9x + 544/9 = 0

Output:
x^3 - 9x^2 + 74/9x + 544/9 = 0
(x - -2)(x - 17/3)(x - 16/3) = 0
x - -2 = 0
x - 17/3 = 0
x - 16/3 = 0
x = -2
x = 17/3
x = 16/3


Input:
Solve the equations:
7x + 3y = 38
3x + 8y = 93/2

Output:
7x + 3y = 38
3x + 8y = 93/2

Using elimination
3*(7x + 3y = 38)
7*(3x + 8y = 93/2)
21x + 9y = 114
21x + 56y = 651/2
Subtract equations
-47y = -423/2
y = -423/2/-47
y = 9/2

Substitute y
7x + 3(9/2) = 38
7x = 49/2
x = 49/2/7
x = 7/2


Input: Solve quickly: x^2 + 13/5x - 6/5 = 0

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


Input:
Solve the system:
6x + 9y = 21/2
1x + 4y = 1/2

Output:
6x + 9y = 21/2
1x + 4y = 1/2

Using elimination
1*(6x + 9y = 21/2)
6*(1x + 4y = 1/2)
6x + 9y = 21/2
6x + 24y = 3
Subtract equations
-15y = 15/2
y = 15/2/-15
y = -1/2

Substitute y
6x + 9(-1/2) = 21/2
6x = 15
x = 15/6
x = 5/2


Input: Solve the equation x^3 + 15/4x^2 + 13/8x  = 0

Output:
x^3 + 15/4x^2 + 13/8x  = 0
(x - -13/4)(x - -1/2)(x - 0) = 0
x - -13/4 = 0
x - -1/2 = 0
x - 0 = 0
x = -13/4
x = -1/2
x = 0


Input: Find the solution to 6x + 24/5 = 0

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


Input:
Solve the equations:
5x + 8y = -161/5
10x + 2y = -84/5

Output:
5x + 8y = -161/5
10x + 2y = -84/5

Using elimination
10*(5x + 8y = -161/5)
5*(10x + 2y = -84/5)
50x + 80y = -322
50x + 10y = -84
Subtract equations
70y = -238
y = -238/70
y = -17/5

Substitute y
5x + 8(-17/5) = -161/5
5x = -5
x = -5/5
x = -1


Input: Find x for 5x + 65/8 = 0

Output:
5x + 65/8 = 0
5x = -65/8
x = -65/8 / 5
x = -13/8


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

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


Input: Solve the equation x^3 - 557/28x^2 - 195/28x + 675/7 = 0

Output:
x^3 - 557/28x^2 - 195/28x + 675/7 = 0
(x - -9/4)(x - 15/7)(x - 20) = 0
x - -9/4 = 0
x - 15/7 = 0
x - 20 = 0
x = -9/4
x = 15/7
x = 20


Input:
Solve the system:
6x + 10y = -97/7
3x + 1y = 31/14

Output:
6x + 10y = -97/7
3x + 1y = 31/14

Using elimination
3*(6x + 10y = -97/7)
6*(3x + 1y = 31/14)
18x + 30y = -291/7
18x + 6y = 93/7
Subtract equations
24y = -384/7
y = -384/7/24
y = -16/7

Substitute y
6x + 10(-16/7) = -97/7
6x = 9
x = 9/6
x = 3/2


Input: Find the solution to 9x + 36/5 = 0

Output:
9x + 36/5 = 0
9x = -36/5
x = -36/5 / 9
x = -4/5


Input: Find x for x^2 + 81/4x + 95/4 = 0

Output:
x^2 + 81/4x + 95/4 = 0
(x - -5/4)(x - -19) = 0
x - -5/4 = 0  or  x - -19 = 0
x = -5/4
x = -19


Input: Compute the solution of x^3 - 1/15x^2 - 1321/300x + 91/25 = 0

Output:
x^3 - 1/15x^2 - 1321/300x + 91/25 = 0
(x - 13/10)(x - 7/6)(x - -12/5) = 0
x - 13/10 = 0
x - 7/6 = 0
x - -12/5 = 0
x = 13/10
x = 7/6
x = -12/5


Input:
Solve the equations:
7x + 2y = 35
5x + 10y = 25

Output:
7x + 2y = 35
5x + 10y = 25

Using elimination
5*(7x + 2y = 35)
7*(5x + 10y = 25)
35x + 10y = 175
35x + 70y = 175
Subtract equations
-60y = 0
y = 0/-60
y = 0

Substitute y
7x + 2(0) = 35
7x = 35
x = 35/7
x = 5


Input:
Solve simultaneously:
7x + 4y = -119/30
2x + 5y = -23/6

Output:
7x + 4y = -119/30
2x + 5y = -23/6

Using elimination
2*(7x + 4y = -119/30)
7*(2x + 5y = -23/6)
14x + 8y = -119/15
14x + 35y = -161/6
Subtract equations
-27y = 189/10
y = 189/10/-27
y = -7/10

Substitute y
7x + 4(-7/10) = -119/30
7x = -7/6
x = -7/6/7
x = -1/6


Input:
Find x and y such that
6x + 8y = -179/20
6x + 1y = -193/20

Output:
6x + 8y = -179/20
6x + 1y = -193/20

Using elimination
6*(6x + 8y = -179/20)
6*(6x + 1y = -193/20)
36x + 48y = -537/10
36x + 6y = -579/10
Subtract equations
42y = 21/5
y = 21/5/42
y = 1/10

Substitute y
6x + 8(1/10) = -179/20
6x = -39/4
x = -39/4/6
x = -13/8


Input: Solve x^3 - 139/72x^2 - 19/18x  = 0

Output:
x^3 - 139/72x^2 - 19/18x  = 0
(x - 0)(x - -4/9)(x - 19/8) = 0
x - 0 = 0
x - -4/9 = 0
x - 19/8 = 0
x = 0
x = -4/9
x = 19/8


Input: Solve the equation x^2 - 7x - 30 = 0

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


Input: Solve quickly: 1x + 15 = 0

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


Input: Determine x in x^3 + 305/56x^2 - 291/28x + 27/8 = 0

Output:
x^3 + 305/56x^2 - 291/28x + 27/8 = 0
(x - 9/8)(x - 3/7)(x - -7) = 0
x - 9/8 = 0
x - 3/7 = 0
x - -7 = 0
x = 9/8
x = 3/7
x = -7


Input: Solve quickly: 3x - 42 = 0

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


Input: Find x in 8x + 32 = 0

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


Input: Find x for 2x - 36 = 0

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


Input:
Solve the system:
3x + 6y = -3
6x + 5y = -13

Output:
3x + 6y = -3
6x + 5y = -13

Using elimination
6*(3x + 6y = -3)
3*(6x + 5y = -13)
18x + 36y = -18
18x + 15y = -39
Subtract equations
21y = 21
y = 21/21
y = 1

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


Input: Solve x^3 - 41/14x^2 - 34/7x + 10 = 0

Output:
x^3 - 41/14x^2 - 34/7x + 10 = 0
(x - 7/2)(x - 10/7)(x - -2) = 0
x - 7/2 = 0
x - 10/7 = 0
x - -2 = 0
x = 7/2
x = 10/7
x = -2


Input:
Find x and y such that
1x + 7y = 23/4
5x + 6y = 7

Output:
1x + 7y = 23/4
5x + 6y = 7

Using elimination
5*(1x + 7y = 23/4)
1*(5x + 6y = 7)
5x + 35y = 115/4
5x + 6y = 7
Subtract equations
29y = 87/4
y = 87/4/29
y = 3/4

Substitute y
1x + 7(3/4) = 23/4
1x = 1/2
x = 1/2/1
x = 1/2


Input: Solve the equation x^2 + 31/7x + 12/7 = 0

Output:
x^2 + 31/7x + 12/7 = 0
(x - -3/7)(x - -4) = 0
x - -3/7 = 0  or  x - -4 = 0
x = -3/7
x = -4


Input: Compute the solution of x^2 + 133/45x - 68/45 = 0

Output:
x^2 + 133/45x - 68/45 = 0
(x - 4/9)(x - -17/5) = 0
x - 4/9 = 0  or  x - -17/5 = 0
x = 4/9
x = -17/5


Input:
Find x and y such that
9x + 4y = 117
2x + 4y = 26

Output:
9x + 4y = 117
2x + 4y = 26

Using elimination
2*(9x + 4y = 117)
9*(2x + 4y = 26)
18x + 8y = 234
18x + 36y = 234
Subtract equations
-28y = 0
y = 0/-28
y = 0

Substitute y
9x + 4(0) = 117
9x = 117
x = 117/9
x = 13


Input: Find x for x^3 - 83/30x^2 - 35/12x + 209/40 = 0

Output:
x^3 - 83/30x^2 - 35/12x + 209/40 = 0
(x - 11/10)(x - 19/6)(x - -3/2) = 0
x - 11/10 = 0
x - 19/6 = 0
x - -3/2 = 0
x = 11/10
x = 19/6
x = -3/2


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: Find x for 3x + 21/2 = 0

Output:
3x + 21/2 = 0
3x = -21/2
x = -21/2 / 3
x = -7/2


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

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


Input:
Find x and y such that
1x + 3y = 24/5
9x + 9y = 297/5

Output:
1x + 3y = 24/5
9x + 9y = 297/5

Using elimination
9*(1x + 3y = 24/5)
1*(9x + 9y = 297/5)
9x + 27y = 216/5
9x + 9y = 297/5
Subtract equations
18y = -81/5
y = -81/5/18
y = -9/10

Substitute y
1x + 3(-9/10) = 24/5
1x = 15/2
x = 15/2/1
x = 15/2


Input:
Solve simultaneously:
1x + 9y = 453/20
2x + 9y = 219/10

Output:
1x + 9y = 453/20
2x + 9y = 219/10

Using elimination
2*(1x + 9y = 453/20)
1*(2x + 9y = 219/10)
2x + 18y = 453/10
2x + 9y = 219/10
Subtract equations
9y = 117/5
y = 117/5/9
y = 13/5

Substitute y
1x + 9(13/5) = 453/20
1x = -3/4
x = -3/4/1
x = -3/4


Input: Determine x in 1x + 3/7 = 0

Output:
1x + 3/7 = 0
1x = -3/7
x = -3/7 / 1
x = -3/7


Input:
Solve the equations:
4x + 10y = -206/3
1x + 5y = -94/3

Output:
4x + 10y = -206/3
1x + 5y = -94/3

Using elimination
1*(4x + 10y = -206/3)
4*(1x + 5y = -94/3)
4x + 10y = -206/3
4x + 20y = -376/3
Subtract equations
-10y = 170/3
y = 170/3/-10
y = -17/3

Substitute y
4x + 10(-17/3) = -206/3
4x = -12
x = -12/4
x = -3


Input: Compute the solution of x^3 - 16/7x^2 - 95/7x  = 0

Output:
x^3 - 16/7x^2 - 95/7x  = 0
(x - 5)(x - -19/7)(x - 0) = 0
x - 5 = 0
x - -19/7 = 0
x - 0 = 0
x = 5
x = -19/7
x = 0


Input: Compute the solution of 6x + 48 = 0

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


Input: Find x in x^3 - 17x^2 + 134/25x + 4256/25 = 0

Output:
x^3 - 17x^2 + 134/25x + 4256/25 = 0
(x - 19/5)(x - 16)(x - -14/5) = 0
x - 19/5 = 0
x - 16 = 0
x - -14/5 = 0
x = 19/5
x = 16
x = -14/5


Input: Find the solution to 10x - 50/3 = 0

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


Input: Find x for 1x - 8/3 = 0

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


Input: Determine x in x^3 + 179/30x^2 + 57/5x + 104/15 = 0

Output:
x^3 + 179/30x^2 + 57/5x + 104/15 = 0
(x - -2)(x - -8/3)(x - -13/10) = 0
x - -2 = 0
x - -8/3 = 0
x - -13/10 = 0
x = -2
x = -8/3
x = -13/10


Input: Solve 10x + 130/9 = 0

Output:
10x + 130/9 = 0
10x = -130/9
x = -130/9 / 10
x = -13/9


Input: Solve x^2 - 14/9x + 13/81 = 0

Output:
x^2 - 14/9x + 13/81 = 0
(x - 13/9)(x - 1/9) = 0
x - 13/9 = 0  or  x - 1/9 = 0
x = 13/9
x = 1/9


Input: Solve 7x + 2 = 0

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


Input: Find the solution to x^3 + 149/40x^2 + 201/200x - 54/25 = 0

Output:
x^3 + 149/40x^2 + 201/200x - 54/25 = 0
(x - 3/5)(x - -16/5)(x - -9/8) = 0
x - 3/5 = 0
x - -16/5 = 0
x - -9/8 = 0
x = 3/5
x = -16/5
x = -9/8


Input: What value of x satisfies 5x - 90 = 0

Output:
5x - 90 = 0
5x = 90
x = 90 / 5
x = 18


Input: What value of x satisfies x^3 - 16/3x^2 + 13/9x + 10/9 = 0

Output:
x^3 - 16/3x^2 + 13/9x + 10/9 = 0
(x - -1/3)(x - 5)(x - 2/3) = 0
x - -1/3 = 0
x - 5 = 0
x - 2/3 = 0
x = -1/3
x = 5
x = 2/3


Input:
Solve the system:
7x + 1y = -51/8
7x + 2y = -53/8

Output:
7x + 1y = -51/8
7x + 2y = -53/8

Using elimination
7*(7x + 1y = -51/8)
7*(7x + 2y = -53/8)
49x + 7y = -357/8
49x + 14y = -371/8
Subtract equations
-7y = 7/4
y = 7/4/-7
y = -1/4

Substitute y
7x + 1(-1/4) = -51/8
7x = -49/8
x = -49/8/7
x = -7/8


Input: Solve 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:
Find x and y such that
1x + 7y = -173/4
8x + 2y = -22

Output:
1x + 7y = -173/4
8x + 2y = -22

Using elimination
8*(1x + 7y = -173/4)
1*(8x + 2y = -22)
8x + 56y = -346
8x + 2y = -22
Subtract equations
54y = -324
y = -324/54
y = -6

Substitute y
1x + 7(-6) = -173/4
1x = -5/4
x = -5/4/1
x = -5/4


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

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


Input: Find x in x^3 + 269/126x^2 + 101/189x + 13/378 = 0

Output:
x^3 + 269/126x^2 + 101/189x + 13/378 = 0
(x - -1/9)(x - -1/6)(x - -13/7) = 0
x - -1/9 = 0
x - -1/6 = 0
x - -13/7 = 0
x = -1/9
x = -1/6
x = -13/7


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

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


Input: What value of x satisfies x^2 + 31/2x + 21 = 0

Output:
x^2 + 31/2x + 21 = 0
(x - -3/2)(x - -14) = 0
x - -3/2 = 0  or  x - -14 = 0
x = -3/2
x = -14


Input: Compute the solution of x^2 + 15/2x + 9 = 0

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


Input: What value of x satisfies x^3  - 21/4x - 5/2 = 0

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


Input: Find x for x^3 - 81/35x^2 - 871/175x + 153/35 = 0

Output:
x^3 - 81/35x^2 - 871/175x + 153/35 = 0
(x - -9/5)(x - 17/5)(x - 5/7) = 0
x - -9/5 = 0
x - 17/5 = 0
x - 5/7 = 0
x = -9/5
x = 17/5
x = 5/7


Input: Determine x in 9x + 8 = 0

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


Input:
Solve simultaneously:
5x + 2y = 9/2
6x + 3y = 15/4

Output:
5x + 2y = 9/2
6x + 3y = 15/4

Using elimination
6*(5x + 2y = 9/2)
5*(6x + 3y = 15/4)
30x + 12y = 27
30x + 15y = 75/4
Subtract equations
-3y = 33/4
y = 33/4/-3
y = -11/4

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


Input:
Solve simultaneously:
5x + 4y = 87/2
8x + 6y = 277/4

Output:
5x + 4y = 87/2
8x + 6y = 277/4

Using elimination
8*(5x + 4y = 87/2)
5*(8x + 6y = 277/4)
40x + 32y = 348
40x + 30y = 1385/4
Subtract equations
2y = 7/4
y = 7/4/2
y = 7/8

Substitute y
5x + 4(7/8) = 87/2
5x = 40
x = 40/5
x = 8


Input: Find the solution to x^3 - 361/70x^2 + 181/35x + 4 = 0

Output:
x^3 - 361/70x^2 + 181/35x + 4 = 0
(x - 14/5)(x - -1/2)(x - 20/7) = 0
x - 14/5 = 0
x - -1/2 = 0
x - 20/7 = 0
x = 14/5
x = -1/2
x = 20/7


Input:
Find x and y such that
6x + 10y = -56/3
4x + 10y = -148/9

Output:
6x + 10y = -56/3
4x + 10y = -148/9

Using elimination
4*(6x + 10y = -56/3)
6*(4x + 10y = -148/9)
24x + 40y = -224/3
24x + 60y = -296/3
Subtract equations
-20y = 24
y = 24/-20
y = -6/5

Substitute y
6x + 10(-6/5) = -56/3
6x = -20/3
x = -20/3/6
x = -10/9


Input: Determine x in x^3 + 38/3x^2 - 485/3x - 300 = 0

Output:
x^3 + 38/3x^2 - 485/3x - 300 = 0
(x - 9)(x - -20)(x - -5/3) = 0
x - 9 = 0
x - -20 = 0
x - -5/3 = 0
x = 9
x = -20
x = -5/3


Input: Find x for x^2 + 11/6x - 13/18 = 0

Output:
x^2 + 11/6x - 13/18 = 0
(x - 1/3)(x - -13/6) = 0
x - 1/3 = 0  or  x - -13/6 = 0
x = 1/3
x = -13/6


Input:
Find x and y such that
6x + 9y = 48
9x + 4y = 53

Output:
6x + 9y = 48
9x + 4y = 53

Using elimination
9*(6x + 9y = 48)
6*(9x + 4y = 53)
54x + 81y = 432
54x + 24y = 318
Subtract equations
57y = 114
y = 114/57
y = 2

