Input:
Solve simultaneously:
1x + 1y = 20/7
2x + 8y = 82/7

Output:
1x + 1y = 20/7
2x + 8y = 82/7

Using elimination
2*(1x + 1y = 20/7)
1*(2x + 8y = 82/7)
2x + 2y = 40/7
2x + 8y = 82/7
Subtract equations
-6y = -6
y = -6/-6
y = 1

Substitute y
1x + 1(1) = 20/7
1x = 13/7
x = 13/7/1
x = 13/7


Input: Solve the equation 7x  = 0

Output:
7x  = 0
7x = 0
x = 0 / 7
x = 0


Input: What value of x satisfies x^3 + 61/6x^2 + 13/2x - 36 = 0

Output:
x^3 + 61/6x^2 + 13/2x - 36 = 0
(x - 3/2)(x - -8/3)(x - -9) = 0
x - 3/2 = 0
x - -8/3 = 0
x - -9 = 0
x = 3/2
x = -8/3
x = -9


Input:
Solve the equations:
2x + 3y = 6
5x + 1y = -1/6

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

Using elimination
5*(2x + 3y = 6)
2*(5x + 1y = -1/6)
10x + 15y = 30
10x + 2y = -1/3
Subtract equations
13y = 91/3
y = 91/3/13
y = 7/3

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


Input: Find x in 9x + 108/5 = 0

Output:
9x + 108/5 = 0
9x = -108/5
x = -108/5 / 9
x = -12/5


Input: Determine x in 7x + 35/9 = 0

Output:
7x + 35/9 = 0
7x = -35/9
x = -35/9 / 7
x = -5/9


Input:
Solve simultaneously:
1x + 4y = 20/9
4x + 6y = -10/9

Output:
1x + 4y = 20/9
4x + 6y = -10/9

Using elimination
4*(1x + 4y = 20/9)
1*(4x + 6y = -10/9)
4x + 16y = 80/9
4x + 6y = -10/9
Subtract equations
10y = 10
y = 10/10
y = 1

Substitute y
1x + 4(1) = 20/9
1x = -16/9
x = -16/9/1
x = -16/9


Input:
Find x and y such that
2x + 7y = -5/3
2x + 1y = -11/3

Output:
2x + 7y = -5/3
2x + 1y = -11/3

Using elimination
2*(2x + 7y = -5/3)
2*(2x + 1y = -11/3)
4x + 14y = -10/3
4x + 2y = -22/3
Subtract equations
12y = 4
y = 4/12
y = 1/3

Substitute y
2x + 7(1/3) = -5/3
2x = -4
x = -4/2
x = -2


Input:
Solve the equations:
9x + 2y = 242/9
9x + 8y = 320/9

Output:
9x + 2y = 242/9
9x + 8y = 320/9

Using elimination
9*(9x + 2y = 242/9)
9*(9x + 8y = 320/9)
81x + 18y = 242
81x + 72y = 320
Subtract equations
-54y = -78
y = -78/-54
y = 13/9

Substitute y
9x + 2(13/9) = 242/9
9x = 24
x = 24/9
x = 8/3


Input: Determine x in 2x  = 0

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


Input:
Solve simultaneously:
9x + 4y = 322/5
3x + 4y = 82/5

Output:
9x + 4y = 322/5
3x + 4y = 82/5

Using elimination
3*(9x + 4y = 322/5)
9*(3x + 4y = 82/5)
27x + 12y = 966/5
27x + 36y = 738/5
Subtract equations
-24y = 228/5
y = 228/5/-24
y = -19/10

Substitute y
9x + 4(-19/10) = 322/5
9x = 72
x = 72/9
x = 8


Input: What value of x satisfies x^2 + 37/5x - 72/5 = 0

Output:
x^2 + 37/5x - 72/5 = 0
(x - -9)(x - 8/5) = 0
x - -9 = 0  or  x - 8/5 = 0
x = -9
x = 8/5


Input: Find the solution to 5x - 25/4 = 0

Output:
5x - 25/4 = 0
5x = 25/4
x = 25/4 / 5
x = 5/4


Input: Find x in x^3 + 167/24x^2 + 46/3x + 65/6 = 0

Output:
x^3 + 167/24x^2 + 46/3x + 65/6 = 0
(x - -13/8)(x - -2)(x - -10/3) = 0
x - -13/8 = 0
x - -2 = 0
x - -10/3 = 0
x = -13/8
x = -2
x = -10/3


Input: Find x in x^3 - 26/15x^2 - 7/5x  = 0

Output:
x^3 - 26/15x^2 - 7/5x  = 0
(x - -3/5)(x - 7/3)(x - 0) = 0
x - -3/5 = 0
x - 7/3 = 0
x - 0 = 0
x = -3/5
x = 7/3
x = 0


Input: Find x for x^3 - 46/9x^2 + 112/27x + 32/27 = 0

Output:
x^3 - 46/9x^2 + 112/27x + 32/27 = 0
(x - 4/3)(x - 4)(x - -2/9) = 0
x - 4/3 = 0
x - 4 = 0
x - -2/9 = 0
x = 4/3
x = 4
x = -2/9


Input: What value of x satisfies x^3 + 317/45x^2 + 2126/135x + 304/27 = 0

Output:
x^3 + 317/45x^2 + 2126/135x + 304/27 = 0
(x - -10/3)(x - -19/9)(x - -8/5) = 0
x - -10/3 = 0
x - -19/9 = 0
x - -8/5 = 0
x = -10/3
x = -19/9
x = -8/5


Input: Find x for x^2 - 83/40x - 18/5 = 0

Output:
x^2 - 83/40x - 18/5 = 0
(x - 16/5)(x - -9/8) = 0
x - 16/5 = 0  or  x - -9/8 = 0
x = 16/5
x = -9/8


Input: Compute the solution of x^2 + 3/4x - 91/64 = 0

Output:
x^2 + 3/4x - 91/64 = 0
(x - -13/8)(x - 7/8) = 0
x - -13/8 = 0  or  x - 7/8 = 0
x = -13/8
x = 7/8


Input: What value of x satisfies x^2 + 89/9x - 10/9 = 0

Output:
x^2 + 89/9x - 10/9 = 0
(x - -10)(x - 1/9) = 0
x - -10 = 0  or  x - 1/9 = 0
x = -10
x = 1/9


Input:
Find x and y such that
3x + 8y = -275/4
6x + 1y = -10

Output:
3x + 8y = -275/4
6x + 1y = -10

Using elimination
6*(3x + 8y = -275/4)
3*(6x + 1y = -10)
18x + 48y = -825/2
18x + 3y = -30
Subtract equations
45y = -765/2
y = -765/2/45
y = -17/2

Substitute y
3x + 8(-17/2) = -275/4
3x = -3/4
x = -3/4/3
x = -1/4


Input:
Solve the system:
4x + 8y = 160/3
10x + 7y = 77

Output:
4x + 8y = 160/3
10x + 7y = 77

Using elimination
10*(4x + 8y = 160/3)
4*(10x + 7y = 77)
40x + 80y = 1600/3
40x + 28y = 308
Subtract equations
52y = 676/3
y = 676/3/52
y = 13/3

Substitute y
4x + 8(13/3) = 160/3
4x = 56/3
x = 56/3/4
x = 14/3


Input: Compute the solution of x^3 + 64/9x^2 + 25/3x + 68/81 = 0

Output:
x^3 + 64/9x^2 + 25/3x + 68/81 = 0
(x - -1/9)(x - -17/3)(x - -4/3) = 0
x - -1/9 = 0
x - -17/3 = 0
x - -4/3 = 0
x = -1/9
x = -17/3
x = -4/3


Input: Determine x in x^3 - 2/63x^2 - 331/189x + 104/189 = 0

Output:
x^3 - 2/63x^2 - 331/189x + 104/189 = 0
(x - 8/7)(x - -13/9)(x - 1/3) = 0
x - 8/7 = 0
x - -13/9 = 0
x - 1/3 = 0
x = 8/7
x = -13/9
x = 1/3


Input: Find the solution to 5x + 25/4 = 0

Output:
5x + 25/4 = 0
5x = -25/4
x = -25/4 / 5
x = -5/4


Input:
Find x and y such that
1x + 9y = 149/2
2x + 3y = 29

Output:
1x + 9y = 149/2
2x + 3y = 29

Using elimination
2*(1x + 9y = 149/2)
1*(2x + 3y = 29)
2x + 18y = 149
2x + 3y = 29
Subtract equations
15y = 120
y = 120/15
y = 8

Substitute y
1x + 9(8) = 149/2
1x = 5/2
x = 5/2/1
x = 5/2


Input:
Solve the system:
4x + 2y = 119/18
6x + 7y = 293/36

Output:
4x + 2y = 119/18
6x + 7y = 293/36

Using elimination
6*(4x + 2y = 119/18)
4*(6x + 7y = 293/36)
24x + 12y = 119/3
24x + 28y = 293/9
Subtract equations
-16y = 64/9
y = 64/9/-16
y = -4/9