Substitute y
6x + 9(2) = 48
6x = 30
x = 30/6
x = 5


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

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


Input:
Solve simultaneously:
7x + 3y = -235/6
7x + 10y = -733/18

Output:
7x + 3y = -235/6
7x + 10y = -733/18

Using elimination
7*(7x + 3y = -235/6)
7*(7x + 10y = -733/18)
49x + 21y = -1645/6
49x + 70y = -5131/18
Subtract equations
-49y = 98/9
y = 98/9/-49
y = -2/9

Substitute y
7x + 3(-2/9) = -235/6
7x = -77/2
x = -77/2/7
x = -11/2


Input: Solve x^3 + 1/3x^2 - 301/81x - 247/81 = 0

Output:
x^3 + 1/3x^2 - 301/81x - 247/81 = 0
(x - -1)(x - -13/9)(x - 19/9) = 0
x - -1 = 0
x - -13/9 = 0
x - 19/9 = 0
x = -1
x = -13/9
x = 19/9


Input: Determine x in x^3 - 136/35x^2 + 689/175x - 16/25 = 0

Output:
x^3 - 136/35x^2 + 689/175x - 16/25 = 0
(x - 7/5)(x - 16/7)(x - 1/5) = 0
x - 7/5 = 0
x - 16/7 = 0
x - 1/5 = 0
x = 7/5
x = 16/7
x = 1/5


Input: Find the solution to x^2 + 80/63x - 16/21 = 0

Output:
x^2 + 80/63x - 16/21 = 0
(x - 4/9)(x - -12/7) = 0
x - 4/9 = 0  or  x - -12/7 = 0
x = 4/9
x = -12/7


Input: Compute the solution of x^2 - 127/7x + 240/7 = 0

Output:
x^2 - 127/7x + 240/7 = 0
(x - 16)(x - 15/7) = 0
x - 16 = 0  or  x - 15/7 = 0
x = 16
x = 15/7


Input: Compute the solution of x^3 + 1/14x^2 - 793/175x - 187/50 = 0

Output:
x^3 + 1/14x^2 - 793/175x - 187/50 = 0
(x - -7/5)(x - 17/7)(x - -11/10) = 0
x - -7/5 = 0
x - 17/7 = 0
x - -11/10 = 0
x = -7/5
x = 17/7
x = -11/10


Input: Solve quickly: 5x + 35/2 = 0

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


Input: What value of x satisfies x^3 + 515/168x^2 - 19/21x - 30/7 = 0

Output:
x^3 + 515/168x^2 - 19/21x - 30/7 = 0
(x - -20/7)(x - -4/3)(x - 9/8) = 0
x - -20/7 = 0
x - -4/3 = 0
x - 9/8 = 0
x = -20/7
x = -4/3
x = 9/8


Input: Find x for 3x - 3 = 0

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


Input:
Solve simultaneously:
6x + 10y = -78/35
7x + 3y = -351/35

Output:
6x + 10y = -78/35
7x + 3y = -351/35

Using elimination
7*(6x + 10y = -78/35)
6*(7x + 3y = -351/35)
42x + 70y = -78/5
42x + 18y = -2106/35
Subtract equations
52y = 312/7
y = 312/7/52
y = 6/7

Substitute y
6x + 10(6/7) = -78/35
6x = -54/5
x = -54/5/6
x = -9/5


Input: Compute the solution of x^3 + 10x^2 + 433/49x - 72/49 = 0

Output:
x^3 + 10x^2 + 433/49x - 72/49 = 0
(x - 1/7)(x - -8/7)(x - -9) = 0
x - 1/7 = 0
x - -8/7 = 0
x - -9 = 0
x = 1/7
x = -8/7
x = -9


Input:
Find x and y such that
1x + 5y = -53/4
9x + 4y = -909/20

Output:
1x + 5y = -53/4
9x + 4y = -909/20

Using elimination
9*(1x + 5y = -53/4)
1*(9x + 4y = -909/20)
9x + 45y = -477/4
9x + 4y = -909/20
Subtract equations
41y = -369/5
y = -369/5/41
y = -9/5

Substitute y
1x + 5(-9/5) = -53/4
1x = -17/4
x = -17/4/1
x = -17/4


Input: What value of x satisfies x^3 - 55/4x^2 + 397/8x - 85/2 = 0

Output:
x^3 - 55/4x^2 + 397/8x - 85/2 = 0
(x - 17/2)(x - 4)(x - 5/4) = 0
x - 17/2 = 0
x - 4 = 0
x - 5/4 = 0
x = 17/2
x = 4
x = 5/4


Input: Find x for x^2 + 19/5x + 84/25 = 0

Output:
x^2 + 19/5x + 84/25 = 0
(x - -7/5)(x - -12/5) = 0
x - -7/5 = 0  or  x - -12/5 = 0
x = -7/5
x = -12/5


Input:
Solve the equations:
10x + 7y = 109/14
1x + 2y = 10/7

Output:
10x + 7y = 109/14
1x + 2y = 10/7

Using elimination
1*(10x + 7y = 109/14)
10*(1x + 2y = 10/7)
10x + 7y = 109/14
10x + 20y = 100/7
Subtract equations
-13y = -13/2
y = -13/2/-13
y = 1/2

Substitute y
10x + 7(1/2) = 109/14
10x = 30/7
x = 30/7/10
x = 3/7


Input: Determine x in x^3 + 4/5x^2 - 1/25x - 4/125 = 0

Output:
x^3 + 4/5x^2 - 1/25x - 4/125 = 0
(x - -4/5)(x - 1/5)(x - -1/5) = 0
x - -4/5 = 0
x - 1/5 = 0
x - -1/5 = 0
x = -4/5
x = 1/5
x = -1/5


Input:
Solve simultaneously:
10x + 1y = 83/4
1x + 4y = 64/5

Output:
10x + 1y = 83/4
1x + 4y = 64/5

Using elimination
1*(10x + 1y = 83/4)
10*(1x + 4y = 64/5)
10x + 1y = 83/4
10x + 40y = 128
Subtract equations
-39y = -429/4
y = -429/4/-39
y = 11/4

Substitute y
10x + 1(11/4) = 83/4
10x = 18
x = 18/10
x = 9/5


Input: Find the solution to x^3 + 117/35x^2 - 72/5x + 324/35 = 0

Output:
x^3 + 117/35x^2 - 72/5x + 324/35 = 0
(x - 6/7)(x - -6)(x - 9/5) = 0
x - 6/7 = 0
x - -6 = 0
x - 9/5 = 0
x = 6/7
x = -6
x = 9/5


Input: Solve x^3 - 239/30x^2 + 103/5x - 171/10 = 0

Output:
x^3 - 239/30x^2 + 103/5x - 171/10 = 0
(x - 3)(x - 19/6)(x - 9/5) = 0
x - 3 = 0
x - 19/6 = 0
x - 9/5 = 0
x = 3
x = 19/6
x = 9/5


Input:
Solve the system:
2x + 8y = -12
9x + 3y = 147/4

Output:
2x + 8y = -12
9x + 3y = 147/4

Using elimination
9*(2x + 8y = -12)
2*(9x + 3y = 147/4)
18x + 72y = -108
18x + 6y = 147/2
Subtract equations
66y = -363/2
y = -363/2/66
y = -11/4

Substitute y
2x + 8(-11/4) = -12
2x = 10
x = 10/2
x = 5


Input: Find the solution to x^3 + 201/20x^2 + 67/2x + 741/20 = 0

Output:
x^3 + 201/20x^2 + 67/2x + 741/20 = 0
(x - -3)(x - -13/4)(x - -19/5) = 0
x - -3 = 0
x - -13/4 = 0
x - -19/5 = 0
x = -3
x = -13/4
x = -19/5


Input: Solve x^2 - 77/18x + 49/18 = 0

Output:
x^2 - 77/18x + 49/18 = 0
(x - 7/2)(x - 7/9) = 0
x - 7/2 = 0  or  x - 7/9 = 0
x = 7/2
x = 7/9


Input:
Solve the system:
3x + 3y = -687/40
6x + 7y = -1459/40

Output:
3x + 3y = -687/40
6x + 7y = -1459/40

Using elimination
6*(3x + 3y = -687/40)
3*(6x + 7y = -1459/40)
18x + 18y = -2061/20
18x + 21y = -4377/40
Subtract equations
-3y = 51/8
y = 51/8/-3
y = -17/8

Substitute y
3x + 3(-17/8) = -687/40
3x = -54/5
x = -54/5/3
x = -18/5


Input: Find x in x^2 + 75/8x + 133/8 = 0

Output:
x^2 + 75/8x + 133/8 = 0
(x - -7)(x - -19/8) = 0
x - -7 = 0  or  x - -19/8 = 0
x = -7
x = -19/8


Input: Find x for x^2 - 59/3x - 20/3 = 0

Output:
x^2 - 59/3x - 20/3 = 0
(x - 20)(x - -1/3) = 0
x - 20 = 0  or  x - -1/3 = 0
x = 20
x = -1/3


Input: Solve quickly: x^3 + 50/9x^2 + 137/27x - 70/9 = 0

Output:
x^3 + 50/9x^2 + 137/27x - 70/9 = 0
(x - 7/9)(x - -3)(x - -10/3) = 0
x - 7/9 = 0
x - -3 = 0
x - -10/3 = 0
x = 7/9
x = -3
x = -10/3


Input: Compute the solution of x^2 - 17x + 30 = 0

Output:
x^2 - 17x + 30 = 0
(x - 2)(x - 15) = 0
x - 2 = 0  or  x - 15 = 0
x = 2
x = 15


Input: Compute the solution of x^3 - 509/210x^2 + 149/210x + 19/35 = 0

Output:
x^3 - 509/210x^2 + 149/210x + 19/35 = 0
(x - -1/3)(x - 19/10)(x - 6/7) = 0
x - -1/3 = 0
x - 19/10 = 0
x - 6/7 = 0
x = -1/3
x = 19/10
x = 6/7


Input:
Solve simultaneously:
4x + 7y = 64/3
9x + 1y = -11

Output:
4x + 7y = 64/3
9x + 1y = -11

Using elimination
9*(4x + 7y = 64/3)
4*(9x + 1y = -11)
36x + 63y = 192
36x + 4y = -44
Subtract equations
59y = 236
y = 236/59
y = 4

Substitute y
4x + 7(4) = 64/3
4x = -20/3
x = -20/3/4
x = -5/3


Input: Determine x in 2x - 22/3 = 0

Output:
2x - 22/3 = 0
2x = 22/3
x = 22/3 / 2
x = 11/3


Input: Find x in 5x + 10 = 0

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


Input: Find the solution to 4x + 8/3 = 0

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


Input: Solve the equation 8x - 60 = 0

Output:
8x - 60 = 0
8x = 60
x = 60 / 8
x = 15/2


Input:
Solve the system:
8x + 6y = 31
4x + 6y = 11

Output:
8x + 6y = 31
4x + 6y = 11

Using elimination
4*(8x + 6y = 31)
8*(4x + 6y = 11)
32x + 24y = 124
32x + 48y = 88
Subtract equations
-24y = 36
y = 36/-24
y = -3/2

Substitute y
8x + 6(-3/2) = 31
8x = 40
x = 40/8
x = 5


Input: Find the solution to 9x + 144/7 = 0

Output:
9x + 144/7 = 0
9x = -144/7
x = -144/7 / 9
x = -16/7


Input:
Solve simultaneously:
10x + 2y = 21
1x + 3y = 7/6

Output:
10x + 2y = 21
1x + 3y = 7/6

Using elimination
1*(10x + 2y = 21)
10*(1x + 3y = 7/6)
10x + 2y = 21
10x + 30y = 35/3
Subtract equations
-28y = 28/3
y = 28/3/-28
y = -1/3

Substitute y
10x + 2(-1/3) = 21
10x = 65/3
x = 65/3/10
x = 13/6


Input: Find the solution to x^3 - 11/2x^2 + 41/6x + 35/27 = 0

Output:
x^3 - 11/2x^2 + 41/6x + 35/27 = 0
(x - 10/3)(x - 7/3)(x - -1/6) = 0
x - 10/3 = 0
x - 7/3 = 0
x - -1/6 = 0
x = 10/3
x = 7/3
x = -1/6


Input: Compute the solution of x^2 - 55/12x + 13/12 = 0

Output:
x^2 - 55/12x + 13/12 = 0
(x - 1/4)(x - 13/3) = 0
x - 1/4 = 0  or  x - 13/3 = 0
x = 1/4
x = 13/3


Input: Find x for x^2 - 6x  = 0

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


Input: Solve quickly: x^2 - 29/40x - 9/20 = 0

Output:
x^2 - 29/40x - 9/20 = 0
(x - -2/5)(x - 9/8) = 0
x - -2/5 = 0  or  x - 9/8 = 0
x = -2/5
x = 9/8


Input: Solve the equation 8x + 24 = 0

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


Input: What value of x satisfies x^2 + 56/15x + 49/15 = 0

Output:
x^2 + 56/15x + 49/15 = 0
(x - -7/3)(x - -7/5) = 0
x - -7/3 = 0  or  x - -7/5 = 0
x = -7/3
x = -7/5


Input: Compute the solution of x^2 + 10x - 171 = 0

Output:
x^2 + 10x - 171 = 0
(x - -19)(x - 9) = 0
x - -19 = 0  or  x - 9 = 0
x = -19
x = 9


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

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


Input: Solve quickly: x^2 - 7/9x - 20/27 = 0

Output:
x^2 - 7/9x - 20/27 = 0
(x - 4/3)(x - -5/9) = 0
x - 4/3 = 0  or  x - -5/9 = 0
x = 4/3
x = -5/9


Input:
Find x and y such that
2x + 4y = 468/7
6x + 2y = 214/7

Output:
2x + 4y = 468/7
6x + 2y = 214/7

Using elimination
6*(2x + 4y = 468/7)
2*(6x + 2y = 214/7)
12x + 24y = 2808/7
12x + 4y = 428/7
Subtract equations
20y = 340
y = 340/20
y = 17

Substitute y
2x + 4(17) = 468/7
2x = -8/7
x = -8/7/2
x = -4/7


Input: Determine x in x^3 - 34/5x^2 + 15x - 54/5 = 0

Output:
x^3 - 34/5x^2 + 15x - 54/5 = 0
(x - 9/5)(x - 2)(x - 3) = 0
x - 9/5 = 0
x - 2 = 0
x - 3 = 0
x = 9/5
x = 2
x = 3


Input: Solve x^3 - 1/6x^2 - 26/3x + 10 = 0

Output:
x^3 - 1/6x^2 - 26/3x + 10 = 0
(x - 3/2)(x - 2)(x - -10/3) = 0
x - 3/2 = 0
x - 2 = 0
x - -10/3 = 0
x = 3/2
x = 2
x = -10/3


Input:
Solve simultaneously:
10x + 8y = 431/12
2x + 2y = 107/12

Output:
10x + 8y = 431/12
2x + 2y = 107/12

Using elimination
2*(10x + 8y = 431/12)
10*(2x + 2y = 107/12)
20x + 16y = 431/6
20x + 20y = 535/6
Subtract equations
-4y = -52/3
y = -52/3/-4
y = 13/3

Substitute y
10x + 8(13/3) = 431/12
10x = 5/4
x = 5/4/10
x = 1/8


Input:
Solve simultaneously:
8x + 5y = -60
8x + 7y = -68

Output:
8x + 5y = -60
8x + 7y = -68

Using elimination
8*(8x + 5y = -60)
8*(8x + 7y = -68)
64x + 40y = -480
64x + 56y = -544
Subtract equations
-16y = 64
y = 64/-16
y = -4

Substitute y
8x + 5(-4) = -60
8x = -40
x = -40/8
x = -5


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

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


Input: Solve quickly: x^2 + 32/3x + 64/3 = 0

Output:
x^2 + 32/3x + 64/3 = 0
(x - -8/3)(x - -8) = 0
x - -8/3 = 0  or  x - -8 = 0
x = -8/3
x = -8


Input: Solve 6x + 51/5 = 0

Output:
6x + 51/5 = 0
6x = -51/5
x = -51/5 / 6
x = -17/10


Input: Find x for x^3 - 25/3x^2 - 8x + 132 = 0

Output:
x^3 - 25/3x^2 - 8x + 132 = 0
(x - -11/3)(x - 6)(x - 6) = 0
x - -11/3 = 0
x - 6 = 0
x - 6 = 0
x = -11/3
x = 6
x = 6


Input: Compute the solution of x^2 + 153/35x + 76/35 = 0

Output:
x^2 + 153/35x + 76/35 = 0
(x - -4/7)(x - -19/5) = 0
x - -4/7 = 0  or  x - -19/5 = 0
x = -4/7
x = -19/5


Input: Find x in x^3 - 34/3x^2 + 112/3x - 32 = 0

Output:
x^3 - 34/3x^2 + 112/3x - 32 = 0
(x - 4/3)(x - 4)(x - 6) = 0
x - 4/3 = 0
x - 4 = 0
x - 6 = 0
x = 4/3
x = 4
x = 6


Input: Solve quickly: 9x + 63/4 = 0

Output:
9x + 63/4 = 0
9x = -63/4
x = -63/4 / 9
x = -7/4


Input: Determine x in x^3 - 3x^2 + 95/64x + 33/32 = 0

Output:
x^3 - 3x^2 + 95/64x + 33/32 = 0
(x - -3/8)(x - 2)(x - 11/8) = 0
x - -3/8 = 0
x - 2 = 0
x - 11/8 = 0
x = -3/8
x = 2
x = 11/8


Input: Find x for x^2 + 5x - 14 = 0

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


Input: Solve x^2 - 47/3x - 68/3 = 0

Output:
x^2 - 47/3x - 68/3 = 0
(x - 17)(x - -4/3) = 0
x - 17 = 0  or  x - -4/3 = 0
x = 17
x = -4/3


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

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


Input: Solve quickly: x^3 + 115/3x^2 + 1174/3x + 456 = 0

Output:
x^3 + 115/3x^2 + 1174/3x + 456 = 0
(x - -19)(x - -4/3)(x - -18) = 0
x - -19 = 0
x - -4/3 = 0
x - -18 = 0
x = -19
x = -4/3
x = -18


Input: Compute the solution of x^3 - 163/90x^2 - 116/27x + 119/30 = 0

Output:
x^3 - 163/90x^2 - 116/27x + 119/30 = 0
(x - 17/6)(x - -9/5)(x - 7/9) = 0
x - 17/6 = 0
x - -9/5 = 0
x - 7/9 = 0
x = 17/6
x = -9/5
x = 7/9


Input: Find x for x^3 + 5/9x^2 - 356/81x - 320/81 = 0

Output:
x^3 + 5/9x^2 - 356/81x - 320/81 = 0
(x - 20/9)(x - -1)(x - -16/9) = 0
x - 20/9 = 0
x - -1 = 0
x - -16/9 = 0
x = 20/9
x = -1
x = -16/9


Input: Find the solution to x^2 - 43/5x - 14 = 0

Output:
x^2 - 43/5x - 14 = 0
(x - -7/5)(x - 10) = 0
x - -7/5 = 0  or  x - 10 = 0
x = -7/5
x = 10


Input: Determine x in x^2 + 38/3x - 361/3 = 0

Output:
x^2 + 38/3x - 361/3 = 0
(x - -19)(x - 19/3) = 0
x - -19 = 0  or  x - 19/3 = 0
x = -19
x = 19/3


Input: Determine x in 5x - 15 = 0

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


Input: Solve 9x + 45 = 0

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


Input: Determine x in x^2 - 35/2x + 75/2 = 0

Output:
x^2 - 35/2x + 75/2 = 0
(x - 15)(x - 5/2) = 0
x - 15 = 0  or  x - 5/2 = 0
x = 15
x = 5/2


Input:
Solve simultaneously:
8x + 1y = 82/5
6x + 3y = 84/5

Output:
8x + 1y = 82/5
6x + 3y = 84/5

Using elimination
6*(8x + 1y = 82/5)
8*(6x + 3y = 84/5)
48x + 6y = 492/5
48x + 24y = 672/5
Subtract equations
-18y = -36
y = -36/-18
y = 2

Substitute y
8x + 1(2) = 82/5
8x = 72/5
x = 72/5/8
x = 9/5


Input:
Find x and y such that
8x + 9y = -53
10x + 2y = -587/9

Output:
8x + 9y = -53
10x + 2y = -587/9

Using elimination
10*(8x + 9y = -53)
8*(10x + 2y = -587/9)
80x + 90y = -530
80x + 16y = -4696/9
Subtract equations
74y = -74/9
y = -74/9/74
y = -1/9

Substitute y
8x + 9(-1/9) = -53
8x = -52
x = -52/8
x = -13/2


Input:
Solve simultaneously:
1x + 1y = -8
6x + 4y = -50

Output:
1x + 1y = -8
6x + 4y = -50

Using elimination
6*(1x + 1y = -8)
1*(6x + 4y = -50)
6x + 6y = -48
6x + 4y = -50
Subtract equations
2y = 2
y = 2/2
y = 1

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


Input: Find x for x^2 - 41/12x + 11/6 = 0

Output:
x^2 - 41/12x + 11/6 = 0
(x - 2/3)(x - 11/4) = 0
x - 2/3 = 0  or  x - 11/4 = 0
x = 2/3
x = 11/4


Input:
Find x and y such that
2x + 5y = 46/7
8x + 2y = -592/35

Output:
2x + 5y = 46/7
8x + 2y = -592/35

Using elimination
8*(2x + 5y = 46/7)
2*(8x + 2y = -592/35)
16x + 40y = 368/7
16x + 4y = -1184/35
Subtract equations
36y = 432/5
y = 432/5/36
y = 12/5

Substitute y
2x + 5(12/5) = 46/7
2x = -38/7
x = -38/7/2
x = -19/7


Input: Solve x^3 - 49/10x^2 - 45x + 612/5 = 0

Output:
x^3 - 49/10x^2 - 45x + 612/5 = 0
(x - 17/2)(x - 12/5)(x - -6) = 0
x - 17/2 = 0
x - 12/5 = 0
x - -6 = 0
x = 17/2
x = 12/5
x = -6


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

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


Input: Compute the solution of 6x  = 0

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


Input: Solve 4x - 5 = 0

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


Input: What value of x satisfies 1x - 15/4 = 0

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


Input: What value of x satisfies 9x + 27/7 = 0

Output:
9x + 27/7 = 0
9x = -27/7
x = -27/7 / 9
x = -3/7


Input: Solve quickly: x^2 + 29/6x + 5 = 0

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


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: Find x in 5x - 7 = 0

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


Input:
Solve the equations:
2x + 10y = -76/3
5x + 9y = -662/15

Output:
2x + 10y = -76/3
5x + 9y = -662/15

Using elimination
5*(2x + 10y = -76/3)
2*(5x + 9y = -662/15)
10x + 50y = -380/3
10x + 18y = -1324/15
Subtract equations
32y = -192/5
y = -192/5/32
y = -6/5

Substitute y
2x + 10(-6/5) = -76/3
2x = -40/3
x = -40/3/2
x = -20/3


Input: What value of x satisfies 5x - 20/3 = 0

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


Input: Compute the solution of 9x - 36 = 0

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


Input: Determine x in x^3 - 131/21x^2 - 1789/21x - 247/7 = 0

Output:
x^3 - 131/21x^2 - 1789/21x - 247/7 = 0
(x - -3/7)(x - -19/3)(x - 13) = 0
x - -3/7 = 0
x - -19/3 = 0
x - 13 = 0
x = -3/7
x = -19/3
x = 13


Input:
Find x and y such that
8x + 6y = 22/3
8x + 2y = 10/3

Output:
8x + 6y = 22/3
8x + 2y = 10/3

Using elimination
8*(8x + 6y = 22/3)
8*(8x + 2y = 10/3)
64x + 48y = 176/3
64x + 16y = 80/3
Subtract equations
32y = 32
y = 32/32
y = 1

Substitute y
8x + 6(1) = 22/3
8x = 4/3
x = 4/3/8
x = 1/6


Input:
Find x and y such that
10x + 4y = -371/9
3x + 8y = -413/18

Output:
10x + 4y = -371/9
3x + 8y = -413/18

Using elimination
3*(10x + 4y = -371/9)
10*(3x + 8y = -413/18)
30x + 12y = -371/3
30x + 80y = -2065/9
Subtract equations
-68y = 952/9
y = 952/9/-68
y = -14/9

Substitute y
10x + 4(-14/9) = -371/9
10x = -35
x = -35/10
x = -7/2


Input: Find the solution to x^2 + 93/4x + 323/4 = 0

Output:
x^2 + 93/4x + 323/4 = 0
(x - -17/4)(x - -19) = 0
x - -17/4 = 0  or  x - -19 = 0
x = -17/4
x = -19


Input:
Find x and y such that
7x + 3y = -167/8
6x + 2y = -77/4

Output:
7x + 3y = -167/8
6x + 2y = -77/4

Using elimination
6*(7x + 3y = -167/8)
7*(6x + 2y = -77/4)
42x + 18y = -501/4
42x + 14y = -539/4
Subtract equations
4y = 19/2
y = 19/2/4
y = 19/8

Substitute y
7x + 3(19/8) = -167/8
7x = -28
x = -28/7
x = -4


Input:
Solve the system:
1x + 6y = -3
5x + 3y = 12

Output:
1x + 6y = -3
5x + 3y = 12

Using elimination
5*(1x + 6y = -3)
1*(5x + 3y = 12)
5x + 30y = -15
5x + 3y = 12
Subtract equations
27y = -27
y = -27/27
y = -1

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


Input: Find x in x^3 - 17/3x^2 + 607/64x - 95/24 = 0

Output:
x^3 - 17/3x^2 + 607/64x - 95/24 = 0
(x - 19/8)(x - 5/8)(x - 8/3) = 0
x - 19/8 = 0
x - 5/8 = 0
x - 8/3 = 0
x = 19/8
x = 5/8
x = 8/3


Input: Find the solution to x^2 - 95/6x + 361/6 = 0

Output:
x^2 - 95/6x + 361/6 = 0
(x - 19/2)(x - 19/3) = 0
x - 19/2 = 0  or  x - 19/3 = 0
x = 19/2
x = 19/3


Input: Solve 2x + 20/7 = 0

Output:
2x + 20/7 = 0
2x = -20/7
x = -20/7 / 2
x = -10/7


Input:
Solve the equations:
3x + 6y = 57/5
7x + 10y = 113/5

Output:
3x + 6y = 57/5
7x + 10y = 113/5

Using elimination
7*(3x + 6y = 57/5)
3*(7x + 10y = 113/5)
21x + 42y = 399/5
21x + 30y = 339/5
Subtract equations
12y = 12
y = 12/12
y = 1

Substitute y
3x + 6(1) = 57/5
3x = 27/5
x = 27/5/3
x = 9/5


Input: What value of x satisfies x^2 + 3x - 45/16 = 0

Output:
x^2 + 3x - 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: Determine x in x^3 - 179/10x^2 + 227/5x - 57/2 = 0

Output:
x^3 - 179/10x^2 + 227/5x - 57/2 = 0
(x - 15)(x - 19/10)(x - 1) = 0
x - 15 = 0
x - 19/10 = 0
x - 1 = 0
x = 15
x = 19/10
x = 1


Input: Find x in 9x - 63/8 = 0

Output:
9x - 63/8 = 0
9x = 63/8
x = 63/8 / 9
x = 7/8


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

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


Input:
Solve the system:
6x + 10y = -131/2
4x + 9y = -53

Output:
6x + 10y = -131/2
4x + 9y = -53

Using elimination
4*(6x + 10y = -131/2)
6*(4x + 9y = -53)
24x + 40y = -262
24x + 54y = -318
Subtract equations
-14y = 56
y = 56/-14
y = -4

Substitute y
6x + 10(-4) = -131/2
6x = -51/2
x = -51/2/6
x = -17/4


Input: Compute the solution of x^3 - 1x^2 - 37/16x + 5/8 = 0

Output:
x^3 - 1x^2 - 37/16x + 5/8 = 0
(x - 1/4)(x - -5/4)(x - 2) = 0
x - 1/4 = 0
x - -5/4 = 0
x - 2 = 0
x = 1/4
x = -5/4
x = 2


Input: Compute the solution of 5x - 100/7 = 0

Output:
5x - 100/7 = 0
5x = 100/7
x = 100/7 / 5
x = 20/7


Input: Find the solution to 6x + 18/7 = 0

Output:
6x + 18/7 = 0
6x = -18/7
x = -18/7 / 6
x = -3/7


Input: Find x in x^2 + 13x + 42 = 0

Output:
x^2 + 13x + 42 = 0
(x - -6)(x - -7) = 0
x - -6 = 0  or  x - -7 = 0
x = -6
x = -7


Input: Find x for x^3 - 24/5x^2 + 84/25x - 16/25 = 0

Output:
x^3 - 24/5x^2 + 84/25x - 16/25 = 0
(x - 4)(x - 2/5)(x - 2/5) = 0
x - 4 = 0
x - 2/5 = 0
x - 2/5 = 0
x = 4
x = 2/5
x = 2/5


Input: Solve quickly: x^2 + 127/63x + 44/63 = 0

Output:
x^2 + 127/63x + 44/63 = 0
(x - -11/7)(x - -4/9) = 0
x - -11/7 = 0  or  x - -4/9 = 0
x = -11/7
x = -4/9


Input: Determine x in x^2 + 74/21x - 16/3 = 0

Output:
x^2 + 74/21x - 16/3 = 0
(x - -14/3)(x - 8/7) = 0
x - -14/3 = 0  or  x - 8/7 = 0
x = -14/3
x = 8/7


Input: Determine x in x^3 + 851/168x^2 + 157/21x + 10/3 = 0

Output:
x^3 + 851/168x^2 + 157/21x + 10/3 = 0
(x - -7/8)(x - -20/7)(x - -4/3) = 0
x - -7/8 = 0
x - -20/7 = 0
x - -4/3 = 0
x = -7/8
x = -20/7
x = -4/3


Input:
Solve the equations:
9x + 10y = -227/7
10x + 9y = -401/14

Output:
9x + 10y = -227/7
10x + 9y = -401/14

Using elimination
10*(9x + 10y = -227/7)
9*(10x + 9y = -401/14)
90x + 100y = -2270/7
90x + 81y = -3609/14
Subtract equations
19y = -133/2
y = -133/2/19
y = -7/2

Substitute y
9x + 10(-7/2) = -227/7
9x = 18/7
x = 18/7/9
x = 2/7


Input: Compute the solution of x^2 + 149/90x + 11/18 = 0

Output:
x^2 + 149/90x + 11/18 = 0
(x - -11/10)(x - -5/9) = 0
x - -11/10 = 0  or  x - -5/9 = 0
x = -11/10
x = -5/9


Input: Find x for 6x - 12 = 0

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


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

Output:
7x + 7/3 = 0
7x = -7/3
x = -7/3 / 7
x = -1/3


Input:
Solve the equations:
9x + 9y = -351/10
1x + 2y = -19/5

Output:
9x + 9y = -351/10
1x + 2y = -19/5

Using elimination
1*(9x + 9y = -351/10)
9*(1x + 2y = -19/5)
9x + 9y = -351/10
9x + 18y = -171/5
Subtract equations
-9y = -9/10
y = -9/10/-9
y = 1/10

Substitute y
9x + 9(1/10) = -351/10
9x = -36
x = -36/9
x = -4


Input:
Solve simultaneously:
1x + 8y = 255/8
6x + 3y = 0

Output:
1x + 8y = 255/8
6x + 3y = 0

Using elimination
6*(1x + 8y = 255/8)
1*(6x + 3y = 0)
6x + 48y = 765/4
6x + 3y = 0
Subtract equations
45y = 765/4
y = 765/4/45
y = 17/4

Substitute y
1x + 8(17/4) = 255/8
1x = -17/8
x = -17/8/1
x = -17/8


Input: Solve quickly: 8x + 8 = 0

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


Input: Find x in x^2 + 37/10x + 7/10 = 0

Output:
x^2 + 37/10x + 7/10 = 0
(x - -1/5)(x - -7/2) = 0
x - -1/5 = 0  or  x - -7/2 = 0
x = -1/5
x = -7/2


Input: Find x for 4x - 20/9 = 0

Output:
4x - 20/9 = 0
4x = 20/9
x = 20/9 / 4
x = 5/9


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

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


Input:
Solve the system:
8x + 2y = 30
1x + 5y = 37

Output:
8x + 2y = 30
1x + 5y = 37

Using elimination
1*(8x + 2y = 30)
8*(1x + 5y = 37)
8x + 2y = 30
8x + 40y = 296
Subtract equations
-38y = -266
y = -266/-38
y = 7

Substitute y
8x + 2(7) = 30
8x = 16
x = 16/8
x = 2


Input: Solve the equation x^3 - 79/10x^2 - 104/5x - 2 = 0

Output:
x^3 - 79/10x^2 - 104/5x - 2 = 0
(x - -1/10)(x - -2)(x - 10) = 0
x - -1/10 = 0
x - -2 = 0
x - 10 = 0
x = -1/10
x = -2
x = 10


Input: Solve quickly: x^2 + 27/10x + 17/10 = 0

Output:
x^2 + 27/10x + 17/10 = 0
(x - -17/10)(x - -1) = 0
x - -17/10 = 0  or  x - -1 = 0
x = -17/10
x = -1


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

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


Input:
Solve simultaneously:
3x + 3y = -11/10
1x + 5y = 5/6

Output:
3x + 3y = -11/10
1x + 5y = 5/6

Using elimination
1*(3x + 3y = -11/10)
3*(1x + 5y = 5/6)
3x + 3y = -11/10
3x + 15y = 5/2
Subtract equations
-12y = -18/5
y = -18/5/-12
y = 3/10

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


Input: Determine x in x^2 + 64/7x + 15 = 0

Output:
x^2 + 64/7x + 15 = 0
(x - -15/7)(x - -7) = 0
x - -15/7 = 0  or  x - -7 = 0
x = -15/7
x = -7


Input: Compute the solution of x^3 + 493/90x^2 + 581/90x + 98/45 = 0

Output:
x^3 + 493/90x^2 + 581/90x + 98/45 = 0
(x - -7/10)(x - -4)(x - -7/9) = 0
x - -7/10 = 0
x - -4 = 0
x - -7/9 = 0
x = -7/10
x = -4
x = -7/9


Input: Compute the solution of x^3 - 8x^2 - 121x - 112 = 0

Output:
x^3 - 8x^2 - 121x - 112 = 0
(x - -7)(x - 16)(x - -1) = 0
x - -7 = 0
x - 16 = 0
x - -1 = 0
x = -7
x = 16
x = -1


Input: Find x in x^3 - 253/12x^2 + 441/4x - 931/6 = 0

Output:
x^3 - 253/12x^2 + 441/4x - 931/6 = 0
(x - 19/4)(x - 14)(x - 7/3) = 0
x - 19/4 = 0
x - 14 = 0
x - 7/3 = 0
x = 19/4
x = 14
x = 7/3


Input:
Find x and y such that
9x + 10y = 243/4
8x + 3y = 55/2

Output:
9x + 10y = 243/4
8x + 3y = 55/2

Using elimination
8*(9x + 10y = 243/4)
9*(8x + 3y = 55/2)
72x + 80y = 486
72x + 27y = 495/2
Subtract equations
53y = 477/2
y = 477/2/53
y = 9/2