Substitute y
4x + 2(-4/9) = 119/18
4x = 15/2
x = 15/2/4
x = 15/8


Input: Find x in x^3 + 91/20x^2 + 79/200x - 187/50 = 0

Output:
x^3 + 91/20x^2 + 79/200x - 187/50 = 0
(x - -17/4)(x - 4/5)(x - -11/10) = 0
x - -17/4 = 0
x - 4/5 = 0
x - -11/10 = 0
x = -17/4
x = 4/5
x = -11/10


Input: Determine x in x^2 - 43/7x - 6 = 0

Output:
x^2 - 43/7x - 6 = 0
(x - -6/7)(x - 7) = 0
x - -6/7 = 0  or  x - 7 = 0
x = -6/7
x = 7


Input:
Solve the system:
9x + 2y = -64
10x + 5y = -60

Output:
9x + 2y = -64
10x + 5y = -60

Using elimination
10*(9x + 2y = -64)
9*(10x + 5y = -60)
90x + 20y = -640
90x + 45y = -540
Subtract equations
-25y = -100
y = -100/-25
y = 4

Substitute y
9x + 2(4) = -64
9x = -72
x = -72/9
x = -8


Input:
Solve simultaneously:
9x + 9y = -163/10
3x + 9y = -121/10

Output:
9x + 9y = -163/10
3x + 9y = -121/10

Using elimination
3*(9x + 9y = -163/10)
9*(3x + 9y = -121/10)
27x + 27y = -489/10
27x + 81y = -1089/10
Subtract equations
-54y = 60
y = 60/-54
y = -10/9

Substitute y
9x + 9(-10/9) = -163/10
9x = -63/10
x = -63/10/9
x = -7/10


Input: Solve quickly: 4x - 2 = 0

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


Input:
Find x and y such that
3x + 6y = -37/3
3x + 8y = -139/9

Output:
3x + 6y = -37/3
3x + 8y = -139/9

Using elimination
3*(3x + 6y = -37/3)
3*(3x + 8y = -139/9)
9x + 18y = -37
9x + 24y = -139/3
Subtract equations
-6y = 28/3
y = 28/3/-6
y = -14/9

Substitute y
3x + 6(-14/9) = -37/3
3x = -3
x = -3/3
x = -1


Input: Compute the solution of x^2 - 27/14x - 10/7 = 0

Output:
x^2 - 27/14x - 10/7 = 0
(x - 5/2)(x - -4/7) = 0
x - 5/2 = 0  or  x - -4/7 = 0
x = 5/2
x = -4/7


Input: Find x for 6x + 96 = 0

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


Input: What value of x satisfies x^3 - 1249/72x^2 + 353/18x + 280/9 = 0

Output:
x^3 - 1249/72x^2 + 353/18x + 280/9 = 0
(x - 20/9)(x - 16)(x - -7/8) = 0
x - 20/9 = 0
x - 16 = 0
x - -7/8 = 0
x = 20/9
x = 16
x = -7/8


Input: Find x in x^3 - 87/14x^2 - 139/49x + 312/49 = 0

Output:
x^3 - 87/14x^2 - 139/49x + 312/49 = 0
(x - 13/2)(x - -8/7)(x - 6/7) = 0
x - 13/2 = 0
x - -8/7 = 0
x - 6/7 = 0
x = 13/2
x = -8/7
x = 6/7


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

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


Input: Solve the equation x^2 + 118/35x + 99/35 = 0

Output:
x^2 + 118/35x + 99/35 = 0
(x - -9/5)(x - -11/7) = 0
x - -9/5 = 0  or  x - -11/7 = 0
x = -9/5
x = -11/7


Input: Compute the solution of x^3 + 1171/210x^2 + 200/21x + 65/14 = 0

Output:
x^3 + 1171/210x^2 + 200/21x + 65/14 = 0
(x - -5/6)(x - -15/7)(x - -13/5) = 0
x - -5/6 = 0
x - -15/7 = 0
x - -13/5 = 0
x = -5/6
x = -15/7
x = -13/5


Input: What value of x satisfies 3x  = 0

Output:
3x  = 0
3x = 0
x = 0 / 3
x = 0


Input: Compute the solution of 7x  = 0

Output:
7x  = 0
7x = 0
x = 0 / 7
x = 0


Input:
Solve the system:
5x + 2y = 47/2
7x + 8y = 19/2

Output:
5x + 2y = 47/2
7x + 8y = 19/2

Using elimination
7*(5x + 2y = 47/2)
5*(7x + 8y = 19/2)
35x + 14y = 329/2
35x + 40y = 95/2
Subtract equations
-26y = 117
y = 117/-26
y = -9/2

Substitute y
5x + 2(-9/2) = 47/2
5x = 65/2
x = 65/2/5
x = 13/2


Input: Find x for 5x - 10/7 = 0

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


Input: Solve quickly: 3x - 45/7 = 0

Output:
3x - 45/7 = 0
3x = 45/7
x = 45/7 / 3
x = 15/7


Input: Solve x^3 + 85/28x^2 - 339/56x + 135/56 = 0

Output:
x^3 + 85/28x^2 - 339/56x + 135/56 = 0
(x - -9/2)(x - 5/7)(x - 3/4) = 0
x - -9/2 = 0
x - 5/7 = 0
x - 3/4 = 0
x = -9/2
x = 5/7
x = 3/4


Input:
Solve the system:
6x + 1y = 68/7
6x + 6y = -72/7

Output:
6x + 1y = 68/7
6x + 6y = -72/7

Using elimination
6*(6x + 1y = 68/7)
6*(6x + 6y = -72/7)
36x + 6y = 408/7
36x + 36y = -432/7
Subtract equations
-30y = 120
y = 120/-30
y = -4

Substitute y
6x + 1(-4) = 68/7
6x = 96/7
x = 96/7/6
x = 16/7


Input: Find x for 1x - 8/9 = 0

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


Input: What value of x satisfies 7x - 56/5 = 0

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


Input: Find x for 1x + 20/9 = 0

Output:
1x + 20/9 = 0
1x = -20/9
x = -20/9 / 1
x = -20/9


Input:
Solve simultaneously:
6x + 7y = -301/10
4x + 9y = -641/30

Output:
6x + 7y = -301/10
4x + 9y = -641/30

Using elimination
4*(6x + 7y = -301/10)
6*(4x + 9y = -641/30)
24x + 28y = -602/5
24x + 54y = -641/5
Subtract equations
-26y = 39/5
y = 39/5/-26
y = -3/10

Substitute y
6x + 7(-3/10) = -301/10
6x = -28
x = -28/6
x = -14/3


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

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


Input:
Solve the equations:
6x + 1y = -149/10
4x + 1y = -121/10

Output:
6x + 1y = -149/10
4x + 1y = -121/10

Using elimination
4*(6x + 1y = -149/10)
6*(4x + 1y = -121/10)
24x + 4y = -298/5
24x + 6y = -363/5
Subtract equations
-2y = 13
y = 13/-2
y = -13/2

Substitute y
6x + 1(-13/2) = -149/10
6x = -42/5
x = -42/5/6
x = -7/5


Input: What value of x satisfies x^3 + 40/9x^2 - 128/27x  = 0

Output:
x^3 + 40/9x^2 - 128/27x  = 0
(x - -16/3)(x - 8/9)(x - 0) = 0
x - -16/3 = 0
x - 8/9 = 0
x - 0 = 0
x = -16/3
x = 8/9
x = 0


Input:
Solve the system:
1x + 10y = 35/3
4x + 3y = 29/3

Output:
1x + 10y = 35/3
4x + 3y = 29/3

Using elimination
4*(1x + 10y = 35/3)
1*(4x + 3y = 29/3)
4x + 40y = 140/3
4x + 3y = 29/3
Subtract equations
37y = 37
y = 37/37
y = 1

Substitute y
1x + 10(1) = 35/3
1x = 5/3
x = 5/3/1
x = 5/3


Input: Determine x in x^2 + 17/2x - 15 = 0

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


Input: Find x in 6x + 15 = 0

Output:
6x + 15 = 0
6x = -15
x = -15 / 6
x = -5/2


Input:
Solve simultaneously:
4x + 10y = -473/5
5x + 8y = -151/2

Output:
4x + 10y = -473/5
5x + 8y = -151/2

Using elimination
5*(4x + 10y = -473/5)
4*(5x + 8y = -151/2)
20x + 50y = -473
20x + 32y = -302
Subtract equations
18y = -171
y = -171/18
y = -19/2

Substitute y
4x + 10(-19/2) = -473/5
4x = 2/5
x = 2/5/4
x = 1/10


Input: Find x in x^2 + 11x - 26 = 0

Output:
x^2 + 11x - 26 = 0
(x - -13)(x - 2) = 0
x - -13 = 0  or  x - 2 = 0
x = -13
x = 2


Input: Solve quickly: x^3 + 299/15x^2 + 269/15x + 19/5 = 0

Output:
x^3 + 299/15x^2 + 269/15x + 19/5 = 0
(x - -3/5)(x - -19)(x - -1/3) = 0
x - -3/5 = 0
x - -19 = 0
x - -1/3 = 0
x = -3/5
x = -19
x = -1/3


Input:
Solve the system:
9x + 3y = 3/2
10x + 7y = 12/5

Output:
9x + 3y = 3/2
10x + 7y = 12/5

Using elimination
10*(9x + 3y = 3/2)
9*(10x + 7y = 12/5)
90x + 30y = 15
90x + 63y = 108/5
Subtract equations
-33y = -33/5
y = -33/5/-33
y = 1/5