Substitute y
9x + 10(9/2) = 243/4
9x = 63/4
x = 63/4/9
x = 7/4


Input: Find x for x^2 + 17/15x - 22/3 = 0

Output:
x^2 + 17/15x - 22/3 = 0
(x - 11/5)(x - -10/3) = 0
x - 11/5 = 0  or  x - -10/3 = 0
x = 11/5
x = -10/3


Input: Solve the equation x^3 + 67/9x^2 - 24x + 140/9 = 0

Output:
x^3 + 67/9x^2 - 24x + 140/9 = 0
(x - 14/9)(x - 1)(x - -10) = 0
x - 14/9 = 0
x - 1 = 0
x - -10 = 0
x = 14/9
x = 1
x = -10


Input: Find x for x^3 + 52/35x^2 - 569/175x + 6/5 = 0

Output:
x^3 + 52/35x^2 - 569/175x + 6/5 = 0
(x - 5/7)(x - 3/5)(x - -14/5) = 0
x - 5/7 = 0
x - 3/5 = 0
x - -14/5 = 0
x = 5/7
x = 3/5
x = -14/5


Input: Find the solution to x^3 - 33/10x^2 - 43/10x + 63/5 = 0

Output:
x^3 - 33/10x^2 - 43/10x + 63/5 = 0
(x - -2)(x - 9/5)(x - 7/2) = 0
x - -2 = 0
x - 9/5 = 0
x - 7/2 = 0
x = -2
x = 9/5
x = 7/2


Input:
Solve the equations:
7x + 8y = -169/18
2x + 6y = -13/3

Output:
7x + 8y = -169/18
2x + 6y = -13/3

Using elimination
2*(7x + 8y = -169/18)
7*(2x + 6y = -13/3)
14x + 16y = -169/9
14x + 42y = -91/3
Subtract equations
-26y = 104/9
y = 104/9/-26
y = -4/9

Substitute y
7x + 8(-4/9) = -169/18
7x = -35/6
x = -35/6/7
x = -5/6


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

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


Input: Determine x in x^3 - 35/12x^2 - 31/8x + 33/8 = 0

Output:
x^3 - 35/12x^2 - 31/8x + 33/8 = 0
(x - -3/2)(x - 11/3)(x - 3/4) = 0
x - -3/2 = 0
x - 11/3 = 0
x - 3/4 = 0
x = -3/2
x = 11/3
x = 3/4


Input:
Solve simultaneously:
8x + 3y = -321/56
4x + 2y = -75/28

Output:
8x + 3y = -321/56
4x + 2y = -75/28

Using elimination
4*(8x + 3y = -321/56)
8*(4x + 2y = -75/28)
32x + 12y = -321/14
32x + 16y = -150/7
Subtract equations
-4y = -3/2
y = -3/2/-4
y = 3/8

Substitute y
8x + 3(3/8) = -321/56
8x = -48/7
x = -48/7/8
x = -6/7


Input: Determine x in 6x - 32 = 0

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


Input: Find the solution to x^2 - 41/45x - 38/15 = 0

Output:
x^2 - 41/45x - 38/15 = 0
(x - 19/9)(x - -6/5) = 0
x - 19/9 = 0  or  x - -6/5 = 0
x = 19/9
x = -6/5


Input:
Solve the equations:
8x + 6y = 652/9
7x + 7y = 728/9

Output:
8x + 6y = 652/9
7x + 7y = 728/9

Using elimination
7*(8x + 6y = 652/9)
8*(7x + 7y = 728/9)
56x + 42y = 4564/9
56x + 56y = 5824/9
Subtract equations
-14y = -140
y = -140/-14
y = 10

Substitute y
8x + 6(10) = 652/9
8x = 112/9
x = 112/9/8
x = 14/9


Input: Compute the solution of x^3 - 49/36x^2 - 49/12x + 95/18 = 0

Output:
x^3 - 49/36x^2 - 49/12x + 95/18 = 0
(x - -2)(x - 5/4)(x - 19/9) = 0
x - -2 = 0
x - 5/4 = 0
x - 19/9 = 0
x = -2
x = 5/4
x = 19/9


Input: Find x for 5x - 80 = 0

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


Input:
Solve the system:
9x + 7y = 1528/9
1x + 4y = 202/9

Output:
9x + 7y = 1528/9
1x + 4y = 202/9

Using elimination
1*(9x + 7y = 1528/9)
9*(1x + 4y = 202/9)
9x + 7y = 1528/9
9x + 36y = 202
Subtract equations
-29y = -290/9
y = -290/9/-29
y = 10/9

Substitute y
9x + 7(10/9) = 1528/9
9x = 162
x = 162/9
x = 18


Input: Find x in 10x - 26 = 0

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


Input: Determine x in x^2 + 79/18x - 1/2 = 0

Output:
x^2 + 79/18x - 1/2 = 0
(x - 1/9)(x - -9/2) = 0
x - 1/9 = 0  or  x - -9/2 = 0
x = 1/9
x = -9/2


Input: Find x in x^3 + 7/4x^2 - 9x  = 0

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


Input: Find the solution to x^2 - 159/70x + 34/35 = 0

Output:
x^2 - 159/70x + 34/35 = 0
(x - 17/10)(x - 4/7) = 0
x - 17/10 = 0  or  x - 4/7 = 0
x = 17/10
x = 4/7


Input: Determine x in x^2 + 17/5x - 8 = 0

Output:
x^2 + 17/5x - 8 = 0
(x - -5)(x - 8/5) = 0
x - -5 = 0  or  x - 8/5 = 0
x = -5
x = 8/5


Input:
Solve the system:
8x + 10y = 84
10x + 2y = 84

Output:
8x + 10y = 84
10x + 2y = 84

Using elimination
10*(8x + 10y = 84)
8*(10x + 2y = 84)
80x + 100y = 840
80x + 16y = 672
Subtract equations
84y = 168
y = 168/84
y = 2

Substitute y
8x + 10(2) = 84
8x = 64
x = 64/8
x = 8


Input: Find x for 8x + 120/7 = 0

Output:
8x + 120/7 = 0
8x = -120/7
x = -120/7 / 8
x = -15/7


Input: Determine x in 10x - 75/2 = 0

Output:
10x - 75/2 = 0
10x = 75/2
x = 75/2 / 10
x = 15/4


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

Output:
7x - 7/2 = 0
7x = 7/2
x = 7/2 / 7
x = 1/2


Input: Find x in 4x + 56/3 = 0

Output:
4x + 56/3 = 0
4x = -56/3
x = -56/3 / 4
x = -14/3


Input: Solve quickly: x^3 - 14/5x^2 - 1001/20x + 338/5 = 0

Output:
x^3 - 14/5x^2 - 1001/20x + 338/5 = 0
(x - 8)(x - -13/2)(x - 13/10) = 0
x - 8 = 0
x - -13/2 = 0
x - 13/10 = 0
x = 8
x = -13/2
x = 13/10


Input: Solve quickly: x^2 + 12/7x - 27/7 = 0

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


Input: Solve the equation 5x + 95/4 = 0

Output:
5x + 95/4 = 0
5x = -95/4
x = -95/4 / 5
x = -19/4


Input:
Find x and y such that
9x + 2y = 182/5
9x + 3y = 183/5

Output:
9x + 2y = 182/5
9x + 3y = 183/5

Using elimination
9*(9x + 2y = 182/5)
9*(9x + 3y = 183/5)
81x + 18y = 1638/5
81x + 27y = 1647/5
Subtract equations
-9y = -9/5
y = -9/5/-9
y = 1/5

Substitute y
9x + 2(1/5) = 182/5
9x = 36
x = 36/9
x = 4


Input: Find x in x^2 + 39/7x + 20/7 = 0

Output:
x^2 + 39/7x + 20/7 = 0
(x - -4/7)(x - -5) = 0
x - -4/7 = 0  or  x - -5 = 0
x = -4/7
x = -5


Input: What value of x satisfies x^2 + 2/5x - 24/25 = 0

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


Input:
Solve the equations:
8x + 9y = 76/15
6x + 10y = 9

Output:
8x + 9y = 76/15
6x + 10y = 9

Using elimination
6*(8x + 9y = 76/15)
8*(6x + 10y = 9)
48x + 54y = 152/5
48x + 80y = 72
Subtract equations
-26y = -208/5
y = -208/5/-26
y = 8/5

Substitute y
8x + 9(8/5) = 76/15
8x = -28/3
x = -28/3/8
x = -7/6


Input: Solve the equation x^3 - 8/9x^2 - 19/3x  = 0

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


Input:
Solve simultaneously:
3x + 3y = -279/14
10x + 1y = -330/7

Output:
3x + 3y = -279/14
10x + 1y = -330/7

Using elimination
10*(3x + 3y = -279/14)
3*(10x + 1y = -330/7)
30x + 30y = -1395/7
30x + 3y = -990/7
Subtract equations
27y = -405/7
y = -405/7/27
y = -15/7

Substitute y
3x + 3(-15/7) = -279/14
3x = -27/2
x = -27/2/3
x = -9/2


Input: Solve quickly: x^3 - 139/28x^2 - 89/28x + 15 = 0

Output:
x^3 - 139/28x^2 - 89/28x + 15 = 0
(x - -7/4)(x - 5)(x - 12/7) = 0
x - -7/4 = 0
x - 5 = 0
x - 12/7 = 0
x = -7/4
x = 5
x = 12/7


Input: Solve the equation x^3 + 4/5x^2 - 147/25x + 54/25 = 0

Output:
x^3 + 4/5x^2 - 147/25x + 54/25 = 0
(x - -3)(x - 2/5)(x - 9/5) = 0
x - -3 = 0
x - 2/5 = 0
x - 9/5 = 0
x = -3
x = 2/5
x = 9/5


Input:
Find x and y such that
5x + 2y = 49/18
4x + 9y = -22/5

Output:
5x + 2y = 49/18
4x + 9y = -22/5

Using elimination
4*(5x + 2y = 49/18)
5*(4x + 9y = -22/5)
20x + 8y = 98/9
20x + 45y = -22
Subtract equations
-37y = 296/9
y = 296/9/-37
y = -8/9

Substitute y
5x + 2(-8/9) = 49/18
5x = 9/2
x = 9/2/5
x = 9/10


Input: What value of x satisfies x^2 - 14/3x + 8/3 = 0

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


Input: Solve quickly: x^3 - 76/21x^2 + 76/21x - 16/21 = 0

Output:
x^3 - 76/21x^2 + 76/21x - 16/21 = 0
(x - 2)(x - 4/3)(x - 2/7) = 0
x - 2 = 0
x - 4/3 = 0
x - 2/7 = 0
x = 2
x = 4/3
x = 2/7


Input: Compute the solution of x^2 - 14/9x + 16/27 = 0

Output:
x^2 - 14/9x + 16/27 = 0
(x - 8/9)(x - 2/3) = 0
x - 8/9 = 0  or  x - 2/3 = 0
x = 8/9
x = 2/3


Input: Compute the solution of x^3 - 365/36x^2 + 431/72x + 19/24 = 0

Output:
x^3 - 365/36x^2 + 431/72x + 19/24 = 0
(x - 19/2)(x - -1/9)(x - 3/4) = 0
x - 19/2 = 0
x - -1/9 = 0
x - 3/4 = 0
x = 19/2
x = -1/9
x = 3/4


Input: What value of x satisfies x^3 + 20/9x^2 - 37/3x + 70/9 = 0

Output:
x^3 + 20/9x^2 - 37/3x + 70/9 = 0
(x - -5)(x - 2)(x - 7/9) = 0
x - -5 = 0
x - 2 = 0
x - 7/9 = 0
x = -5
x = 2
x = 7/9


Input: Find x for 10x + 25 = 0

Output:
10x + 25 = 0
10x = -25
x = -25 / 10
x = -5/2


Input:
Solve the equations:
9x + 6y = 339/20
9x + 3y = 327/20

Output:
9x + 6y = 339/20
9x + 3y = 327/20

Using elimination
9*(9x + 6y = 339/20)
9*(9x + 3y = 327/20)
81x + 54y = 3051/20
81x + 27y = 2943/20
Subtract equations
27y = 27/5
y = 27/5/27
y = 1/5

Substitute y
9x + 6(1/5) = 339/20
9x = 63/4
x = 63/4/9
x = 7/4


Input: Find x for x^3 - 51/7x^2 + 108/7x - 64/7 = 0

Output:
x^3 - 51/7x^2 + 108/7x - 64/7 = 0
(x - 4)(x - 1)(x - 16/7) = 0
x - 4 = 0
x - 1 = 0
x - 16/7 = 0
x = 4
x = 1
x = 16/7


Input: Solve quickly: 2x + 2 = 0

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


Input: Solve the equation x^2 + 247/30x + 361/30 = 0

Output:
x^2 + 247/30x + 361/30 = 0
(x - -19/3)(x - -19/10) = 0
x - -19/3 = 0  or  x - -19/10 = 0
x = -19/3
x = -19/10


Input: Solve x^2 + 44/45x - 64/45 = 0

Output:
x^2 + 44/45x - 64/45 = 0
(x - -16/9)(x - 4/5) = 0
x - -16/9 = 0  or  x - 4/5 = 0
x = -16/9
x = 4/5


Input:
Solve the equations:
5x + 10y = -245/4
6x + 8y = -66

Output:
5x + 10y = -245/4
6x + 8y = -66

Using elimination
6*(5x + 10y = -245/4)
5*(6x + 8y = -66)
30x + 60y = -735/2
30x + 40y = -330
Subtract equations
20y = -75/2
y = -75/2/20
y = -15/8

Substitute y
5x + 10(-15/8) = -245/4
5x = -85/2
x = -85/2/5
x = -17/2


Input:
Find x and y such that
8x + 2y = -82/5
3x + 8y = -96/5

Output:
8x + 2y = -82/5
3x + 8y = -96/5

Using elimination
3*(8x + 2y = -82/5)
8*(3x + 8y = -96/5)
24x + 6y = -246/5
24x + 64y = -768/5
Subtract equations
-58y = 522/5
y = 522/5/-58
y = -9/5

Substitute y
8x + 2(-9/5) = -82/5
8x = -64/5
x = -64/5/8
x = -8/5


Input: Find x for 5x - 25/6 = 0

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


Input: Find the solution to 1x + 5 = 0

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


Input: Solve x^2 + 53/6x + 55/3 = 0

Output:
x^2 + 53/6x + 55/3 = 0
(x - -11/2)(x - -10/3) = 0
x - -11/2 = 0  or  x - -10/3 = 0
x = -11/2
x = -10/3


Input: Find x for 6x + 8/3 = 0

Output:
6x + 8/3 = 0
6x = -8/3
x = -8/3 / 6
x = -4/9


Input: What value of x satisfies 2x + 36/7 = 0

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


Input:
Find x and y such that
9x + 5y = 138/7
5x + 7y = 102/7

Output:
9x + 5y = 138/7
5x + 7y = 102/7

Using elimination
5*(9x + 5y = 138/7)
9*(5x + 7y = 102/7)
45x + 25y = 690/7
45x + 63y = 918/7
Subtract equations
-38y = -228/7
y = -228/7/-38
y = 6/7

Substitute y
9x + 5(6/7) = 138/7
9x = 108/7
x = 108/7/9
x = 12/7


Input: Find x for 1x + 8/5 = 0

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


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

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

Using elimination
6*(3x + 1y = 5/4)
3*(6x + 4y = -1)
18x + 6y = 15/2
18x + 12y = -3
Subtract equations
-6y = 21/2
y = 21/2/-6
y = -7/4

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


Input:
Solve the system:
10x + 5y = -27
7x + 1y = -77/5

Output:
10x + 5y = -27
7x + 1y = -77/5

Using elimination
7*(10x + 5y = -27)
10*(7x + 1y = -77/5)
70x + 35y = -189
70x + 10y = -154
Subtract equations
25y = -35
y = -35/25
y = -7/5

Substitute y
10x + 5(-7/5) = -27
10x = -20
x = -20/10
x = -2


Input: Determine x in 1x - 5 = 0

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


Input: Solve quickly: x^2 - 11/2x - 38 = 0

Output:
x^2 - 11/2x - 38 = 0
(x - -4)(x - 19/2) = 0
x - -4 = 0  or  x - 19/2 = 0
x = -4
x = 19/2


Input: Find x for x^3 + 341/90x^2 + 34/9x + 16/15 = 0

Output:
x^3 + 341/90x^2 + 34/9x + 16/15 = 0
(x - -8/9)(x - -12/5)(x - -1/2) = 0
x - -8/9 = 0
x - -12/5 = 0
x - -1/2 = 0
x = -8/9
x = -12/5
x = -1/2


Input: Solve the equation x^3 + 93/70x^2 - 313/70x - 153/35 = 0

Output:
x^3 + 93/70x^2 - 313/70x - 153/35 = 0
(x - -9/10)(x - 2)(x - -17/7) = 0
x - -9/10 = 0
x - 2 = 0
x - -17/7 = 0
x = -9/10
x = 2
x = -17/7


Input:
Solve the equations:
9x + 10y = -1493/24
1x + 9y = -455/8

Output:
9x + 10y = -1493/24
1x + 9y = -455/8

Using elimination
1*(9x + 10y = -1493/24)
9*(1x + 9y = -455/8)
9x + 10y = -1493/24
9x + 81y = -4095/8
Subtract equations
-71y = 1349/3
y = 1349/3/-71
y = -19/3

Substitute y
9x + 10(-19/3) = -1493/24
9x = 9/8
x = 9/8/9
x = 1/8


Input: Find x in x^3 - 1/5x^2 - 13/20x - 3/20 = 0

Output:
x^3 - 1/5x^2 - 13/20x - 3/20 = 0
(x - -3/10)(x - -1/2)(x - 1) = 0
x - -3/10 = 0
x - -1/2 = 0
x - 1 = 0
x = -3/10
x = -1/2
x = 1