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


Input: What value of x satisfies x^3 + 13/10x^2 - 627/50x - 459/25 = 0

Output:
x^3 + 13/10x^2 - 627/50x - 459/25 = 0
(x - 18/5)(x - -3/2)(x - -17/5) = 0
x - 18/5 = 0
x - -3/2 = 0
x - -17/5 = 0
x = 18/5
x = -3/2
x = -17/5


Input: Find x for x^3 + 34/15x^2 - 1864/75x + 448/15 = 0

Output:
x^3 + 34/15x^2 - 1864/75x + 448/15 = 0
(x - 8/5)(x - 14/5)(x - -20/3) = 0
x - 8/5 = 0
x - 14/5 = 0
x - -20/3 = 0
x = 8/5
x = 14/5
x = -20/3


Input:
Find x and y such that
1x + 5y = 11/4
1x + 2y = 1/2

Output:
1x + 5y = 11/4
1x + 2y = 1/2

Using elimination
1*(1x + 5y = 11/4)
1*(1x + 2y = 1/2)
1x + 5y = 11/4
1x + 2y = 1/2
Subtract equations
3y = 9/4
y = 9/4/3
y = 3/4

Substitute y
1x + 5(3/4) = 11/4
1x = -1
x = -1/1
x = -1


Input:
Solve the system:
4x + 7y = 21
9x + 5y = 339/14

Output:
4x + 7y = 21
9x + 5y = 339/14

Using elimination
9*(4x + 7y = 21)
4*(9x + 5y = 339/14)
36x + 63y = 189
36x + 20y = 678/7
Subtract equations
43y = 645/7
y = 645/7/43
y = 15/7

Substitute y
4x + 7(15/7) = 21
4x = 6
x = 6/4
x = 3/2


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

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


Input:
Solve the system:
3x + 5y = 187/12
4x + 5y = 49/3

Output:
3x + 5y = 187/12
4x + 5y = 49/3

Using elimination
4*(3x + 5y = 187/12)
3*(4x + 5y = 49/3)
12x + 20y = 187/3
12x + 15y = 49
Subtract equations
5y = 40/3
y = 40/3/5
y = 8/3

Substitute y
3x + 5(8/3) = 187/12
3x = 9/4
x = 9/4/3
x = 3/4


Input: Solve x^3 + 43/20x^2 - 29/20x - 7/2 = 0

Output:
x^3 + 43/20x^2 - 29/20x - 7/2 = 0
(x - -2)(x - 5/4)(x - -7/5) = 0
x - -2 = 0
x - 5/4 = 0
x - -7/5 = 0
x = -2
x = 5/4
x = -7/5


Input: What value of x satisfies x^2 + 47/36x - 7/18 = 0

Output:
x^2 + 47/36x - 7/18 = 0
(x - -14/9)(x - 1/4) = 0
x - -14/9 = 0  or  x - 1/4 = 0
x = -14/9
x = 1/4


Input: Solve quickly: x^2 - 71/10x + 33/5 = 0

Output:
x^2 - 71/10x + 33/5 = 0
(x - 6)(x - 11/10) = 0
x - 6 = 0  or  x - 11/10 = 0
x = 6
x = 11/10


Input: Compute the solution of x^2 + 3x - 34/25 = 0

Output:
x^2 + 3x - 34/25 = 0
(x - 2/5)(x - -17/5) = 0
x - 2/5 = 0  or  x - -17/5 = 0
x = 2/5
x = -17/5


Input: Solve x^3 - 159/10x^2 - 93/5x - 17/10 = 0

Output:
x^3 - 159/10x^2 - 93/5x - 17/10 = 0
(x - 17)(x - -1/10)(x - -1) = 0
x - 17 = 0
x - -1/10 = 0
x - -1 = 0
x = 17
x = -1/10
x = -1


Input:
Find x and y such that
10x + 4y = -296/9
3x + 10y = -320/3

Output:
10x + 4y = -296/9
3x + 10y = -320/3

Using elimination
3*(10x + 4y = -296/9)
10*(3x + 10y = -320/3)
30x + 12y = -296/3
30x + 100y = -3200/3
Subtract equations
-88y = 968
y = 968/-88
y = -11

Substitute y
10x + 4(-11) = -296/9
10x = 100/9
x = 100/9/10
x = 10/9


Input: Solve 6x + 19 = 0

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


Input:
Find x and y such that
8x + 1y = 116/15
9x + 7y = -7/10

Output:
8x + 1y = 116/15
9x + 7y = -7/10

Using elimination
9*(8x + 1y = 116/15)
8*(9x + 7y = -7/10)
72x + 9y = 348/5
72x + 56y = -28/5
Subtract equations
-47y = 376/5
y = 376/5/-47
y = -8/5

Substitute y
8x + 1(-8/5) = 116/15
8x = 28/3
x = 28/3/8
x = 7/6


Input:
Solve the equations:
7x + 10y = 559/12
10x + 4y = 317/6

Output:
7x + 10y = 559/12
10x + 4y = 317/6

Using elimination
10*(7x + 10y = 559/12)
7*(10x + 4y = 317/6)
70x + 100y = 2795/6
70x + 28y = 2219/6
Subtract equations
72y = 96
y = 96/72
y = 4/3

Substitute y
7x + 10(4/3) = 559/12
7x = 133/4
x = 133/4/7
x = 19/4


Input: What value of x satisfies x^3 - 77/45x^2 - 10/9x + 16/15 = 0

Output:
x^3 - 77/45x^2 - 10/9x + 16/15 = 0
(x - 3/5)(x - -8/9)(x - 2) = 0
x - 3/5 = 0
x - -8/9 = 0
x - 2 = 0
x = 3/5
x = -8/9
x = 2


Input:
Solve the system:
8x + 3y = -239/3
3x + 9y = -359/2

Output:
8x + 3y = -239/3
3x + 9y = -359/2

Using elimination
3*(8x + 3y = -239/3)
8*(3x + 9y = -359/2)
24x + 9y = -239
24x + 72y = -1436
Subtract equations
-63y = 1197
y = 1197/-63
y = -19

Substitute y
8x + 3(-19) = -239/3
8x = -68/3
x = -68/3/8
x = -17/6


Input: Solve 4x + 6 = 0

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


Input: Find x in x^2 + 21/4x + 17/4 = 0

Output:
x^2 + 21/4x + 17/4 = 0
(x - -1)(x - -17/4) = 0
x - -1 = 0  or  x - -17/4 = 0
x = -1
x = -17/4


Input: Find the solution to x^3 + 108/5x^2 + 247/5x  = 0

Output:
x^3 + 108/5x^2 + 247/5x  = 0
(x - -13/5)(x - 0)(x - -19) = 0
x - -13/5 = 0
x - 0 = 0
x - -19 = 0
x = -13/5
x = 0
x = -19


Input:
Solve the system:
10x + 3y = -59/6
3x + 10y = -361/36

Output:
10x + 3y = -59/6
3x + 10y = -361/36

Using elimination
3*(10x + 3y = -59/6)
10*(3x + 10y = -361/36)
30x + 9y = -59/2
30x + 100y = -1805/18
Subtract equations
-91y = 637/9
y = 637/9/-91
y = -7/9

Substitute y
10x + 3(-7/9) = -59/6
10x = -15/2
x = -15/2/10
x = -3/4


Input:
Solve the equations:
3x + 6y = 47/6
5x + 3y = 155/36

Output:
3x + 6y = 47/6
5x + 3y = 155/36

Using elimination
5*(3x + 6y = 47/6)
3*(5x + 3y = 155/36)
15x + 30y = 235/6
15x + 9y = 155/12
Subtract equations
21y = 105/4
y = 105/4/21
y = 5/4

Substitute y
3x + 6(5/4) = 47/6
3x = 1/3
x = 1/3/3
x = 1/9


Input: Find x for 4x - 3/2 = 0

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


Input: Find x in 5x - 8 = 0

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


Input: Solve the equation x^2 + 75/14x + 13/2 = 0

Output:
x^2 + 75/14x + 13/2 = 0
(x - -7/2)(x - -13/7) = 0
x - -7/2 = 0  or  x - -13/7 = 0
x = -7/2
x = -13/7


Input: Solve the equation x^3 + 3/14x^2 - 613/112x + 57/16 = 0

Output:
x^3 + 3/14x^2 - 613/112x + 57/16 = 0
(x - -19/7)(x - 3/4)(x - 7/4) = 0
x - -19/7 = 0
x - 3/4 = 0
x - 7/4 = 0
x = -19/7
x = 3/4
x = 7/4


Input:
Find x and y such that
3x + 8y = 75/14
1x + 5y = 53/14

Output:
3x + 8y = 75/14
1x + 5y = 53/14

Using elimination
1*(3x + 8y = 75/14)
3*(1x + 5y = 53/14)
3x + 8y = 75/14
3x + 15y = 159/14
Subtract equations
-7y = -6
y = -6/-7
y = 6/7

Substitute y
3x + 8(6/7) = 75/14
3x = -3/2
x = -3/2/3
x = -1/2


Input:
Solve the system:
5x + 9y = 158/5
10x + 2y = 124/5

Output:
5x + 9y = 158/5
10x + 2y = 124/5

Using elimination
10*(5x + 9y = 158/5)
5*(10x + 2y = 124/5)
50x + 90y = 316
50x + 10y = 124
Subtract equations
80y = 192
y = 192/80
y = 12/5

Substitute y
5x + 9(12/5) = 158/5
5x = 10
x = 10/5
x = 2


Input:
Find x and y such that
6x + 7y = 4/15
2x + 5y = -52/15

Output:
6x + 7y = 4/15
2x + 5y = -52/15

Using elimination
2*(6x + 7y = 4/15)
6*(2x + 5y = -52/15)
12x + 14y = 8/15
12x + 30y = -104/5
Subtract equations
-16y = 64/3
y = 64/3/-16
y = -4/3

Substitute y
6x + 7(-4/3) = 4/15
6x = 48/5
x = 48/5/6
x = 8/5


Input: Solve the equation 6x - 3/2 = 0

Output:
6x - 3/2 = 0
6x = 3/2
x = 3/2 / 6
x = 1/4


Input:
Solve the equations:
4x + 9y = 629/10
10x + 5y = 17/2

Output:
4x + 9y = 629/10
10x + 5y = 17/2

Using elimination
10*(4x + 9y = 629/10)
4*(10x + 5y = 17/2)
40x + 90y = 629
40x + 20y = 34
Subtract equations
70y = 595
y = 595/70
y = 17/2

Substitute y
4x + 9(17/2) = 629/10
4x = -68/5
x = -68/5/4
x = -17/5


Input: Find x in 10x - 20/7 = 0

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


Input: Solve x^2 - 23/5x + 26/5 = 0

Output:
x^2 - 23/5x + 26/5 = 0
(x - 2)(x - 13/5) = 0
x - 2 = 0  or  x - 13/5 = 0
x = 2
x = 13/5


Input: Find x in x^3 + 8/3x^2 - 77/3x + 98/3 = 0

Output:
x^3 + 8/3x^2 - 77/3x + 98/3 = 0
(x - 7/3)(x - -7)(x - 2) = 0
x - 7/3 = 0
x - -7 = 0
x - 2 = 0
x = 7/3
x = -7
x = 2


Input: Determine x in 10x - 5/4 = 0

Output:
10x - 5/4 = 0
10x = 5/4
x = 5/4 / 10
x = 1/8


Input: Solve x^3 - 727/180x^2 + 23/5x - 8/5 = 0

Output:
x^3 - 727/180x^2 + 23/5x - 8/5 = 0
(x - 12/5)(x - 3/4)(x - 8/9) = 0
x - 12/5 = 0
x - 3/4 = 0
x - 8/9 = 0
x = 12/5
x = 3/4
x = 8/9


Input:
Find x and y such that
6x + 10y = -118/21
3x + 1y = -107/21

Output:
6x + 10y = -118/21
3x + 1y = -107/21

Using elimination
3*(6x + 10y = -118/21)
6*(3x + 1y = -107/21)
18x + 30y = -118/7
18x + 6y = -214/7
Subtract equations
24y = 96/7
y = 96/7/24
y = 4/7

Substitute y
6x + 10(4/7) = -118/21
6x = -34/3
x = -34/3/6
x = -17/9


Input: Find x for x^2 - 17/21x - 10/7 = 0

Output:
x^2 - 17/21x - 10/7 = 0
(x - -6/7)(x - 5/3) = 0
x - -6/7 = 0  or  x - 5/3 = 0
x = -6/7
x = 5/3


Input: Find x for x^3 - 53/18x^2 - 31/54x + 68/27 = 0

Output:
x^3 - 53/18x^2 - 31/54x + 68/27 = 0
(x - 17/6)(x - -8/9)(x - 1) = 0
x - 17/6 = 0
x - -8/9 = 0
x - 1 = 0
x = 17/6
x = -8/9
x = 1


Input: What value of x satisfies x^2 - 5/12x - 77/12 = 0

Output:
x^2 - 5/12x - 77/12 = 0
(x - 11/4)(x - -7/3) = 0
x - 11/4 = 0  or  x - -7/3 = 0
x = 11/4
x = -7/3


Input: Solve the equation x^2 + 3/5x - 26/5 = 0

Output:
x^2 + 3/5x - 26/5 = 0
(x - -13/5)(x - 2) = 0
x - -13/5 = 0  or  x - 2 = 0
x = -13/5
x = 2


Input: Compute the solution of x^2 + 16/21x - 85/21 = 0

Output:
x^2 + 16/21x - 85/21 = 0
(x - 5/3)(x - -17/7) = 0
x - 5/3 = 0  or  x - -17/7 = 0
x = 5/3
x = -17/7


Input: Find the solution to x^3 + 35/4x^2 + 77/8x + 15/8 = 0

Output:
x^3 + 35/4x^2 + 77/8x + 15/8 = 0
(x - -1)(x - -1/4)(x - -15/2) = 0
x - -1 = 0
x - -1/4 = 0
x - -15/2 = 0
x = -1
x = -1/4
x = -15/2


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

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


Input:
Solve simultaneously:
7x + 3y = 23
9x + 6y = 36

Output:
7x + 3y = 23
9x + 6y = 36

Using elimination
9*(7x + 3y = 23)
7*(9x + 6y = 36)
63x + 27y = 207
63x + 42y = 252
Subtract equations
-15y = -45
y = -45/-15
y = 3

Substitute y
7x + 3(3) = 23
7x = 14
x = 14/7
x = 2


Input: Solve x^3 - 11/2x^2 - 29/4x + 39/8 = 0

Output:
x^3 - 11/2x^2 - 29/4x + 39/8 = 0
(x - 1/2)(x - -3/2)(x - 13/2) = 0
x - 1/2 = 0
x - -3/2 = 0
x - 13/2 = 0
x = 1/2
x = -3/2
x = 13/2


Input:
Solve the system:
8x + 4y = 6
10x + 6y = 3

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

Using elimination
10*(8x + 4y = 6)
8*(10x + 6y = 3)
80x + 40y = 60
80x + 48y = 24
Subtract equations
-8y = 36
y = 36/-8
y = -9/2

Substitute y
8x + 4(-9/2) = 6
8x = 24
x = 24/8
x = 3


Input: Determine x in 7x - 21/4 = 0

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


Input: Determine x in 5x - 5/4 = 0

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


Input: Solve x^3 + 187/18x^2 + 175/18x - 25 = 0

Output:
x^3 + 187/18x^2 + 175/18x - 25 = 0
(x - 10/9)(x - -5/2)(x - -9) = 0
x - 10/9 = 0
x - -5/2 = 0
x - -9 = 0
x = 10/9
x = -5/2
x = -9


Input: Solve the equation x^3 - 7/2x^2 - 231/16x + 765/16 = 0

Output:
x^3 - 7/2x^2 - 231/16x + 765/16 = 0
(x - 17/4)(x - 3)(x - -15/4) = 0
x - 17/4 = 0
x - 3 = 0
x - -15/4 = 0
x = 17/4
x = 3
x = -15/4


Input: Solve quickly: 5x + 95/2 = 0

Output:
5x + 95/2 = 0
5x = -95/2
x = -95/2 / 5
x = -19/2


Input: Solve the equation x^3 + 174/35x^2 + 207/35x + 68/35 = 0

Output:
x^3 + 174/35x^2 + 207/35x + 68/35 = 0
(x - -17/5)(x - -1)(x - -4/7) = 0
x - -17/5 = 0
x - -1 = 0
x - -4/7 = 0
x = -17/5
x = -1
x = -4/7


Input: Determine x in 9x - 18 = 0

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


Input:
Solve simultaneously:
5x + 9y = -15/2
8x + 7y = -83/10

Output:
5x + 9y = -15/2
8x + 7y = -83/10

Using elimination
8*(5x + 9y = -15/2)
5*(8x + 7y = -83/10)
40x + 72y = -60
40x + 35y = -83/2
Subtract equations
37y = -37/2
y = -37/2/37
y = -1/2

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


Input: Find x in x^2 - 7/5x - 24/5 = 0

Output:
x^2 - 7/5x - 24/5 = 0
(x - 3)(x - -8/5) = 0
x - 3 = 0  or  x - -8/5 = 0
x = 3
x = -8/5


Input: Determine x in 2x - 2 = 0

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


Input: Find x in x^3 - 121/56x^2 - 1079/392x + 95/28 = 0

Output:
x^3 - 121/56x^2 - 1079/392x + 95/28 = 0
(x - 7/8)(x - 19/7)(x - -10/7) = 0
x - 7/8 = 0
x - 19/7 = 0
x - -10/7 = 0
x = 7/8
x = 19/7
x = -10/7


Input:
Solve simultaneously:
4x + 8y = 191/14
5x + 9y = 835/56

Output:
4x + 8y = 191/14
5x + 9y = 835/56

Using elimination
5*(4x + 8y = 191/14)
4*(5x + 9y = 835/56)
20x + 40y = 955/14
20x + 36y = 835/14
Subtract equations
4y = 60/7
y = 60/7/4
y = 15/7