Input: Determine x in x^3 - 9/8x^2 - 695/32x + 1425/32 = 0

Output:
x^3 - 9/8x^2 - 695/32x + 1425/32 = 0
(x - -5)(x - 15/4)(x - 19/8) = 0
x - -5 = 0
x - 15/4 = 0
x - 19/8 = 0
x = -5
x = 15/4
x = 19/8


Input: Determine x in x^2 - 19/4x + 15/4 = 0

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


Input: Solve quickly: x^2 - 11/2x - 38 = 0

Output:
x^2 - 11/2x - 38 = 0
(x - -4)(x - 19/2) = 0
x - -4 = 0  or  x - 19/2 = 0
x = -4
x = 19/2


Input: Solve quickly: x^2 + 7/10x - 6/5 = 0

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


Input: Find the solution to x^2 + 14/3x - 17/3 = 0

Output:
x^2 + 14/3x - 17/3 = 0
(x - -17/3)(x - 1) = 0
x - -17/3 = 0  or  x - 1 = 0
x = -17/3
x = 1


Input:
Solve the equations:
8x + 10y = 13
4x + 6y = 19/2

Output:
8x + 10y = 13
4x + 6y = 19/2

Using elimination
4*(8x + 10y = 13)
8*(4x + 6y = 19/2)
32x + 40y = 52
32x + 48y = 76
Subtract equations
-8y = -24
y = -24/-8
y = 3

Substitute y
8x + 10(3) = 13
8x = -17
x = -17/8
x = -17/8


Input: Find x for x^2 + 4x - 12 = 0

Output:
x^2 + 4x - 12 = 0
(x - -6)(x - 2) = 0
x - -6 = 0  or  x - 2 = 0
x = -6
x = 2


Input: Determine x in x^2 + 21x + 20 = 0

Output:
x^2 + 21x + 20 = 0
(x - -1)(x - -20) = 0
x - -1 = 0  or  x - -20 = 0
x = -1
x = -20


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

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


Input: Solve the equation x^2 - 18x + 17 = 0

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


Input: Find x in x^3 + 37/15x^2 + 2x + 8/15 = 0

Output:
x^3 + 37/15x^2 + 2x + 8/15 = 0
(x - -1)(x - -2/3)(x - -4/5) = 0
x - -1 = 0
x - -2/3 = 0
x - -4/5 = 0
x = -1
x = -2/3
x = -4/5


Input: Find the solution to x^2 - 73/30x + 11/10 = 0

Output:
x^2 - 73/30x + 11/10 = 0
(x - 3/5)(x - 11/6) = 0
x - 3/5 = 0  or  x - 11/6 = 0
x = 3/5
x = 11/6


Input: Determine x in x^2 - 86/9x - 143/9 = 0

Output:
x^2 - 86/9x - 143/9 = 0
(x - -13/9)(x - 11) = 0
x - -13/9 = 0  or  x - 11 = 0
x = -13/9
x = 11


Input:
Solve the equations:
5x + 7y = -689/30
6x + 9y = -281/10

Output:
5x + 7y = -689/30
6x + 9y = -281/10

Using elimination
6*(5x + 7y = -689/30)
5*(6x + 9y = -281/10)
30x + 42y = -689/5
30x + 45y = -281/2
Subtract equations
-3y = 27/10
y = 27/10/-3
y = -9/10

Substitute y
5x + 7(-9/10) = -689/30
5x = -50/3
x = -50/3/5
x = -10/3


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

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


Input: Solve quickly: x^2 - 41/3x - 14/3 = 0

Output:
x^2 - 41/3x - 14/3 = 0
(x - -1/3)(x - 14) = 0
x - -1/3 = 0  or  x - 14 = 0
x = -1/3
x = 14


Input:
Solve the system:
9x + 4y = -476/15
2x + 3y = -81/5

Output:
9x + 4y = -476/15
2x + 3y = -81/5

Using elimination
2*(9x + 4y = -476/15)
9*(2x + 3y = -81/5)
18x + 8y = -952/15
18x + 27y = -729/5
Subtract equations
-19y = 247/3
y = 247/3/-19
y = -13/3

Substitute y
9x + 4(-13/3) = -476/15
9x = -72/5
x = -72/5/9
x = -8/5


Input:
Solve simultaneously:
7x + 4y = 593/10
6x + 7y = 222/5

Output:
7x + 4y = 593/10
6x + 7y = 222/5

Using elimination
6*(7x + 4y = 593/10)
7*(6x + 7y = 222/5)
42x + 24y = 1779/5
42x + 49y = 1554/5
Subtract equations
-25y = 45
y = 45/-25
y = -9/5

Substitute y
7x + 4(-9/5) = 593/10
7x = 133/2
x = 133/2/7
x = 19/2


Input: Find the solution to 7x - 21/2 = 0

Output:
7x - 21/2 = 0
7x = 21/2
x = 21/2 / 7
x = 3/2


Input: Solve x^2 - 59/18x - 7/9 = 0

Output:
x^2 - 59/18x - 7/9 = 0
(x - -2/9)(x - 7/2) = 0
x - -2/9 = 0  or  x - 7/2 = 0
x = -2/9
x = 7/2


Input: Compute the solution of x^3 - 8x^2 - 309/4x - 189/2 = 0

Output:
x^3 - 8x^2 - 309/4x - 189/2 = 0
(x - -3/2)(x - -9/2)(x - 14) = 0
x - -3/2 = 0
x - -9/2 = 0
x - 14 = 0
x = -3/2
x = -9/2
x = 14


Input: Solve the equation x^3 - 373/36x^2 + 233/12x - 38/9 = 0

Output:
x^3 - 373/36x^2 + 233/12x - 38/9 = 0
(x - 8)(x - 19/9)(x - 1/4) = 0
x - 8 = 0
x - 19/9 = 0
x - 1/4 = 0
x = 8
x = 19/9
x = 1/4


Input: Find x in x^2 + 67/6x + 76/3 = 0

Output:
x^2 + 67/6x + 76/3 = 0
(x - -8)(x - -19/6) = 0
x - -8 = 0  or  x - -19/6 = 0
x = -8
x = -19/6


Input: Solve the equation 1x - 20/3 = 0

Output:
1x - 20/3 = 0
1x = 20/3
x = 20/3 / 1
x = 20/3


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

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


Input:
Find x and y such that
5x + 9y = 73
7x + 8y = 281/5

Output:
5x + 9y = 73
7x + 8y = 281/5

Using elimination
7*(5x + 9y = 73)
5*(7x + 8y = 281/5)
35x + 63y = 511
35x + 40y = 281
Subtract equations
23y = 230
y = 230/23
y = 10

Substitute y
5x + 9(10) = 73
5x = -17
x = -17/5
x = -17/5


Input:
Solve the equations:
6x + 10y = 125/2
10x + 8y = 76

Output:
6x + 10y = 125/2
10x + 8y = 76

Using elimination
10*(6x + 10y = 125/2)
6*(10x + 8y = 76)
60x + 100y = 625
60x + 48y = 456
Subtract equations
52y = 169
y = 169/52
y = 13/4

Substitute y
6x + 10(13/4) = 125/2
6x = 30
x = 30/6
x = 5


Input: Find the solution to x^2 + 20/9x + 4/9 = 0

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


Input: Solve x^2 + 2/9x  = 0

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


Input: Solve 8x - 120/7 = 0

Output:
8x - 120/7 = 0
8x = 120/7
x = 120/7 / 8
x = 15/7


Input: Solve quickly: x^2 - 27/20x - 81/10 = 0

Output:
x^2 - 27/20x - 81/10 = 0
(x - -9/4)(x - 18/5) = 0
x - -9/4 = 0  or  x - 18/5 = 0
x = -9/4
x = 18/5


Input: Solve x^3 + 4x^2 + 21/4x + 9/4 = 0

Output:
x^3 + 4x^2 + 21/4x + 9/4 = 0
(x - -1)(x - -3/2)(x - -3/2) = 0
x - -1 = 0
x - -3/2 = 0
x - -3/2 = 0
x = -1
x = -3/2
x = -3/2


Input: Solve quickly: 6x + 57/2 = 0

Output:
6x + 57/2 = 0
6x = -57/2
x = -57/2 / 6
x = -19/4


Input:
Find x and y such that
6x + 6y = -36
2x + 1y = -15

Output:
6x + 6y = -36
2x + 1y = -15

Using elimination
2*(6x + 6y = -36)
6*(2x + 1y = -15)
12x + 12y = -72
12x + 6y = -90
Subtract equations
6y = 18
y = 18/6
y = 3

Substitute y
6x + 6(3) = -36
6x = -54
x = -54/6
x = -9


Input:
Find x and y such that
3x + 7y = 4
5x + 7y = 2

Output:
3x + 7y = 4
5x + 7y = 2

Using elimination
5*(3x + 7y = 4)
3*(5x + 7y = 2)
15x + 35y = 20
15x + 21y = 6
Subtract equations
14y = 14
y = 14/14
y = 1

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


Input: Solve quickly: x^3 + 73/36x^2 - 1/2x  = 0

Output:
x^3 + 73/36x^2 - 1/2x  = 0
(x - 0)(x - -9/4)(x - 2/9) = 0
x - 0 = 0
x - -9/4 = 0
x - 2/9 = 0
x = 0
x = -9/4
x = 2/9


Input: Compute the solution of x^2 - 8/3x + 140/81 = 0

Output:
x^2 - 8/3x + 140/81 = 0
(x - 10/9)(x - 14/9) = 0
x - 10/9 = 0  or  x - 14/9 = 0
x = 10/9
x = 14/9


Input: Find x in x^2 + 9x + 18 = 0

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


Input: Find the solution to x^2 - 25/18x - 152/27 = 0

Output:
x^2 - 25/18x - 152/27 = 0
(x - -16/9)(x - 19/6) = 0
x - -16/9 = 0  or  x - 19/6 = 0
x = -16/9
x = 19/6


Input: Compute the solution of x^2 + 7/9x - 136/27 = 0

Output:
x^2 + 7/9x - 136/27 = 0
(x - -8/3)(x - 17/9) = 0
x - -8/3 = 0  or  x - 17/9 = 0
x = -8/3
x = 17/9


Input: Compute the solution of x^3 + 33/4x^2 - 185/2x + 525/4 = 0

Output:
x^3 + 33/4x^2 - 185/2x + 525/4 = 0
(x - 5)(x - -15)(x - 7/4) = 0
x - 5 = 0
x - -15 = 0
x - 7/4 = 0
x = 5
x = -15
x = 7/4


Input: Find the solution to x^3  - 9x  = 0

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


Input: Find x for x^2 + 83/24x + 17/6 = 0

Output:
x^2 + 83/24x + 17/6 = 0
(x - -4/3)(x - -17/8) = 0
x - -4/3 = 0  or  x - -17/8 = 0
x = -4/3
x = -17/8


Input: What value of x satisfies 1x + 11/4 = 0

Output:
1x + 11/4 = 0
1x = -11/4
x = -11/4 / 1
x = -11/4


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

Output:
2x - 11/4 = 0
2x = 11/4
x = 11/4 / 2
x = 11/8


Input: Solve the equation x^3 + 58/35x^2 - 313/35x + 12/7 = 0

Output:
x^3 + 58/35x^2 - 313/35x + 12/7 = 0
(x - 15/7)(x - -4)(x - 1/5) = 0
x - 15/7 = 0
x - -4 = 0
x - 1/5 = 0
x = 15/7
x = -4
x = 1/5


Input:
Solve the equations:
2x + 6y = 68/5
8x + 7y = 136/5

Output:
2x + 6y = 68/5
8x + 7y = 136/5

Using elimination
8*(2x + 6y = 68/5)
2*(8x + 7y = 136/5)
16x + 48y = 544/5
16x + 14y = 272/5
Subtract equations
34y = 272/5
y = 272/5/34
y = 8/5

Substitute y
2x + 6(8/5) = 68/5
2x = 4
x = 4/2
x = 2


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

Output:
2x + 40/7 = 0
2x = -40/7
x = -40/7 / 2
x = -20/7


Input: Compute the solution of x^3 - 5/4x^2 - 63/8x - 45/8 = 0

Output:
x^3 - 5/4x^2 - 63/8x - 45/8 = 0
(x - 15/4)(x - -1)(x - -3/2) = 0
x - 15/4 = 0
x - -1 = 0
x - -3/2 = 0
x = 15/4
x = -1
x = -3/2


Input: Solve 1x + 3 = 0

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


Input:
Solve the equations:
9x + 5y = 96/5
6x + 2y = 48/5

Output:
9x + 5y = 96/5
6x + 2y = 48/5

Using elimination
6*(9x + 5y = 96/5)
9*(6x + 2y = 48/5)
54x + 30y = 576/5
54x + 18y = 432/5
Subtract equations
12y = 144/5
y = 144/5/12
y = 12/5

Substitute y
9x + 5(12/5) = 96/5
9x = 36/5
x = 36/5/9
x = 4/5


Input:
Solve the system:
4x + 1y = -174/5
9x + 2y = -393/5

Output:
4x + 1y = -174/5
9x + 2y = -393/5

Using elimination
9*(4x + 1y = -174/5)
4*(9x + 2y = -393/5)
36x + 9y = -1566/5
36x + 8y = -1572/5
Subtract equations
1y = 6/5
y = 6/5/1
y = 6/5

Substitute y
4x + 1(6/5) = -174/5
4x = -36
x = -36/4
x = -9


Input: Determine x in x^3 - 23/9x^2 + 76/81x  = 0

Output:
x^3 - 23/9x^2 + 76/81x  = 0
(x - 19/9)(x - 4/9)(x - 0) = 0
x - 19/9 = 0
x - 4/9 = 0
x - 0 = 0
x = 19/9
x = 4/9
x = 0


Input: What value of x satisfies 3x + 9/4 = 0

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


Input:
Solve the equations:
2x + 4y = 29/5
2x + 2y = 19/5

Output:
2x + 4y = 29/5
2x + 2y = 19/5

Using elimination
2*(2x + 4y = 29/5)
2*(2x + 2y = 19/5)
4x + 8y = 58/5
4x + 4y = 38/5
Subtract equations
4y = 4
y = 4/4
y = 1

Substitute y
2x + 4(1) = 29/5
2x = 9/5
x = 9/5/2
x = 9/10


Input: Solve quickly: x^2 - 151/8x + 63/4 = 0

Output:
x^2 - 151/8x + 63/4 = 0
(x - 7/8)(x - 18) = 0
x - 7/8 = 0  or  x - 18 = 0
x = 7/8
x = 18


Input: Solve the equation 9x + 13 = 0

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


Input: Solve quickly: x^3 - 47/10x^2 - 71/80x + 91/5 = 0

Output:
x^3 - 47/10x^2 - 71/80x + 91/5 = 0
(x - 13/4)(x - -7/4)(x - 16/5) = 0
x - 13/4 = 0
x - -7/4 = 0
x - 16/5 = 0
x = 13/4
x = -7/4
x = 16/5


Input: Solve the equation x^2 - 129/40x + 13/5 = 0

Output:
x^2 - 129/40x + 13/5 = 0
(x - 13/8)(x - 8/5) = 0
x - 13/8 = 0  or  x - 8/5 = 0
x = 13/8
x = 8/5


Input: Find the solution to x^2 - 17/4x + 1 = 0

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


Input: Solve quickly: x^3 - 7/5x^2 + 53/100x - 1/25 = 0

Output:
x^3 - 7/5x^2 + 53/100x - 1/25 = 0
(x - 1/10)(x - 1/2)(x - 4/5) = 0
x - 1/10 = 0
x - 1/2 = 0
x - 4/5 = 0
x = 1/10
x = 1/2
x = 4/5


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

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


Input: Solve the equation x^2 - 29/18x - 19/18 = 0

Output:
x^2 - 29/18x - 19/18 = 0
(x - 19/9)(x - -1/2) = 0
x - 19/9 = 0  or  x - -1/2 = 0
x = 19/9
x = -1/2


Input: Determine x in x^2 - 10/9x - 56/81 = 0

Output:
x^2 - 10/9x - 56/81 = 0
(x - -4/9)(x - 14/9) = 0
x - -4/9 = 0  or  x - 14/9 = 0
x = -4/9
x = 14/9


Input:
Solve the system:
3x + 10y = -1121/30
3x + 9y = -171/5

Output:
3x + 10y = -1121/30
3x + 9y = -171/5

Using elimination
3*(3x + 10y = -1121/30)
3*(3x + 9y = -171/5)
9x + 30y = -1121/10
9x + 27y = -513/5
Subtract equations
3y = -19/2
y = -19/2/3
y = -19/6

Substitute y
3x + 10(-19/6) = -1121/30
3x = -57/10
x = -57/10/3
x = -19/10


Input: What value of x satisfies x^3 - 4/9x^2 - 85/36x + 7/6 = 0

Output:
x^3 - 4/9x^2 - 85/36x + 7/6 = 0
(x - 3/2)(x - -14/9)(x - 1/2) = 0
x - 3/2 = 0
x - -14/9 = 0
x - 1/2 = 0
x = 3/2
x = -14/9
x = 1/2


Input: Solve 3x + 12 = 0

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


Input: Determine x in x^3 + 76/15x^2 + 32/5x  = 0

Output:
x^3 + 76/15x^2 + 32/5x  = 0
(x - -12/5)(x - 0)(x - -8/3) = 0
x - -12/5 = 0
x - 0 = 0
x - -8/3 = 0
x = -12/5
x = 0
x = -8/3


Input:
Solve the system:
7x + 7y = 28
6x + 1y = 53/2

Output:
7x + 7y = 28
6x + 1y = 53/2

Using elimination
6*(7x + 7y = 28)
7*(6x + 1y = 53/2)
42x + 42y = 168
42x + 7y = 371/2
Subtract equations
35y = -35/2
y = -35/2/35
y = -1/2

Substitute y
7x + 7(-1/2) = 28
7x = 63/2
x = 63/2/7
x = 9/2


Input: Find x for x^2 + 15/2x - 77/2 = 0

Output:
x^2 + 15/2x - 77/2 = 0
(x - -11)(x - 7/2) = 0
x - -11 = 0  or  x - 7/2 = 0
x = -11
x = 7/2