Substitute y
4x + 8(15/7) = 191/14
4x = -7/2
x = -7/2/4
x = -7/8


Input: Find x for x^3 - 401/210x^2 - 382/105x - 38/35 = 0

Output:
x^3 - 401/210x^2 - 382/105x - 38/35 = 0
(x - 19/6)(x - -2/5)(x - -6/7) = 0
x - 19/6 = 0
x - -2/5 = 0
x - -6/7 = 0
x = 19/6
x = -2/5
x = -6/7


Input: Solve x^2 + 10x + 24 = 0

Output:
x^2 + 10x + 24 = 0
(x - -6)(x - -4) = 0
x - -6 = 0  or  x - -4 = 0
x = -6
x = -4


Input: Determine x in x^2 + 5/8x - 51/16 = 0

Output:
x^2 + 5/8x - 51/16 = 0
(x - -17/8)(x - 3/2) = 0
x - -17/8 = 0  or  x - 3/2 = 0
x = -17/8
x = 3/2


Input:
Solve the system:
4x + 6y = 49/6
1x + 9y = 123/8

Output:
4x + 6y = 49/6
1x + 9y = 123/8

Using elimination
1*(4x + 6y = 49/6)
4*(1x + 9y = 123/8)
4x + 6y = 49/6
4x + 36y = 123/2
Subtract equations
-30y = -160/3
y = -160/3/-30
y = 16/9

Substitute y
4x + 6(16/9) = 49/6
4x = -5/2
x = -5/2/4
x = -5/8


Input:
Solve simultaneously:
6x + 10y = 14
7x + 2y = -3

Output:
6x + 10y = 14
7x + 2y = -3

Using elimination
7*(6x + 10y = 14)
6*(7x + 2y = -3)
42x + 70y = 98
42x + 12y = -18
Subtract equations
58y = 116
y = 116/58
y = 2

Substitute y
6x + 10(2) = 14
6x = -6
x = -6/6
x = -1


Input: Solve the equation 10x + 50/3 = 0

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


Input: Find the solution to x^2 - 51/7x + 2 = 0

Output:
x^2 - 51/7x + 2 = 0
(x - 2/7)(x - 7) = 0
x - 2/7 = 0  or  x - 7 = 0
x = 2/7
x = 7


Input: Solve the equation x^2 - 229/56x + 57/14 = 0

Output:
x^2 - 229/56x + 57/14 = 0
(x - 19/8)(x - 12/7) = 0
x - 19/8 = 0  or  x - 12/7 = 0
x = 19/8
x = 12/7


Input: Solve quickly: x^2 - 221/90x + 7/5 = 0

Output:
x^2 - 221/90x + 7/5 = 0
(x - 9/10)(x - 14/9) = 0
x - 9/10 = 0  or  x - 14/9 = 0
x = 9/10
x = 14/9


Input: Determine x in x^3 - 115/63x^2 - 11/3x + 3/7 = 0

Output:
x^3 - 115/63x^2 - 11/3x + 3/7 = 0
(x - 1/9)(x - 3)(x - -9/7) = 0
x - 1/9 = 0
x - 3 = 0
x - -9/7 = 0
x = 1/9
x = 3
x = -9/7


Input:
Solve simultaneously:
3x + 7y = 7/3
4x + 5y = 5/3

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

Using elimination
4*(3x + 7y = 7/3)
3*(4x + 5y = 5/3)
12x + 28y = 28/3
12x + 15y = 5
Subtract equations
13y = 13/3
y = 13/3/13
y = 1/3

Substitute y
3x + 7(1/3) = 7/3
3x = 0
x = 0/3
x = 0


Input: Solve 8x - 2 = 0

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


Input: Solve the equation 10x - 40 = 0

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


Input: Solve the equation x^2 + 3/2x - 136/25 = 0

Output:
x^2 + 3/2x - 136/25 = 0
(x - 17/10)(x - -16/5) = 0
x - 17/10 = 0  or  x - -16/5 = 0
x = 17/10
x = -16/5


Input: Find x in 9x + 81/5 = 0

Output:
9x + 81/5 = 0
9x = -81/5
x = -81/5 / 9
x = -9/5


Input: Find the solution to x^3 + 29/10x^2 - 283/10x + 14/5 = 0

Output:
x^3 + 29/10x^2 - 283/10x + 14/5 = 0
(x - 4)(x - 1/10)(x - -7) = 0
x - 4 = 0
x - 1/10 = 0
x - -7 = 0
x = 4
x = 1/10
x = -7


Input: Find the solution to 8x + 14 = 0

Output:
8x + 14 = 0
8x = -14
x = -14 / 8
x = -7/4


Input: Determine x in 6x - 96/5 = 0

Output:
6x - 96/5 = 0
6x = 96/5
x = 96/5 / 6
x = 16/5


Input:
Find x and y such that
4x + 10y = 57/2
1x + 4y = 429/40

Output:
4x + 10y = 57/2
1x + 4y = 429/40

Using elimination
1*(4x + 10y = 57/2)
4*(1x + 4y = 429/40)
4x + 10y = 57/2
4x + 16y = 429/10
Subtract equations
-6y = -72/5
y = -72/5/-6
y = 12/5

Substitute y
4x + 10(12/5) = 57/2
4x = 9/2
x = 9/2/4
x = 9/8


Input: What value of x satisfies x^3 + 23/5x^2 + 2x - 8/5 = 0

Output:
x^3 + 23/5x^2 + 2x - 8/5 = 0
(x - -1)(x - -4)(x - 2/5) = 0
x - -1 = 0
x - -4 = 0
x - 2/5 = 0
x = -1
x = -4
x = 2/5


Input: Solve quickly: x^2 - 29/8x + 13/4 = 0

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


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

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


Input: Solve quickly: 6x - 3 = 0

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


Input: Solve 10x - 70 = 0

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


Input: Solve quickly: 9x + 27/5 = 0

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


Input:
Solve simultaneously:
2x + 6y = -27/7
4x + 2y = 26/7

Output:
2x + 6y = -27/7
4x + 2y = 26/7

Using elimination
4*(2x + 6y = -27/7)
2*(4x + 2y = 26/7)
8x + 24y = -108/7
8x + 4y = 52/7
Subtract equations
20y = -160/7
y = -160/7/20
y = -8/7

Substitute y
2x + 6(-8/7) = -27/7
2x = 3
x = 3/2
x = 3/2


Input: Determine x in x^2 - 57/10x + 7/2 = 0

Output:
x^2 - 57/10x + 7/2 = 0
(x - 7/10)(x - 5) = 0
x - 7/10 = 0  or  x - 5 = 0
x = 7/10
x = 5


Input: Determine x in 7x - 28/5 = 0

Output:
7x - 28/5 = 0
7x = 28/5
x = 28/5 / 7
x = 4/5


Input: Compute the solution of x^3 - 1/4x^2 - 61/36x + 5/9 = 0

Output:
x^3 - 1/4x^2 - 61/36x + 5/9 = 0
(x - -4/3)(x - 1/3)(x - 5/4) = 0
x - -4/3 = 0
x - 1/3 = 0
x - 5/4 = 0
x = -4/3
x = 1/3
x = 5/4


Input: Find the solution to x^2 - 1/72x - 5/4 = 0

Output:
x^2 - 1/72x - 5/4 = 0
(x - 9/8)(x - -10/9) = 0
x - 9/8 = 0  or  x - -10/9 = 0
x = 9/8
x = -10/9


Input: Find the solution to x^2 - 19/12x - 34/3 = 0

Output:
x^2 - 19/12x - 34/3 = 0
(x - 17/4)(x - -8/3) = 0
x - 17/4 = 0  or  x - -8/3 = 0
x = 17/4
x = -8/3


Input: Find the solution to x^3 + 11/3x^2 + 32/9x + 28/27 = 0

Output:
x^3 + 11/3x^2 + 32/9x + 28/27 = 0
(x - -7/3)(x - -2/3)(x - -2/3) = 0
x - -7/3 = 0
x - -2/3 = 0
x - -2/3 = 0
x = -7/3
x = -2/3
x = -2/3


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

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


Input:
Solve the system:
3x + 4y = -7/3
6x + 9y = -41/6

Output:
3x + 4y = -7/3
6x + 9y = -41/6

Using elimination
6*(3x + 4y = -7/3)
3*(6x + 9y = -41/6)
18x + 24y = -14
18x + 27y = -41/2
Subtract equations
-3y = 13/2
y = 13/2/-3
y = -13/6

Substitute y
3x + 4(-13/6) = -7/3
3x = 19/3
x = 19/3/3
x = 19/9


Input: Compute the solution of 4x - 48/5 = 0

Output:
4x - 48/5 = 0
4x = 48/5
x = 48/5 / 4
x = 12/5


Input: Solve the equation 8x - 56/9 = 0

Output:
8x - 56/9 = 0
8x = 56/9
x = 56/9 / 8
x = 7/9


Input: Solve the equation x^2 - 139/45x + 88/45 = 0

Output:
x^2 - 139/45x + 88/45 = 0
(x - 11/5)(x - 8/9) = 0
x - 11/5 = 0  or  x - 8/9 = 0
x = 11/5
x = 8/9


Input: Find the solution to 3x - 21/8 = 0

Output:
3x - 21/8 = 0
3x = 21/8
x = 21/8 / 3
x = 7/8


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

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


Input:
Solve simultaneously:
8x + 2y = 664/45
3x + 7y = 749/45

Output:
8x + 2y = 664/45
3x + 7y = 749/45

Using elimination
3*(8x + 2y = 664/45)
8*(3x + 7y = 749/45)
24x + 6y = 664/15
24x + 56y = 5992/45
Subtract equations
-50y = -800/9
y = -800/9/-50
y = 16/9

Substitute y
8x + 2(16/9) = 664/45
8x = 56/5
x = 56/5/8
x = 7/5


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

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


Input: Solve quickly: 1x - 7/5 = 0

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


Input: Find x in x^2 + 6/5x + 1/5 = 0

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


Input:
Find x and y such that
6x + 3y = 117/10
4x + 10y = 23

Output:
6x + 3y = 117/10
4x + 10y = 23

Using elimination
4*(6x + 3y = 117/10)
6*(4x + 10y = 23)
24x + 12y = 234/5
24x + 60y = 138
Subtract equations
-48y = -456/5
y = -456/5/-48
y = 19/10

Substitute y
6x + 3(19/10) = 117/10
6x = 6
x = 6/6
x = 1


Input: Determine x in x^2 + 73/10x + 21/10 = 0

Output:
x^2 + 73/10x + 21/10 = 0
(x - -3/10)(x - -7) = 0
x - -3/10 = 0  or  x - -7 = 0
x = -3/10
x = -7


Input:
Solve simultaneously:
6x + 6y = -84/5
6x + 9y = -111/5

Output:
6x + 6y = -84/5
6x + 9y = -111/5

Using elimination
6*(6x + 6y = -84/5)
6*(6x + 9y = -111/5)
36x + 36y = -504/5
36x + 54y = -666/5
Subtract equations
-18y = 162/5
y = 162/5/-18
y = -9/5

Substitute y
6x + 6(-9/5) = -84/5
6x = -6
x = -6/6
x = -1


Input:
Find x and y such that
3x + 7y = -23/8
10x + 3y = -97/8

Output:
3x + 7y = -23/8
10x + 3y = -97/8

Using elimination
10*(3x + 7y = -23/8)
3*(10x + 3y = -97/8)
30x + 70y = -115/4
30x + 9y = -291/8
Subtract equations
61y = 61/8
y = 61/8/61
y = 1/8

Substitute y
3x + 7(1/8) = -23/8
3x = -15/4
x = -15/4/3
x = -5/4


Input: Find the solution to x^3 + 227/40x^2 + 253/40x - 3/2 = 0

Output:
x^3 + 227/40x^2 + 253/40x - 3/2 = 0
(x - 1/5)(x - -4)(x - -15/8) = 0
x - 1/5 = 0
x - -4 = 0
x - -15/8 = 0
x = 1/5
x = -4
x = -15/8


Input: Find x in x^3 - 2/5x^2 - 141/100x - 9/25 = 0

Output:
x^3 - 2/5x^2 - 141/100x - 9/25 = 0
(x - -4/5)(x - 3/2)(x - -3/10) = 0
x - -4/5 = 0
x - 3/2 = 0
x - -3/10 = 0
x = -4/5
x = 3/2
x = -3/10


Input: Solve x^3 - 11x^2 - 18x + 72 = 0

Output:
x^3 - 11x^2 - 18x + 72 = 0
(x - 2)(x - -3)(x - 12) = 0
x - 2 = 0
x - -3 = 0
x - 12 = 0
x = 2
x = -3
x = 12


Input: Solve the equation x^3 - 223/90x^2 - 388/135x + 238/45 = 0

Output:
x^3 - 223/90x^2 - 388/135x + 238/45 = 0
(x - 17/6)(x - 6/5)(x - -14/9) = 0
x - 17/6 = 0
x - 6/5 = 0
x - -14/9 = 0
x = 17/6
x = 6/5
x = -14/9


Input:
Solve the equations:
8x + 4y = 34
4x + 7y = 19/2

Output:
8x + 4y = 34
4x + 7y = 19/2

Using elimination
4*(8x + 4y = 34)
8*(4x + 7y = 19/2)
32x + 16y = 136
32x + 56y = 76
Subtract equations
-40y = 60
y = 60/-40
y = -3/2

Substitute y
8x + 4(-3/2) = 34
8x = 40
x = 40/8
x = 5


Input: Find x in x^2 - 21/5x + 18/5 = 0

Output:
x^2 - 21/5x + 18/5 = 0
(x - 6/5)(x - 3) = 0
x - 6/5 = 0  or  x - 3 = 0
x = 6/5
x = 3


Input: Solve the equation x^3 + 29/20x^2 - 18/5x - 81/20 = 0

Output:
x^3 + 29/20x^2 - 18/5x - 81/20 = 0
(x - 9/5)(x - -1)(x - -9/4) = 0
x - 9/5 = 0
x - -1 = 0
x - -9/4 = 0
x = 9/5
x = -1
x = -9/4


Input: Compute the solution of x^2 + 38x + 360 = 0

Output:
x^2 + 38x + 360 = 0
(x - -20)(x - -18) = 0
x - -20 = 0  or  x - -18 = 0
x = -20
x = -18


Input: Solve x^3 + 125/12x^2 - 293/12x - 65 = 0

Output:
x^3 + 125/12x^2 - 293/12x - 65 = 0
(x - 13/4)(x - -12)(x - -5/3) = 0
x - 13/4 = 0
x - -12 = 0
x - -5/3 = 0
x = 13/4
x = -12
x = -5/3


Input: Solve quickly: x^3 + 107/6x^2 - 85/2x + 50/3 = 0

Output:
x^3 + 107/6x^2 - 85/2x + 50/3 = 0
(x - 1/2)(x - -20)(x - 5/3) = 0
x - 1/2 = 0
x - -20 = 0
x - 5/3 = 0
x = 1/2
x = -20
x = 5/3


Input: Compute the solution of x^2 - 25/3x + 16 = 0

Output:
x^2 - 25/3x + 16 = 0
(x - 3)(x - 16/3) = 0
x - 3 = 0  or  x - 16/3 = 0
x = 3
x = 16/3


Input:
Solve the equations:
6x + 5y = 502/21
10x + 4y = 230/21

Output:
6x + 5y = 502/21
10x + 4y = 230/21

Using elimination
10*(6x + 5y = 502/21)
6*(10x + 4y = 230/21)
60x + 50y = 5020/21
60x + 24y = 460/7
Subtract equations
26y = 520/3
y = 520/3/26
y = 20/3

Substitute y
6x + 5(20/3) = 502/21
6x = -66/7
x = -66/7/6
x = -11/7


Input: Solve 1x - 14 = 0

Output:
1x - 14 = 0
1x = 14
x = 14 / 1
x = 14


Input: Find the solution to x^3 + 37/5x^2 + 216/25x + 36/25 = 0

Output:
x^3 + 37/5x^2 + 216/25x + 36/25 = 0
(x - -6/5)(x - -1/5)(x - -6) = 0
x - -6/5 = 0
x - -1/5 = 0
x - -6 = 0
x = -6/5
x = -1/5
x = -6


Input: What value of x satisfies x^2 - 3/10x - 9/5 = 0

Output:
x^2 - 3/10x - 9/5 = 0
(x - -6/5)(x - 3/2) = 0
x - -6/5 = 0  or  x - 3/2 = 0
x = -6/5
x = 3/2


Input: Solve the equation x^3 - 19/5x^2 - 187/20x  = 0

Output:
x^3 - 19/5x^2 - 187/20x  = 0
(x - 11/2)(x - 0)(x - -17/10) = 0
x - 11/2 = 0
x - 0 = 0
x - -17/10 = 0
x = 11/2
x = 0
x = -17/10


Input:
Solve the equations:
3x + 1y = 47/6
5x + 8y = 74/3

Output:
3x + 1y = 47/6
5x + 8y = 74/3

Using elimination
5*(3x + 1y = 47/6)
3*(5x + 8y = 74/3)
15x + 5y = 235/6
15x + 24y = 74
Subtract equations
-19y = -209/6
y = -209/6/-19
y = 11/6

Substitute y
3x + 1(11/6) = 47/6
3x = 6
x = 6/3
x = 2


Input:
Solve the equations:
8x + 2y = -45
8x + 4y = -50

Output:
8x + 2y = -45
8x + 4y = -50

Using elimination
8*(8x + 2y = -45)
8*(8x + 4y = -50)
64x + 16y = -360
64x + 32y = -400
Subtract equations
-16y = 40
y = 40/-16
y = -5/2

Substitute y
8x + 2(-5/2) = -45
8x = -40
x = -40/8
x = -5


Input: Find the solution to x^2 - 22/9x + 40/27 = 0

Output:
x^2 - 22/9x + 40/27 = 0
(x - 10/9)(x - 4/3) = 0
x - 10/9 = 0  or  x - 4/3 = 0
x = 10/9
x = 4/3