Input: Solve x^3 - 73/5x^2 + 242/5x - 24 = 0

Output:
x^3 - 73/5x^2 + 242/5x - 24 = 0
(x - 10)(x - 3/5)(x - 4) = 0
x - 10 = 0
x - 3/5 = 0
x - 4 = 0
x = 10
x = 3/5
x = 4


Input: Find the solution to x^3 - 47/10x^2 + 1/10x + 18/5 = 0

Output:
x^3 - 47/10x^2 + 1/10x + 18/5 = 0
(x - 1)(x - -4/5)(x - 9/2) = 0
x - 1 = 0
x - -4/5 = 0
x - 9/2 = 0
x = 1
x = -4/5
x = 9/2


Input:
Solve the equations:
8x + 10y = 8
6x + 5y = 11

Output:
8x + 10y = 8
6x + 5y = 11

Using elimination
6*(8x + 10y = 8)
8*(6x + 5y = 11)
48x + 60y = 48
48x + 40y = 88
Subtract equations
20y = -40
y = -40/20
y = -2

Substitute y
8x + 10(-2) = 8
8x = 28
x = 28/8
x = 7/2


Input:
Solve the equations:
7x + 9y = -99/8
2x + 7y = 47/8

Output:
7x + 9y = -99/8
2x + 7y = 47/8

Using elimination
2*(7x + 9y = -99/8)
7*(2x + 7y = 47/8)
14x + 18y = -99/4
14x + 49y = 329/8
Subtract equations
-31y = -527/8
y = -527/8/-31
y = 17/8

Substitute y
7x + 9(17/8) = -99/8
7x = -63/2
x = -63/2/7
x = -9/2


Input: Find x for x^3 + 55/6x^2 - 9x - 20/3 = 0

Output:
x^3 + 55/6x^2 - 9x - 20/3 = 0
(x - -1/2)(x - -10)(x - 4/3) = 0
x - -1/2 = 0
x - -10 = 0
x - 4/3 = 0
x = -1/2
x = -10
x = 4/3


Input: Find x in 1x - 1 = 0

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


Input: Find x for x^2 - 20/7x  = 0

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


Input: Find x for 1x + 13/4 = 0

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


Input:
Solve the system:
6x + 1y = 19/6
1x + 1y = 47/18

Output:
6x + 1y = 19/6
1x + 1y = 47/18

Using elimination
1*(6x + 1y = 19/6)
6*(1x + 1y = 47/18)
6x + 1y = 19/6
6x + 6y = 47/3
Subtract equations
-5y = -25/2
y = -25/2/-5
y = 5/2

Substitute y
6x + 1(5/2) = 19/6
6x = 2/3
x = 2/3/6
x = 1/9


Input: Find x for 4x + 8 = 0

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


Input: Compute the solution of 9x - 6 = 0

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


Input: What value of x satisfies x^2 - 9/28x - 81/14 = 0

Output:
x^2 - 9/28x - 81/14 = 0
(x - -9/4)(x - 18/7) = 0
x - -9/4 = 0  or  x - 18/7 = 0
x = -9/4
x = 18/7


Input: Solve quickly: x^3 - 568/35x^2 + 1559/35x - 234/7 = 0

Output:
x^3 - 568/35x^2 + 1559/35x - 234/7 = 0
(x - 13)(x - 10/7)(x - 9/5) = 0
x - 13 = 0
x - 10/7 = 0
x - 9/5 = 0
x = 13
x = 10/7
x = 9/5


Input: Find x for x^2 + 13/30x - 11/15 = 0

Output:
x^2 + 13/30x - 11/15 = 0
(x - 2/3)(x - -11/10) = 0
x - 2/3 = 0  or  x - -11/10 = 0
x = 2/3
x = -11/10


Input: Find the solution to x^3 - 323/30x^2 + 121/12x + 741/40 = 0

Output:
x^3 - 323/30x^2 + 121/12x + 741/40 = 0
(x - 19/2)(x - 13/6)(x - -9/10) = 0
x - 19/2 = 0
x - 13/6 = 0
x - -9/10 = 0
x = 19/2
x = 13/6
x = -9/10


Input: Solve quickly: x^2 - 166/45x + 17/5 = 0

Output:
x^2 - 166/45x + 17/5 = 0
(x - 9/5)(x - 17/9) = 0
x - 9/5 = 0  or  x - 17/9 = 0
x = 9/5
x = 17/9


Input: Solve the equation x^3 + 85/28x^2 + 7/4x - 9/14 = 0

Output:
x^3 + 85/28x^2 + 7/4x - 9/14 = 0
(x - -2)(x - 1/4)(x - -9/7) = 0
x - -2 = 0
x - 1/4 = 0
x - -9/7 = 0
x = -2
x = 1/4
x = -9/7


Input: Solve quickly: x^3 + 8/3x^2 - 5/9x - 28/9 = 0

Output:
x^3 + 8/3x^2 - 5/9x - 28/9 = 0
(x - 1)(x - -7/3)(x - -4/3) = 0
x - 1 = 0
x - -7/3 = 0
x - -4/3 = 0
x = 1
x = -7/3
x = -4/3


Input:
Find x and y such that
7x + 1y = 53/3
4x + 3y = 74/3

Output:
7x + 1y = 53/3
4x + 3y = 74/3

Using elimination
4*(7x + 1y = 53/3)
7*(4x + 3y = 74/3)
28x + 4y = 212/3
28x + 21y = 518/3
Subtract equations
-17y = -102
y = -102/-17
y = 6

Substitute y
7x + 1(6) = 53/3
7x = 35/3
x = 35/3/7
x = 5/3


Input: Find x in x^2 + 269/63x + 38/9 = 0

Output:
x^2 + 269/63x + 38/9 = 0
(x - -14/9)(x - -19/7) = 0
x - -14/9 = 0  or  x - -19/7 = 0
x = -14/9
x = -19/7


Input: What value of x satisfies x^3 - 25/12x^2 - 191/36x + 10 = 0

Output:
x^3 - 25/12x^2 - 191/36x + 10 = 0
(x - -9/4)(x - 8/3)(x - 5/3) = 0
x - -9/4 = 0
x - 8/3 = 0
x - 5/3 = 0
x = -9/4
x = 8/3
x = 5/3


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

Output:
7x - 7/2 = 0
7x = 7/2
x = 7/2 / 7
x = 1/2


Input: Find x in x^2 - 24/35x - 27/35 = 0

Output:
x^2 - 24/35x - 27/35 = 0
(x - -3/5)(x - 9/7) = 0
x - -3/5 = 0  or  x - 9/7 = 0
x = -3/5
x = 9/7


Input: Solve quickly: x^2 - 4x  = 0

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


Input: Solve quickly: 5x - 10 = 0

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


Input: Determine x in x^2 + 10x + 9 = 0

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


Input: Find x for 7x - 91/10 = 0

Output:
7x - 91/10 = 0
7x = 91/10
x = 91/10 / 7
x = 13/10


Input: Find x in x^3 + 44/45x^2 - 359/135x - 76/135 = 0

Output:
x^3 + 44/45x^2 - 359/135x - 76/135 = 0
(x - -1/5)(x - 4/3)(x - -19/9) = 0
x - -1/5 = 0
x - 4/3 = 0
x - -19/9 = 0
x = -1/5
x = 4/3
x = -19/9


Input: Determine x in x^3 - 94/35x^2 + 481/245x - 8/35 = 0

Output:
x^3 - 94/35x^2 + 481/245x - 8/35 = 0
(x - 8/7)(x - 1/7)(x - 7/5) = 0
x - 8/7 = 0
x - 1/7 = 0
x - 7/5 = 0
x = 8/7
x = 1/7
x = 7/5


Input: Solve quickly: 6x - 15/4 = 0

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


Input: Find x in x^2 + 1/8x - 17/4 = 0

Output:
x^2 + 1/8x - 17/4 = 0
(x - 2)(x - -17/8) = 0
x - 2 = 0  or  x - -17/8 = 0
x = 2
x = -17/8


Input: Compute the solution of x^3 - 7/2x^2 - 7x + 20 = 0

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


Input: Solve x^3 - 337/40x^2 + 89/4x - 91/5 = 0

Output:
x^3 - 337/40x^2 + 89/4x - 91/5 = 0
(x - 4)(x - 13/8)(x - 14/5) = 0
x - 4 = 0
x - 13/8 = 0
x - 14/5 = 0
x = 4
x = 13/8
x = 14/5


Input: Find x for x^3 - 59/8x^2 + 7/32x + 539/32 = 0

Output:
x^3 - 59/8x^2 + 7/32x + 539/32 = 0
(x - 7)(x - 7/4)(x - -11/8) = 0
x - 7 = 0
x - 7/4 = 0
x - -11/8 = 0
x = 7
x = 7/4
x = -11/8


Input: Determine x in 6x + 38/3 = 0

Output:
6x + 38/3 = 0
6x = -38/3
x = -38/3 / 6
x = -19/9


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

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


Input: Find x for x^2 - 71/10x + 44/5 = 0

Output:
x^2 - 71/10x + 44/5 = 0
(x - 8/5)(x - 11/2) = 0
x - 8/5 = 0  or  x - 11/2 = 0
x = 8/5
x = 11/2


Input: Find x for x^2 - 41/10x + 91/25 = 0

Output:
x^2 - 41/10x + 91/25 = 0
(x - 14/5)(x - 13/10) = 0
x - 14/5 = 0  or  x - 13/10 = 0
x = 14/5
x = 13/10


Input:
Find x and y such that
6x + 8y = 32
3x + 8y = -22

Output:
6x + 8y = 32
3x + 8y = -22

Using elimination
3*(6x + 8y = 32)
6*(3x + 8y = -22)
18x + 24y = 96
18x + 48y = -132
Subtract equations
-24y = 228
y = 228/-24
y = -19/2

Substitute y
6x + 8(-19/2) = 32
6x = 108
x = 108/6
x = 18


Input: Determine x in x^3 + 22x^2 + 57x  = 0

Output:
x^3 + 22x^2 + 57x  = 0
(x - 0)(x - -19)(x - -3) = 0
x - 0 = 0
x - -19 = 0
x - -3 = 0
x = 0
x = -19
x = -3


Input: What value of x satisfies x^3 + 11/2x^2 + 39/16x - 171/32 = 0

Output:
x^3 + 11/2x^2 + 39/16x - 171/32 = 0
(x - -19/4)(x - 3/4)(x - -3/2) = 0
x - -19/4 = 0
x - 3/4 = 0
x - -3/2 = 0
x = -19/4
x = 3/4
x = -3/2


Input:
Solve simultaneously:
6x + 1y = 209/21
8x + 7y = 83/9

Output:
6x + 1y = 209/21
8x + 7y = 83/9

Using elimination
8*(6x + 1y = 209/21)
6*(8x + 7y = 83/9)
48x + 8y = 1672/21
48x + 42y = 166/3
Subtract equations
-34y = 170/7
y = 170/7/-34
y = -5/7

Substitute y
6x + 1(-5/7) = 209/21
6x = 32/3
x = 32/3/6
x = 16/9


Input:
Find x and y such that
10x + 8y = 14
2x + 8y = 142/5

Output:
10x + 8y = 14
2x + 8y = 142/5

Using elimination
2*(10x + 8y = 14)
10*(2x + 8y = 142/5)
20x + 16y = 28
20x + 80y = 284
Subtract equations
-64y = -256
y = -256/-64
y = 4

Substitute y
10x + 8(4) = 14
10x = -18
x = -18/10
x = -9/5


Input:
Solve the equations:
4x + 8y = 28
4x + 2y = -2

Output:
4x + 8y = 28
4x + 2y = -2

Using elimination
4*(4x + 8y = 28)
4*(4x + 2y = -2)
16x + 32y = 112
16x + 8y = -8
Subtract equations
24y = 120
y = 120/24
y = 5

Substitute y
4x + 8(5) = 28
4x = -12
x = -12/4
x = -3


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

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


Input:
Solve the equations:
2x + 8y = -92/5
2x + 7y = -323/20

Output:
2x + 8y = -92/5
2x + 7y = -323/20

Using elimination
2*(2x + 8y = -92/5)
2*(2x + 7y = -323/20)
4x + 16y = -184/5
4x + 14y = -323/10
Subtract equations
2y = -9/2
y = -9/2/2
y = -9/4

Substitute y
2x + 8(-9/4) = -92/5
2x = -2/5
x = -2/5/2
x = -1/5


Input:
Solve the system:
3x + 8y = -151/20
7x + 1y = 213/20

Output:
3x + 8y = -151/20
7x + 1y = 213/20

Using elimination
7*(3x + 8y = -151/20)
3*(7x + 1y = 213/20)
21x + 56y = -1057/20
21x + 3y = 639/20
Subtract equations
53y = -424/5
y = -424/5/53
y = -8/5

Substitute y
3x + 8(-8/5) = -151/20
3x = 21/4
x = 21/4/3
x = 7/4


Input: Find x in x^3 - 236/21x^2 + 60/7x + 800/21 = 0

Output:
x^3 - 236/21x^2 + 60/7x + 800/21 = 0
(x - 8/3)(x - -10/7)(x - 10) = 0
x - 8/3 = 0
x - -10/7 = 0
x - 10 = 0
x = 8/3
x = -10/7
x = 10


Input: Solve 2x - 20/9 = 0

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


Input: Determine x in x^2 + 11/4x + 9/8 = 0

Output:
x^2 + 11/4x + 9/8 = 0
(x - -1/2)(x - -9/4) = 0
x - -1/2 = 0  or  x - -9/4 = 0
x = -1/2
x = -9/4


Input: Find the solution to 8x + 160/9 = 0

Output:
8x + 160/9 = 0
8x = -160/9
x = -160/9 / 8
x = -20/9


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

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


Input: Find the solution to x^3 - 14x^2 - 1469/16x - 969/16 = 0

Output:
x^3 - 14x^2 - 1469/16x - 969/16 = 0
(x - 19)(x - -17/4)(x - -3/4) = 0
x - 19 = 0
x - -17/4 = 0
x - -3/4 = 0
x = 19
x = -17/4
x = -3/4


Input:
Solve the system:
9x + 1y = 13/3
7x + 9y = 43/3

Output:
9x + 1y = 13/3
7x + 9y = 43/3

Using elimination
7*(9x + 1y = 13/3)
9*(7x + 9y = 43/3)
63x + 7y = 91/3
63x + 81y = 129
Subtract equations
-74y = -296/3
y = -296/3/-74
y = 4/3

Substitute y
9x + 1(4/3) = 13/3
9x = 3
x = 3/9
x = 1/3


Input:
Solve the system:
5x + 8y = 185/6
7x + 10y = 235/6

Output:
5x + 8y = 185/6
7x + 10y = 235/6

Using elimination
7*(5x + 8y = 185/6)
5*(7x + 10y = 235/6)
35x + 56y = 1295/6
35x + 50y = 1175/6
Subtract equations
6y = 20
y = 20/6
y = 10/3

Substitute y
5x + 8(10/3) = 185/6
5x = 25/6
x = 25/6/5
x = 5/6


Input: Find x for x^2 - 92/35x - 64/35 = 0

Output:
x^2 - 92/35x - 64/35 = 0
(x - 16/5)(x - -4/7) = 0
x - 16/5 = 0  or  x - -4/7 = 0
x = 16/5
x = -4/7


Input:
Find x and y such that
6x + 8y = -224/5
4x + 7y = -171/5

Output:
6x + 8y = -224/5
4x + 7y = -171/5

Using elimination
4*(6x + 8y = -224/5)
6*(4x + 7y = -171/5)
24x + 32y = -896/5
24x + 42y = -1026/5
Subtract equations
-10y = 26
y = 26/-10
y = -13/5

Substitute y
6x + 8(-13/5) = -224/5
6x = -24
x = -24/6
x = -4


Input: Compute the solution of x^3 - 139/42x^2 - 1811/42x - 510/7 = 0

Output:
x^3 - 139/42x^2 - 1811/42x - 510/7 = 0
(x - 9)(x - -17/6)(x - -20/7) = 0
x - 9 = 0
x - -17/6 = 0
x - -20/7 = 0
x = 9
x = -17/6
x = -20/7


Input: Determine x in x^2 - 128/7x + 36/7 = 0

Output:
x^2 - 128/7x + 36/7 = 0
(x - 2/7)(x - 18) = 0
x - 2/7 = 0  or  x - 18 = 0
x = 2/7
x = 18


Input:
Find x and y such that
7x + 4y = 148/5
4x + 1y = 46/5

Output:
7x + 4y = 148/5
4x + 1y = 46/5

Using elimination
4*(7x + 4y = 148/5)
7*(4x + 1y = 46/5)
28x + 16y = 592/5
28x + 7y = 322/5
Subtract equations
9y = 54
y = 54/9
y = 6

Substitute y
7x + 4(6) = 148/5
7x = 28/5
x = 28/5/7
x = 4/5


Input:
Solve simultaneously:
8x + 8y = -52/3
2x + 3y = -4

Output:
8x + 8y = -52/3
2x + 3y = -4

Using elimination
2*(8x + 8y = -52/3)
8*(2x + 3y = -4)
16x + 16y = -104/3
16x + 24y = -32
Subtract equations
-8y = -8/3
y = -8/3/-8
y = 1/3

Substitute y
8x + 8(1/3) = -52/3
8x = -20
x = -20/8
x = -5/2


Input: Find the solution to 9x + 54 = 0

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


Input: Determine x in 3x + 9/5 = 0

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


Input:
Solve the equations:
2x + 9y = 49/2
5x + 5y = 35/4

Output:
2x + 9y = 49/2
5x + 5y = 35/4

Using elimination
5*(2x + 9y = 49/2)
2*(5x + 5y = 35/4)
10x + 45y = 245/2
10x + 10y = 35/2
Subtract equations
35y = 105
y = 105/35
y = 3