Input:
Solve simultaneously:
9x + 1y = -367/20
3x + 10y = -91/5

Output:
9x + 1y = -367/20
3x + 10y = -91/5

Using elimination
3*(9x + 1y = -367/20)
9*(3x + 10y = -91/5)
27x + 3y = -1101/20
27x + 90y = -819/5
Subtract equations
-87y = 435/4
y = 435/4/-87
y = -5/4

Substitute y
9x + 1(-5/4) = -367/20
9x = -171/10
x = -171/10/9
x = -19/10


Input: Solve x^3 - 11/3x^2 - 20/3x  = 0

Output:
x^3 - 11/3x^2 - 20/3x  = 0
(x - 5)(x - 0)(x - -4/3) = 0
x - 5 = 0
x - 0 = 0
x - -4/3 = 0
x = 5
x = 0
x = -4/3


Input:
Find x and y such that
1x + 5y = 43/4
4x + 8y = 59/5

Output:
1x + 5y = 43/4
4x + 8y = 59/5

Using elimination
4*(1x + 5y = 43/4)
1*(4x + 8y = 59/5)
4x + 20y = 43
4x + 8y = 59/5
Subtract equations
12y = 156/5
y = 156/5/12
y = 13/5

Substitute y
1x + 5(13/5) = 43/4
1x = -9/4
x = -9/4/1
x = -9/4


Input: Find x in 1x - 6 = 0

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


Input: Solve 6x + 12 = 0

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


Input: Solve the equation x^2 + 27/5x + 28/5 = 0

Output:
x^2 + 27/5x + 28/5 = 0
(x - -4)(x - -7/5) = 0
x - -4 = 0  or  x - -7/5 = 0
x = -4
x = -7/5


Input: Solve the equation x^3 - 269/90x^2 + 386/135x - 77/90 = 0

Output:
x^3 - 269/90x^2 + 386/135x - 77/90 = 0
(x - 7/6)(x - 3/5)(x - 11/9) = 0
x - 7/6 = 0
x - 3/5 = 0
x - 11/9 = 0
x = 7/6
x = 3/5
x = 11/9


Input:
Solve the equations:
9x + 2y = 67/3
1x + 4y = -19/3

Output:
9x + 2y = 67/3
1x + 4y = -19/3

Using elimination
1*(9x + 2y = 67/3)
9*(1x + 4y = -19/3)
9x + 2y = 67/3
9x + 36y = -57
Subtract equations
-34y = 238/3
y = 238/3/-34
y = -7/3

Substitute y
9x + 2(-7/3) = 67/3
9x = 27
x = 27/9
x = 3


Input: Determine x in x^2 + 35/12x + 13/8 = 0

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


Input: Find x for 1x + 7 = 0

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


Input: Solve quickly: x^3 + 67/40x^2 - 941/200x + 14/25 = 0

Output:
x^3 + 67/40x^2 - 941/200x + 14/25 = 0
(x - 1/8)(x - -16/5)(x - 7/5) = 0
x - 1/8 = 0
x - -16/5 = 0
x - 7/5 = 0
x = 1/8
x = -16/5
x = 7/5


Input: Find the solution to x^3 - 45/7x^2 + 2x + 24/7 = 0

Output:
x^3 - 45/7x^2 + 2x + 24/7 = 0
(x - 1)(x - 6)(x - -4/7) = 0
x - 1 = 0
x - 6 = 0
x - -4/7 = 0
x = 1
x = 6
x = -4/7


Input:
Solve the system:
10x + 2y = 68
3x + 4y = 85

Output:
10x + 2y = 68
3x + 4y = 85

Using elimination
3*(10x + 2y = 68)
10*(3x + 4y = 85)
30x + 6y = 204
30x + 40y = 850
Subtract equations
-34y = -646
y = -646/-34
y = 19

Substitute y
10x + 2(19) = 68
10x = 30
x = 30/10
x = 3


Input:
Solve the equations:
6x + 9y = -3/5
4x + 4y = 0

Output:
6x + 9y = -3/5
4x + 4y = 0

Using elimination
4*(6x + 9y = -3/5)
6*(4x + 4y = 0)
24x + 36y = -12/5
24x + 24y = 0
Subtract equations
12y = -12/5
y = -12/5/12
y = -1/5

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


Input: Solve the equation 1x + 1/6 = 0

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


Input: Solve quickly: 1x - 4/7 = 0

Output:
1x - 4/7 = 0
1x = 4/7
x = 4/7 / 1
x = 4/7


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

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

Using elimination
1*(10x + 10y = 10/7)
10*(1x + 2y = -5/7)
10x + 10y = 10/7
10x + 20y = -50/7
Subtract equations
-10y = 60/7
y = 60/7/-10
y = -6/7

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


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

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


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

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


Input:
Solve the system:
8x + 2y = 34
9x + 1y = 69/2

Output:
8x + 2y = 34
9x + 1y = 69/2

Using elimination
9*(8x + 2y = 34)
8*(9x + 1y = 69/2)
72x + 18y = 306
72x + 8y = 276
Subtract equations
10y = 30
y = 30/10
y = 3

Substitute y
8x + 2(3) = 34
8x = 28
x = 28/8
x = 7/2


Input:
Solve the system:
7x + 8y = -104/5
10x + 6y = -8

Output:
7x + 8y = -104/5
10x + 6y = -8

Using elimination
10*(7x + 8y = -104/5)
7*(10x + 6y = -8)
70x + 80y = -208
70x + 42y = -56
Subtract equations
38y = -152
y = -152/38
y = -4

Substitute y
7x + 8(-4) = -104/5
7x = 56/5
x = 56/5/7
x = 8/5


Input: Find x for x^2 - 22/3x + 7/3 = 0

Output:
x^2 - 22/3x + 7/3 = 0
(x - 7)(x - 1/3) = 0
x - 7 = 0  or  x - 1/3 = 0
x = 7
x = 1/3


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

Output:
2x - 14/3 = 0
2x = 14/3
x = 14/3 / 2
x = 7/3


Input: Find x in x^3 + 61/70x^2 - 17/10x - 33/35 = 0

Output:
x^3 + 61/70x^2 - 17/10x - 33/35 = 0
(x - -1/2)(x - -11/7)(x - 6/5) = 0
x - -1/2 = 0
x - -11/7 = 0
x - 6/5 = 0
x = -1/2
x = -11/7
x = 6/5


Input: Find x in 10x + 200/7 = 0

Output:
10x + 200/7 = 0
10x = -200/7
x = -200/7 / 10
x = -20/7


Input:
Solve the equations:
7x + 1y = -21/5
6x + 4y = 4/5

Output:
7x + 1y = -21/5
6x + 4y = 4/5

Using elimination
6*(7x + 1y = -21/5)
7*(6x + 4y = 4/5)
42x + 6y = -126/5
42x + 28y = 28/5
Subtract equations
-22y = -154/5
y = -154/5/-22
y = 7/5

Substitute y
7x + 1(7/5) = -21/5
7x = -28/5
x = -28/5/7
x = -4/5


Input: Solve the equation 6x - 114/7 = 0

Output:
6x - 114/7 = 0
6x = 114/7
x = 114/7 / 6
x = 19/7


Input:
Find x and y such that
10x + 9y = -1254/7
10x + 10y = -1380/7

Output:
10x + 9y = -1254/7
10x + 10y = -1380/7

Using elimination
10*(10x + 9y = -1254/7)
10*(10x + 10y = -1380/7)
100x + 90y = -12540/7
100x + 100y = -13800/7
Subtract equations
-10y = 180
y = 180/-10
y = -18

Substitute y
10x + 9(-18) = -1254/7
10x = -120/7
x = -120/7/10
x = -12/7


Input: Solve x^3 + 137/12x^2 + 69/8x - 665/12 = 0

Output:
x^3 + 137/12x^2 + 69/8x - 665/12 = 0
(x - -19/6)(x - 7/4)(x - -10) = 0
x - -19/6 = 0
x - 7/4 = 0
x - -10 = 0
x = -19/6
x = 7/4
x = -10


Input: Find the solution to x^2 - 21x + 98 = 0

Output:
x^2 - 21x + 98 = 0
(x - 14)(x - 7) = 0
x - 14 = 0  or  x - 7 = 0
x = 14
x = 7


Input: Find the solution to 5x + 10 = 0

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


Input: Compute the solution of x^3 - 11/8x^2 - 1/16x + 7/16 = 0

Output:
x^3 - 11/8x^2 - 1/16x + 7/16 = 0
(x - 1)(x - -1/2)(x - 7/8) = 0
x - 1 = 0
x - -1/2 = 0
x - 7/8 = 0
x = 1
x = -1/2
x = 7/8


Input: Determine x in 1x - 1 = 0

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


Input: Solve x^2 + 1x - 14/25 = 0

Output:
x^2 + 1x - 14/25 = 0
(x - -7/5)(x - 2/5) = 0
x - -7/5 = 0  or  x - 2/5 = 0
x = -7/5
x = 2/5


Input: Find x in x^3 + 161/30x^2 + 79/9x + 68/15 = 0

Output:
x^3 + 161/30x^2 + 79/9x + 68/15 = 0
(x - -4/3)(x - -17/6)(x - -6/5) = 0
x - -4/3 = 0
x - -17/6 = 0
x - -6/5 = 0
x = -4/3
x = -17/6
x = -6/5