Substitute y
2x + 9(3) = 49/2
2x = -5/2
x = -5/2/2
x = -5/4


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

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


Input: Find the solution to x^2 - 109/36x + 20/9 = 0

Output:
x^2 - 109/36x + 20/9 = 0
(x - 5/4)(x - 16/9) = 0
x - 5/4 = 0  or  x - 16/9 = 0
x = 5/4
x = 16/9


Input: Find x for 9x - 90/7 = 0

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


Input:
Solve the system:
3x + 3y = -621/35
8x + 10y = -1846/35

Output:
3x + 3y = -621/35
8x + 10y = -1846/35

Using elimination
8*(3x + 3y = -621/35)
3*(8x + 10y = -1846/35)
24x + 24y = -4968/35
24x + 30y = -5538/35
Subtract equations
-6y = 114/7
y = 114/7/-6
y = -19/7

Substitute y
3x + 3(-19/7) = -621/35
3x = -48/5
x = -48/5/3
x = -16/5


Input:
Find x and y such that
4x + 6y = 0
5x + 9y = 3/7

Output:
4x + 6y = 0
5x + 9y = 3/7

Using elimination
5*(4x + 6y = 0)
4*(5x + 9y = 3/7)
20x + 30y = 0
20x + 36y = 12/7
Subtract equations
-6y = -12/7
y = -12/7/-6
y = 2/7

Substitute y
4x + 6(2/7) = 0
4x = -12/7
x = -12/7/4
x = -3/7


Input: Find the solution to x^3 - 144/35x^2 + 629/175x + 156/175 = 0

Output:
x^3 - 144/35x^2 + 629/175x + 156/175 = 0
(x - 13/5)(x - 12/7)(x - -1/5) = 0
x - 13/5 = 0
x - 12/7 = 0
x - -1/5 = 0
x = 13/5
x = 12/7
x = -1/5


Input:
Solve simultaneously:
8x + 6y = -28
3x + 9y = -87/4

Output:
8x + 6y = -28
3x + 9y = -87/4

Using elimination
3*(8x + 6y = -28)
8*(3x + 9y = -87/4)
24x + 18y = -84
24x + 72y = -174
Subtract equations
-54y = 90
y = 90/-54
y = -5/3

Substitute y
8x + 6(-5/3) = -28
8x = -18
x = -18/8
x = -9/4


Input:
Find x and y such that
2x + 5y = 118/3
5x + 4y = 125/3

Output:
2x + 5y = 118/3
5x + 4y = 125/3

Using elimination
5*(2x + 5y = 118/3)
2*(5x + 4y = 125/3)
10x + 25y = 590/3
10x + 8y = 250/3
Subtract equations
17y = 340/3
y = 340/3/17
y = 20/3

Substitute y
2x + 5(20/3) = 118/3
2x = 6
x = 6/2
x = 3


Input: Find x for x^3 + 124/7x^2 + 73/7x - 204/7 = 0

Output:
x^3 + 124/7x^2 + 73/7x - 204/7 = 0
(x - -17)(x - 1)(x - -12/7) = 0
x - -17 = 0
x - 1 = 0
x - -12/7 = 0
x = -17
x = 1
x = -12/7


Input: Determine x in x^2 - 31/6x - 133/18 = 0

Output:
x^2 - 31/6x - 133/18 = 0
(x - 19/3)(x - -7/6) = 0
x - 19/3 = 0  or  x - -7/6 = 0
x = 19/3
x = -7/6


Input: Solve 6x - 20 = 0

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


Input: Determine x in x^3 - 12/5x^2 + 3/4x + 1/10 = 0

Output:
x^3 - 12/5x^2 + 3/4x + 1/10 = 0
(x - 1/2)(x - 2)(x - -1/10) = 0
x - 1/2 = 0
x - 2 = 0
x - -1/10 = 0
x = 1/2
x = 2
x = -1/10


Input: Determine x in x^2 + 7/4x - 15/2 = 0

Output:
x^2 + 7/4x - 15/2 = 0
(x - -15/4)(x - 2) = 0
x - -15/4 = 0  or  x - 2 = 0
x = -15/4
x = 2


Input:
Solve the equations:
4x + 2y = -344/21
5x + 6y = -274/7

Output:
4x + 2y = -344/21
5x + 6y = -274/7

Using elimination
5*(4x + 2y = -344/21)
4*(5x + 6y = -274/7)
20x + 10y = -1720/21
20x + 24y = -1096/7
Subtract equations
-14y = 224/3
y = 224/3/-14
y = -16/3

Substitute y
4x + 2(-16/3) = -344/21
4x = -40/7
x = -40/7/4
x = -10/7


Input: What value of x satisfies 7x + 35/4 = 0

Output:
7x + 35/4 = 0
7x = -35/4
x = -35/4 / 7
x = -5/4


Input: Compute the solution of x^3 - 217/40x^2 - 1239/40x - 54/5 = 0

Output:
x^3 - 217/40x^2 - 1239/40x - 54/5 = 0
(x - -3/8)(x - 9)(x - -16/5) = 0
x - -3/8 = 0
x - 9 = 0
x - -16/5 = 0
x = -3/8
x = 9
x = -16/5


Input: Find x for x^2 - 14/3x - 32/9 = 0

Output:
x^2 - 14/3x - 32/9 = 0
(x - 16/3)(x - -2/3) = 0
x - 16/3 = 0  or  x - -2/3 = 0
x = 16/3
x = -2/3


Input: Find x for 3x - 3/2 = 0

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


Input: Find the solution to x^3 - 64/3x^2 + 73/3x + 140/3 = 0

Output:
x^3 - 64/3x^2 + 73/3x + 140/3 = 0
(x - 20)(x - 7/3)(x - -1) = 0
x - 20 = 0
x - 7/3 = 0
x - -1 = 0
x = 20
x = 7/3
x = -1


Input: Solve the equation x^3 - 349/40x^2 - 243/80x + 81/16 = 0

Output:
x^3 - 349/40x^2 - 243/80x + 81/16 = 0
(x - 9)(x - -9/10)(x - 5/8) = 0
x - 9 = 0
x - -9/10 = 0
x - 5/8 = 0
x = 9
x = -9/10
x = 5/8


Input:
Solve simultaneously:
9x + 7y = -173/4
1x + 4y = -45/4

Output:
9x + 7y = -173/4
1x + 4y = -45/4

Using elimination
1*(9x + 7y = -173/4)
9*(1x + 4y = -45/4)
9x + 7y = -173/4
9x + 36y = -405/4
Subtract equations
-29y = 58
y = 58/-29
y = -2

Substitute y
9x + 7(-2) = -173/4
9x = -117/4
x = -117/4/9
x = -13/4


Input: What value of x satisfies 4x + 13/2 = 0

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


Input:
Solve the system:
8x + 3y = 150
7x + 6y = 129

Output:
8x + 3y = 150
7x + 6y = 129

Using elimination
7*(8x + 3y = 150)
8*(7x + 6y = 129)
56x + 21y = 1050
56x + 48y = 1032
Subtract equations
-27y = 18
y = 18/-27
y = -2/3

Substitute y
8x + 3(-2/3) = 150
8x = 152
x = 152/8
x = 19


Input: Find x for x^2 + 129/35x + 34/35 = 0

Output:
x^2 + 129/35x + 34/35 = 0
(x - -2/7)(x - -17/5) = 0
x - -2/7 = 0  or  x - -17/5 = 0
x = -2/7
x = -17/5


Input:
Solve the equations:
3x + 2y = -109/18
3x + 1y = -77/18

Output:
3x + 2y = -109/18
3x + 1y = -77/18

Using elimination
3*(3x + 2y = -109/18)
3*(3x + 1y = -77/18)
9x + 6y = -109/6
9x + 3y = -77/6
Subtract equations
3y = -16/3
y = -16/3/3
y = -16/9

Substitute y
3x + 2(-16/9) = -109/18
3x = -5/2
x = -5/2/3
x = -5/6


Input:
Solve the equations:
8x + 8y = -108/5
10x + 6y = -23

Output:
8x + 8y = -108/5
10x + 6y = -23

Using elimination
10*(8x + 8y = -108/5)
8*(10x + 6y = -23)
80x + 80y = -216
80x + 48y = -184
Subtract equations
32y = -32
y = -32/32
y = -1

Substitute y
8x + 8(-1) = -108/5
8x = -68/5
x = -68/5/8
x = -17/10


Input:
Solve the equations:
9x + 5y = -53
1x + 10y = -59/2

Output:
9x + 5y = -53
1x + 10y = -59/2

Using elimination
1*(9x + 5y = -53)
9*(1x + 10y = -59/2)
9x + 5y = -53
9x + 90y = -531/2
Subtract equations
-85y = 425/2
y = 425/2/-85
y = -5/2

Substitute y
9x + 5(-5/2) = -53
9x = -81/2
x = -81/2/9
x = -9/2


Input: Solve the equation x^2 + 19/18x - 65/18 = 0

Output:
x^2 + 19/18x - 65/18 = 0
(x - 13/9)(x - -5/2) = 0
x - 13/9 = 0  or  x - -5/2 = 0
x = 13/9
x = -5/2


Input:
Solve the equations:
6x + 5y = 125/8
10x + 5y = 205/8

Output:
6x + 5y = 125/8
10x + 5y = 205/8

Using elimination
10*(6x + 5y = 125/8)
6*(10x + 5y = 205/8)
60x + 50y = 625/4
60x + 30y = 615/4
Subtract equations
20y = 5/2
y = 5/2/20
y = 1/8

Substitute y
6x + 5(1/8) = 125/8
6x = 15
x = 15/6
x = 5/2


Input: Compute the solution of x^2 + 112/9x + 16/3 = 0

Output:
x^2 + 112/9x + 16/3 = 0
(x - -4/9)(x - -12) = 0
x - -4/9 = 0  or  x - -12 = 0
x = -4/9
x = -12


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

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


Input: Find x in 1x - 5/3 = 0

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


Input: Determine x in x^2 - 59/42x + 10/21 = 0

Output:
x^2 - 59/42x + 10/21 = 0
(x - 5/6)(x - 4/7) = 0
x - 5/6 = 0  or  x - 4/7 = 0
x = 5/6
x = 4/7


Input: Determine x in x^2 + 17/14x + 5/14 = 0

Output:
x^2 + 17/14x + 5/14 = 0
(x - -1/2)(x - -5/7) = 0
x - -1/2 = 0  or  x - -5/7 = 0
x = -1/2
x = -5/7


Input: Determine x in 6x + 27/5 = 0

Output:
6x + 27/5 = 0
6x = -27/5
x = -27/5 / 6
x = -9/10


Input: What value of x satisfies 10x - 5 = 0

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


Input: Find x in 9x - 30 = 0

Output:
9x - 30 = 0
9x = 30
x = 30 / 9
x = 10/3


Input: Find x in x^2 - 23/10x + 6/5 = 0

Output:
x^2 - 23/10x + 6/5 = 0
(x - 4/5)(x - 3/2) = 0
x - 4/5 = 0  or  x - 3/2 = 0
x = 4/5
x = 3/2


Input:
Find x and y such that
5x + 5y = -40/3
3x + 2y = -12

Output:
5x + 5y = -40/3
3x + 2y = -12

Using elimination
3*(5x + 5y = -40/3)
5*(3x + 2y = -12)
15x + 15y = -40
15x + 10y = -60
Subtract equations
5y = 20
y = 20/5
y = 4

Substitute y
5x + 5(4) = -40/3
5x = -100/3
x = -100/3/5
x = -20/3


Input: Determine x in 5x - 6 = 0

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


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

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


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

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


Input:
Solve simultaneously:
4x + 5y = -95/18
3x + 1y = -175/72

Output:
4x + 5y = -95/18
3x + 1y = -175/72

Using elimination
3*(4x + 5y = -95/18)
4*(3x + 1y = -175/72)
12x + 15y = -95/6
12x + 4y = -175/18
Subtract equations
11y = -55/9
y = -55/9/11
y = -5/9

Substitute y
4x + 5(-5/9) = -95/18
4x = -5/2
x = -5/2/4
x = -5/8


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

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


Input: What value of x satisfies 7x - 12 = 0

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


Input: Solve x^3 + 16/3x^2 - 251x + 494/3 = 0

Output:
x^3 + 16/3x^2 - 251x + 494/3 = 0
(x - 2/3)(x - -19)(x - 13) = 0
x - 2/3 = 0
x - -19 = 0
x - 13 = 0
x = 2/3
x = -19
x = 13


Input:
Solve the system:
8x + 5y = -231/2
9x + 1y = -283/2

Output:
8x + 5y = -231/2
9x + 1y = -283/2

Using elimination
9*(8x + 5y = -231/2)
8*(9x + 1y = -283/2)
72x + 45y = -2079/2
72x + 8y = -1132
Subtract equations
37y = 185/2
y = 185/2/37
y = 5/2

Substitute y
8x + 5(5/2) = -231/2
8x = -128
x = -128/8
x = -16


Input: Find the solution to x^3 + 59/14x^2 + 342/175x - 162/175 = 0

Output:
x^3 + 59/14x^2 + 342/175x - 162/175 = 0
(x - -18/5)(x - 2/7)(x - -9/10) = 0
x - -18/5 = 0
x - 2/7 = 0
x - -9/10 = 0
x = -18/5
x = 2/7
x = -9/10


Input: Find x for x^3 - 23/10x^2 + 1/5x + 4/5 = 0

Output:
x^3 - 23/10x^2 + 1/5x + 4/5 = 0
(x - -1/2)(x - 2)(x - 4/5) = 0
x - -1/2 = 0
x - 2 = 0
x - 4/5 = 0
x = -1/2
x = 2
x = 4/5


Input: What value of x satisfies x^3 - 33/14x^2 - 151/7x + 585/14 = 0

Output:
x^3 - 33/14x^2 - 151/7x + 585/14 = 0
(x - 5)(x - -9/2)(x - 13/7) = 0
x - 5 = 0
x - -9/2 = 0
x - 13/7 = 0
x = 5
x = -9/2
x = 13/7


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

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


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

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


Input: What value of x satisfies x^3 + 4/7x^2 - 36/7x  = 0

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


Input: Find the solution to 8x - 12/5 = 0

Output:
8x - 12/5 = 0
8x = 12/5
x = 12/5 / 8
x = 3/10


Input: What value of x satisfies x^3 + 17/18x^2 - 178/27x + 38/27 = 0

Output:
x^3 + 17/18x^2 - 178/27x + 38/27 = 0
(x - 2/9)(x - 2)(x - -19/6) = 0
x - 2/9 = 0
x - 2 = 0
x - -19/6 = 0
x = 2/9
x = 2
x = -19/6


Input:
Solve the system:
10x + 7y = 26
8x + 10y = 216/7

Output:
10x + 7y = 26
8x + 10y = 216/7

Using elimination
8*(10x + 7y = 26)
10*(8x + 10y = 216/7)
80x + 56y = 208
80x + 100y = 2160/7
Subtract equations
-44y = -704/7
y = -704/7/-44
y = 16/7

Substitute y
10x + 7(16/7) = 26
10x = 10
x = 10/10
x = 1


Input:
Solve the system:
1x + 2y = -63/8
3x + 9y = -291/8

Output:
1x + 2y = -63/8
3x + 9y = -291/8

Using elimination
3*(1x + 2y = -63/8)
1*(3x + 9y = -291/8)
3x + 6y = -189/8
3x + 9y = -291/8
Subtract equations
-3y = 51/4
y = 51/4/-3
y = -17/4

Substitute y
1x + 2(-17/4) = -63/8
1x = 5/8
x = 5/8/1
x = 5/8


Input:
Solve the equations:
2x + 1y = -23/12
8x + 2y = -1/3

Output:
2x + 1y = -23/12
8x + 2y = -1/3

Using elimination
8*(2x + 1y = -23/12)
2*(8x + 2y = -1/3)
16x + 8y = -46/3
16x + 4y = -2/3
Subtract equations
4y = -44/3
y = -44/3/4
y = -11/3

Substitute y
2x + 1(-11/3) = -23/12
2x = 7/4
x = 7/4/2
x = 7/8


Input:
Solve the system:
10x + 4y = -343/15
4x + 8y = 74/15

Output:
10x + 4y = -343/15
4x + 8y = 74/15

Using elimination
4*(10x + 4y = -343/15)
10*(4x + 8y = 74/15)
40x + 16y = -1372/15
40x + 80y = 148/3
Subtract equations
-64y = -704/5
y = -704/5/-64
y = 11/5

Substitute y
10x + 4(11/5) = -343/15
10x = -95/3
x = -95/3/10
x = -19/6


Input: Solve x^3 + 11/4x^2 - 123/2x - 189/4 = 0

Output:
x^3 + 11/4x^2 - 123/2x - 189/4 = 0
(x - -9)(x - 7)(x - -3/4) = 0
x - -9 = 0
x - 7 = 0
x - -3/4 = 0
x = -9
x = 7
x = -3/4


Input: Solve x^2 + 80/9x - 1 = 0

Output:
x^2 + 80/9x - 1 = 0
(x - -9)(x - 1/9) = 0
x - -9 = 0  or  x - 1/9 = 0
x = -9
x = 1/9


Input: Find the solution to x^2 + 16/9x - 4/9 = 0

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


Input: Solve quickly: 9x + 9 = 0

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


Input: Solve the equation 1x - 11/5 = 0

Output:
1x - 11/5 = 0
1x = 11/5
x = 11/5 / 1
x = 11/5


Input: Solve the equation x^2 + 1/24x - 11/6 = 0

Output:
x^2 + 1/24x - 11/6 = 0
(x - 4/3)(x - -11/8) = 0
x - 4/3 = 0  or  x - -11/8 = 0
x = 4/3
x = -11/8


Input:
Solve the equations:
4x + 5y = -53/12
10x + 9y = -185/12

Output:
4x + 5y = -53/12
10x + 9y = -185/12

Using elimination
10*(4x + 5y = -53/12)
4*(10x + 9y = -185/12)
40x + 50y = -265/6
40x + 36y = -185/3
Subtract equations
14y = 35/2
y = 35/2/14
y = 5/4

Substitute y
4x + 5(5/4) = -53/12
4x = -32/3
x = -32/3/4
x = -8/3


Input: Find x in x^3 + 189/10x^2 + 321/10x - 17/5 = 0

Output:
x^3 + 189/10x^2 + 321/10x - 17/5 = 0
(x - -2)(x - -17)(x - 1/10) = 0
x - -2 = 0
x - -17 = 0
x - 1/10 = 0
x = -2
x = -17
x = 1/10


Input: Solve 4x + 24/5 = 0

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


Input:
Solve the equations:
9x + 5y = -265/6
10x + 5y = -305/6

Output:
9x + 5y = -265/6
10x + 5y = -305/6

Using elimination
10*(9x + 5y = -265/6)
9*(10x + 5y = -305/6)
90x + 50y = -1325/3
90x + 45y = -915/2
Subtract equations
5y = 95/6
y = 95/6/5
y = 19/6

Substitute y
9x + 5(19/6) = -265/6
9x = -60
x = -60/9
x = -20/3


Input:
Solve the system:
9x + 4y = 353/8
8x + 5y = 58

Output:
9x + 4y = 353/8
8x + 5y = 58

Using elimination
8*(9x + 4y = 353/8)
9*(8x + 5y = 58)
72x + 32y = 353
72x + 45y = 522
Subtract equations
-13y = -169
y = -169/-13
y = 13

Substitute y
9x + 4(13) = 353/8
9x = -63/8
x = -63/8/9
x = -7/8


Input: Find x in x^3 - 41/24x^2 + 59/96x - 5/96 = 0

Output:
x^3 - 41/24x^2 + 59/96x - 5/96 = 0
(x - 5/4)(x - 1/3)(x - 1/8) = 0
x - 5/4 = 0
x - 1/3 = 0
x - 1/8 = 0
x = 5/4
x = 1/3
x = 1/8


Input:
Solve simultaneously:
9x + 1y = -221/4
10x + 5y = -515/12

Output:
9x + 1y = -221/4
10x + 5y = -515/12

Using elimination
10*(9x + 1y = -221/4)
9*(10x + 5y = -515/12)
90x + 10y = -1105/2
90x + 45y = -1545/4
Subtract equations
-35y = -665/4
y = -665/4/-35
y = 19/4

Substitute y
9x + 1(19/4) = -221/4
9x = -60
x = -60/9
x = -20/3


Input: Solve x^2 - 1/8x - 17/4 = 0

Output:
x^2 - 1/8x - 17/4 = 0
(x - 17/8)(x - -2) = 0
x - 17/8 = 0  or  x - -2 = 0
x = 17/8
x = -2


Input: What value of x satisfies x^2 + 104/21x + 128/21 = 0

Output:
x^2 + 104/21x + 128/21 = 0
(x - -16/7)(x - -8/3) = 0
x - -16/7 = 0  or  x - -8/3 = 0
x = -16/7
x = -8/3


Input:
Solve the equations:
6x + 1y = 8/7
7x + 8y = -26

Output:
6x + 1y = 8/7
7x + 8y = -26

Using elimination
7*(6x + 1y = 8/7)
6*(7x + 8y = -26)
42x + 7y = 8
42x + 48y = -156
Subtract equations
-41y = 164
y = 164/-41
y = -4

Substitute y
6x + 1(-4) = 8/7
6x = 36/7
x = 36/7/6
x = 6/7


Input: What value of x satisfies x^3 + 33/10x^2 + 72/25x + 32/125 = 0

Output:
x^3 + 33/10x^2 + 72/25x + 32/125 = 0
(x - -8/5)(x - -8/5)(x - -1/10) = 0
x - -8/5 = 0
x - -8/5 = 0
x - -1/10 = 0
x = -8/5
x = -8/5
x = -1/10


Input: Compute the solution of x^2 - 23/6x + 5/3 = 0

Output:
x^2 - 23/6x + 5/3 = 0
(x - 10/3)(x - 1/2) = 0
x - 10/3 = 0  or  x - 1/2 = 0
x = 10/3
x = 1/2


Input:
Solve the system:
8x + 5y = 131/3
7x + 9y = 184/3

Output:
8x + 5y = 131/3
7x + 9y = 184/3

Using elimination
7*(8x + 5y = 131/3)
8*(7x + 9y = 184/3)
56x + 35y = 917/3
56x + 72y = 1472/3
Subtract equations
-37y = -185
y = -185/-37
y = 5

Substitute y
8x + 5(5) = 131/3
8x = 56/3
x = 56/3/8
x = 7/3


Input: Determine x in 2x + 4 = 0

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


Input: Solve the equation 4x - 24/7 = 0

Output:
4x - 24/7 = 0
4x = 24/7
x = 24/7 / 4
x = 6/7


Input:
Solve simultaneously:
4x + 10y = 227/7
6x + 5y = 331/14

Output:
4x + 10y = 227/7
6x + 5y = 331/14

Using elimination
6*(4x + 10y = 227/7)
4*(6x + 5y = 331/14)
24x + 60y = 1362/7
24x + 20y = 662/7
Subtract equations
40y = 100
y = 100/40
y = 5/2

Substitute y
4x + 10(5/2) = 227/7
4x = 52/7
x = 52/7/4
x = 13/7


Input: Solve the equation x^3 + 88/21x^2 + 4/7x - 160/21 = 0

Output:
x^3 + 88/21x^2 + 4/7x - 160/21 = 0
(x - -2)(x - 8/7)(x - -10/3) = 0
x - -2 = 0
x - 8/7 = 0
x - -10/3 = 0
x = -2
x = 8/7
x = -10/3


Input: Compute the solution of x^2 - 4/3x - 28 = 0

Output:
x^2 - 4/3x - 28 = 0
(x - 6)(x - -14/3) = 0
x - 6 = 0  or  x - -14/3 = 0
x = 6
x = -14/3


Input: Find the solution to x^2 + 62/21x + 32/21 = 0

Output:
x^2 + 62/21x + 32/21 = 0
(x - -2/3)(x - -16/7) = 0
x - -2/3 = 0  or  x - -16/7 = 0
x = -2/3
x = -16/7


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

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


Input:
Find x and y such that
8x + 7y = -187/12
1x + 10y = -217/6

Output:
8x + 7y = -187/12
1x + 10y = -217/6

Using elimination
1*(8x + 7y = -187/12)
8*(1x + 10y = -217/6)
8x + 7y = -187/12
8x + 80y = -868/3
Subtract equations
-73y = 1095/4
y = 1095/4/-73
y = -15/4

Substitute y
8x + 7(-15/4) = -187/12
8x = 32/3
x = 32/3/8
x = 4/3


Input: Find the solution to x^3 - 26/35x^2 - 53/35x + 8/35 = 0

Output:
x^3 - 26/35x^2 - 53/35x + 8/35 = 0
(x - -1)(x - 8/5)(x - 1/7) = 0
x - -1 = 0
x - 8/5 = 0
x - 1/7 = 0
x = -1
x = 8/5
x = 1/7


Input: What value of x satisfies 7x + 14 = 0

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


Input: Solve x^2 - 41/9x - 26/3 = 0

Output:
x^2 - 41/9x - 26/3 = 0
(x - -13/9)(x - 6) = 0
x - -13/9 = 0  or  x - 6 = 0
x = -13/9
x = 6


Input: Solve quickly: x^3 + 31/6x^2 - 62/3x + 16 = 0

Output:
x^3 + 31/6x^2 - 62/3x + 16 = 0
(x - 4/3)(x - -8)(x - 3/2) = 0
x - 4/3 = 0
x - -8 = 0
x - 3/2 = 0
x = 4/3
x = -8
x = 3/2


Input:
Solve the system:
7x + 10y = -89
9x + 5y = -194/3

Output:
7x + 10y = -89
9x + 5y = -194/3

Using elimination
9*(7x + 10y = -89)
7*(9x + 5y = -194/3)
63x + 90y = -801
63x + 35y = -1358/3
Subtract equations
55y = -1045/3
y = -1045/3/55
y = -19/3

Substitute y
7x + 10(-19/3) = -89
7x = -77/3
x = -77/3/7
x = -11/3


Input: Compute the solution of 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: Solve quickly: x^2 - 19/4x + 45/8 = 0

Output:
x^2 - 19/4x + 45/8 = 0
(x - 5/2)(x - 9/4) = 0
x - 5/2 = 0  or  x - 9/4 = 0
x = 5/2
x = 9/4


Input: Find x in 2x - 2 = 0

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


Input:
Find x and y such that
6x + 9y = -144/5
7x + 5y = -43/2

Output:
6x + 9y = -144/5
7x + 5y = -43/2

Using elimination
7*(6x + 9y = -144/5)
6*(7x + 5y = -43/2)
42x + 63y = -1008/5
42x + 30y = -129
Subtract equations
33y = -363/5
y = -363/5/33
y = -11/5

Substitute y
6x + 9(-11/5) = -144/5
6x = -9
x = -9/6
x = -3/2


Input: Compute the solution of 3x + 45/2 = 0

Output:
3x + 45/2 = 0
3x = -45/2
x = -45/2 / 3
x = -15/2


Input: Determine x in x^3 - 49/20x^2 - 219/40x + 459/40 = 0

Output:
x^3 - 49/20x^2 - 219/40x + 459/40 = 0
(x - 17/10)(x - -9/4)(x - 3) = 0
x - 17/10 = 0
x - -9/4 = 0
x - 3 = 0
x = 17/10
x = -9/4
x = 3


Input:
Solve the equations:
10x + 2y = 934/15
1x + 5y = 59/3

Output:
10x + 2y = 934/15
1x + 5y = 59/3

Using elimination
1*(10x + 2y = 934/15)
10*(1x + 5y = 59/3)
10x + 2y = 934/15
10x + 50y = 590/3
Subtract equations
-48y = -672/5
y = -672/5/-48
y = 14/5

Substitute y
10x + 2(14/5) = 934/15
10x = 170/3
x = 170/3/10
x = 17/3


Input: Determine x in x^2 + 16/5x + 11/5 = 0

Output:
x^2 + 16/5x + 11/5 = 0
(x - -11/5)(x - -1) = 0
x - -11/5 = 0  or  x - -1 = 0
x = -11/5
x = -1


Input: What value of x satisfies x^2 + 44/9x - 119/27 = 0

Output:
x^2 + 44/9x - 119/27 = 0
(x - 7/9)(x - -17/3) = 0
x - 7/9 = 0  or  x - -17/3 = 0
x = 7/9
x = -17/3


Input: Determine x in x^2 - 211/24x + 85/6 = 0

Output:
x^2 - 211/24x + 85/6 = 0
(x - 20/3)(x - 17/8) = 0
x - 20/3 = 0  or  x - 17/8 = 0
x = 20/3
x = 17/8


Input: Compute the solution of x^2 + 11/8x + 3/8 = 0

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


Input:
Solve the equations:
4x + 10y = -207/7
7x + 4y = -18

Output:
4x + 10y = -207/7
7x + 4y = -18

Using elimination
7*(4x + 10y = -207/7)
4*(7x + 4y = -18)
28x + 70y = -207
28x + 16y = -72
Subtract equations
54y = -135
y = -135/54
y = -5/2

Substitute y
4x + 10(-5/2) = -207/7
4x = -32/7
x = -32/7/4
x = -8/7


Input: Find x for x^2 + 10/3x + 1 = 0

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


Input: Determine x in 10x + 10 = 0

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


Input: Solve quickly: x^3 - 3/4x^2 - 35/18x + 25/36 = 0

Output:
x^3 - 3/4x^2 - 35/18x + 25/36 = 0
(x - 5/3)(x - 1/3)(x - -5/4) = 0
x - 5/3 = 0
x - 1/3 = 0
x - -5/4 = 0
x = 5/3
x = 1/3
x = -5/4


Input: Solve quickly: x^3 + 203/72x^2 + 161/162x - 95/648 = 0

Output:
x^3 + 203/72x^2 + 161/162x - 95/648 = 0
(x - -5/9)(x - 1/9)(x - -19/8) = 0
x - -5/9 = 0
x - 1/9 = 0
x - -19/8 = 0
x = -5/9
x = 1/9
x = -19/8


Input: Find x in 9x - 18 = 0

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


Input: Find x for 1x + 15/7 = 0

Output:
1x + 15/7 = 0
1x = -15/7
x = -15/7 / 1
x = -15/7


Input: Solve the equation x^2 - 29/20x + 21/40 = 0

Output:
x^2 - 29/20x + 21/40 = 0
(x - 3/4)(x - 7/10) = 0
x - 3/4 = 0  or  x - 7/10 = 0
x = 3/4
x = 7/10


Input:
Solve the equations:
8x + 10y = 266/15
6x + 1y = 167/15

Output:
8x + 10y = 266/15
6x + 1y = 167/15

Using elimination
6*(8x + 10y = 266/15)
8*(6x + 1y = 167/15)
48x + 60y = 532/5
48x + 8y = 1336/15
Subtract equations
52y = 52/3
y = 52/3/52
y = 1/3

Substitute y
8x + 10(1/3) = 266/15
8x = 72/5
x = 72/5/8
x = 9/5


Input: Solve quickly: 6x  = 0

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


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

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


Input: Find x for 10x + 45/2 = 0

Output:
10x + 45/2 = 0
10x = -45/2
x = -45/2 / 10
x = -9/4


Input: Find the solution to 6x - 3/2 = 0

Output:
6x - 3/2 = 0
6x = 3/2
x = 3/2 / 6
x = 1/4


Input: Find the solution to 1x - 13/10 = 0

Output:
1x - 13/10 = 0
1x = 13/10
x = 13/10 / 1
x = 13/10


Input: Solve quickly: x^3 + 4x^2 - 639/49x - 306/49 = 0

Output:
x^3 + 4x^2 - 639/49x - 306/49 = 0
(x - 17/7)(x - -6)(x - -3/7) = 0
x - 17/7 = 0
x - -6 = 0
x - -3/7 = 0
x = 17/7
x = -6
x = -3/7


Input: Compute the solution of 7x - 12 = 0

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


Input: Find x in 7x + 21/2 = 0

Output:
7x + 21/2 = 0
7x = -21/2
x = -21/2 / 7
x = -3/2


Input: Solve 6x - 8 = 0

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


Input: Find x in x^3 + 1/6x^2 - 26/3x - 10 = 0

Output:
x^3 + 1/6x^2 - 26/3x - 10 = 0
(x - 10/3)(x - -3/2)(x - -2) = 0
x - 10/3 = 0
x - -3/2 = 0
x - -2 = 0
x = 10/3
x = -3/2
x = -2


Input:
Solve the equations:
10x + 9y = -1367/9
8x + 7y = -1063/9

Output:
10x + 9y = -1367/9
8x + 7y = -1063/9

Using elimination
8*(10x + 9y = -1367/9)
10*(8x + 7y = -1063/9)
80x + 72y = -10936/9
80x + 70y = -10630/9
Subtract equations
2y = -34
y = -34/2
y = -17

Substitute y
10x + 9(-17) = -1367/9
10x = 10/9
x = 10/9/10
x = 1/9


Input: Solve the equation x^3 - 5x^2 - 1x + 5 = 0

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


Input:
Solve the equations:
6x + 8y = -136
8x + 5y = -629/4

Output:
6x + 8y = -136
8x + 5y = -629/4

Using elimination
8*(6x + 8y = -136)
6*(8x + 5y = -629/4)
48x + 64y = -1088
48x + 30y = -1887/2
Subtract equations
34y = -289/2
y = -289/2/34
y = -17/4

Substitute y
6x + 8(-17/4) = -136
6x = -102
x = -102/6
x = -17


Input: Solve the equation 10x + 25 = 0

Output:
10x + 25 = 0
10x = -25
x = -25 / 10
x = -5/2


Input: Compute the solution of x^3 + 209/15x^2 + 842/15x + 208/3 = 0

Output:
x^3 + 209/15x^2 + 842/15x + 208/3 = 0
(x - -13/5)(x - -10/3)(x - -8) = 0
x - -13/5 = 0
x - -10/3 = 0
x - -8 = 0
x = -13/5
x = -10/3
x = -8


Input: Solve x^2 - 35/2x - 50 = 0

Output:
x^2 - 35/2x - 50 = 0
(x - -5/2)(x - 20) = 0
x - -5/2 = 0  or  x - 20 = 0
x = -5/2
x = 20


Input: Solve x^2 + 29/10x + 9/5 = 0

Output:
x^2 + 29/10x + 9/5 = 0
(x - -2)(x - -9/10) = 0
x - -2 = 0  or  x - -9/10 = 0
x = -2
x = -9/10


Input: Determine x in x^2 - 44/7x + 64/7 = 0

Output:
x^2 - 44/7x + 64/7 = 0
(x - 16/7)(x - 4) = 0
x - 16/7 = 0  or  x - 4 = 0
x = 16/7
x = 4


Input:
Solve the equations:
9x + 2y = 16
9x + 5y = 22

Output:
9x + 2y = 16
9x + 5y = 22

Using elimination
9*(9x + 2y = 16)
9*(9x + 5y = 22)
81x + 18y = 144
81x + 45y = 198
Subtract equations
-27y = -54
y = -54/-27
y = 2

Substitute y
9x + 2(2) = 16
9x = 12
x = 12/9
x = 4/3


Input: Solve the equation x^3 - 697/180x^2 + 193/120x + 1463/360 = 0

Output:
x^3 - 697/180x^2 + 193/120x + 1463/360 = 0
(x - -7/9)(x - 19/10)(x - 11/4) = 0
x - -7/9 = 0
x - 19/10 = 0
x - 11/4 = 0
x = -7/9
x = 19/10
x = 11/4