Input:
Solve simultaneously:
3x + 8y = -131/5
9x + 4y = -43/5

Output:
3x + 8y = -131/5
9x + 4y = -43/5

Using elimination
9*(3x + 8y = -131/5)
3*(9x + 4y = -43/5)
27x + 72y = -1179/5
27x + 12y = -129/5
Subtract equations
60y = -210
y = -210/60
y = -7/2

Substitute y
3x + 8(-7/2) = -131/5
3x = 9/5
x = 9/5/3
x = 3/5


Input:
Solve simultaneously:
3x + 6y = -49/2
6x + 10y = -127/3

Output:
3x + 6y = -49/2
6x + 10y = -127/3

Using elimination
6*(3x + 6y = -49/2)
3*(6x + 10y = -127/3)
18x + 36y = -147
18x + 30y = -127
Subtract equations
6y = -20
y = -20/6
y = -10/3

Substitute y
3x + 6(-10/3) = -49/2
3x = -9/2
x = -9/2/3
x = -3/2


Input: Find x in x^3 - 83/24x^2 - 5/96x + 25/16 = 0

Output:
x^3 - 83/24x^2 - 5/96x + 25/16 = 0
(x - 10/3)(x - 3/4)(x - -5/8) = 0
x - 10/3 = 0
x - 3/4 = 0
x - -5/8 = 0
x = 10/3
x = 3/4
x = -5/8


Input: Solve quickly: x^3 - 18x^2 + 95x - 150 = 0

Output:
x^3 - 18x^2 + 95x - 150 = 0
(x - 3)(x - 5)(x - 10) = 0
x - 3 = 0
x - 5 = 0
x - 10 = 0
x = 3
x = 5
x = 10


Input: Find x in x^3 + 225/8x^2 + 2717/16x - 1083/16 = 0

Output:
x^3 + 225/8x^2 + 2717/16x - 1083/16 = 0
(x - 3/8)(x - -19/2)(x - -19) = 0
x - 3/8 = 0
x - -19/2 = 0
x - -19 = 0
x = 3/8
x = -19/2
x = -19


Input:
Solve simultaneously:
1x + 8y = -33
8x + 1y = 141/4

Output:
1x + 8y = -33
8x + 1y = 141/4

Using elimination
8*(1x + 8y = -33)
1*(8x + 1y = 141/4)
8x + 64y = -264
8x + 1y = 141/4
Subtract equations
63y = -1197/4
y = -1197/4/63
y = -19/4

Substitute y
1x + 8(-19/4) = -33
1x = 5
x = 5/1
x = 5


Input:
Find x and y such that
5x + 7y = 27/4
6x + 1y = 25/4

Output:
5x + 7y = 27/4
6x + 1y = 25/4

Using elimination
6*(5x + 7y = 27/4)
5*(6x + 1y = 25/4)
30x + 42y = 81/2
30x + 5y = 125/4
Subtract equations
37y = 37/4
y = 37/4/37
y = 1/4

Substitute y
5x + 7(1/4) = 27/4
5x = 5
x = 5/5
x = 1


Input:
Solve the system:
2x + 8y = 858/35
10x + 5y = 221/7

Output:
2x + 8y = 858/35
10x + 5y = 221/7

Using elimination
10*(2x + 8y = 858/35)
2*(10x + 5y = 221/7)
20x + 80y = 1716/7
20x + 10y = 442/7
Subtract equations
70y = 182
y = 182/70
y = 13/5

Substitute y
2x + 8(13/5) = 858/35
2x = 26/7
x = 26/7/2
x = 13/7


Input:
Find x and y such that
9x + 6y = 87
3x + 3y = 46

Output:
9x + 6y = 87
3x + 3y = 46

Using elimination
3*(9x + 6y = 87)
9*(3x + 3y = 46)
27x + 18y = 261
27x + 27y = 414
Subtract equations
-9y = -153
y = -153/-9
y = 17

Substitute y
9x + 6(17) = 87
9x = -15
x = -15/9
x = -5/3


Input: Find x for x^2 + 17/7x + 6/7 = 0

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


Input: Solve x^2 + 11/2x - 51/2 = 0

Output:
x^2 + 11/2x - 51/2 = 0
(x - 3)(x - -17/2) = 0
x - 3 = 0  or  x - -17/2 = 0
x = 3
x = -17/2


Input:
Solve simultaneously:
6x + 7y = -323/20
9x + 10y = -185/8

Output:
6x + 7y = -323/20
9x + 10y = -185/8

Using elimination
9*(6x + 7y = -323/20)
6*(9x + 10y = -185/8)
54x + 63y = -2907/20
54x + 60y = -555/4
Subtract equations
3y = -33/5
y = -33/5/3
y = -11/5

Substitute y
6x + 7(-11/5) = -323/20
6x = -3/4
x = -3/4/6
x = -1/8


Input: Find x for x^2 + 3/4x - 1/4 = 0

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


Input:
Solve the system:
6x + 1y = -103/15
3x + 4y = -383/30

Output:
6x + 1y = -103/15
3x + 4y = -383/30

Using elimination
3*(6x + 1y = -103/15)
6*(3x + 4y = -383/30)
18x + 3y = -103/5
18x + 24y = -383/5
Subtract equations
-21y = 56
y = 56/-21
y = -8/3

Substitute y
6x + 1(-8/3) = -103/15
6x = -21/5
x = -21/5/6
x = -7/10


Input: What value of x satisfies x^2 + 27/4x + 19/2 = 0

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


Input: Determine x in x^3 + 41/24x^2 - 641/144x + 19/36 = 0

Output:
x^3 + 41/24x^2 - 641/144x + 19/36 = 0
(x - -19/6)(x - 4/3)(x - 1/8) = 0
x - -19/6 = 0
x - 4/3 = 0
x - 1/8 = 0
x = -19/6
x = 4/3
x = 1/8


Input: Determine x in 9x - 36 = 0

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


Input: What value of x satisfies 10x + 65/3 = 0

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


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

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


Input:
Solve simultaneously:
10x + 10y = 185/6
1x + 7y = 163/12

Output:
10x + 10y = 185/6
1x + 7y = 163/12

Using elimination
1*(10x + 10y = 185/6)
10*(1x + 7y = 163/12)
10x + 10y = 185/6
10x + 70y = 815/6
Subtract equations
-60y = -105
y = -105/-60
y = 7/4

Substitute y
10x + 10(7/4) = 185/6
10x = 40/3
x = 40/3/10
x = 4/3


Input:
Solve the system:
10x + 1y = 58/5
10x + 10y = 8

Output:
10x + 1y = 58/5
10x + 10y = 8

Using elimination
10*(10x + 1y = 58/5)
10*(10x + 10y = 8)
100x + 10y = 116
100x + 100y = 80
Subtract equations
-90y = 36
y = 36/-90
y = -2/5

Substitute y
10x + 1(-2/5) = 58/5
10x = 12
x = 12/10
x = 6/5


Input:
Solve simultaneously:
7x + 9y = -1097/90
1x + 4y = -286/45

Output:
7x + 9y = -1097/90
1x + 4y = -286/45

Using elimination
1*(7x + 9y = -1097/90)
7*(1x + 4y = -286/45)
7x + 9y = -1097/90
7x + 28y = -2002/45
Subtract equations
-19y = 323/10
y = 323/10/-19
y = -17/10

Substitute y
7x + 9(-17/10) = -1097/90
7x = 28/9
x = 28/9/7
x = 4/9


Input: Find x in x^2 - 116/63x - 64/63 = 0

Output:
x^2 - 116/63x - 64/63 = 0
(x - 16/7)(x - -4/9) = 0
x - 16/7 = 0  or  x - -4/9 = 0
x = 16/7
x = -4/9


Input: Find x for 7x + 28 = 0

Output:
7x + 28 = 0
7x = -28
x = -28 / 7
x = -4


Input: Solve quickly: x^3 + 884/63x^2 - 3065/63x + 646/21 = 0

Output:
x^3 + 884/63x^2 - 3065/63x + 646/21 = 0
(x - 19/9)(x - 6/7)(x - -17) = 0
x - 19/9 = 0
x - 6/7 = 0
x - -17 = 0
x = 19/9
x = 6/7
x = -17


Input: What value of x satisfies x^3 + 43/30x^2 - 57/10x - 42/5 = 0

Output:
x^3 + 43/30x^2 - 57/10x - 42/5 = 0
(x - -7/3)(x - -3/2)(x - 12/5) = 0
x - -7/3 = 0
x - -3/2 = 0
x - 12/5 = 0
x = -7/3
x = -3/2
x = 12/5


Input:
Solve the equations:
8x + 7y = 6
6x + 7y = 23/2

Output:
8x + 7y = 6
6x + 7y = 23/2

Using elimination
6*(8x + 7y = 6)
8*(6x + 7y = 23/2)
48x + 42y = 36
48x + 56y = 92
Subtract equations
-14y = -56
y = -56/-14
y = 4

Substitute y
8x + 7(4) = 6
8x = -22
x = -22/8
x = -11/4


Input:
Solve the equations:
8x + 4y = 5/3
5x + 6y = 1/6

Output:
8x + 4y = 5/3
5x + 6y = 1/6

Using elimination
5*(8x + 4y = 5/3)
8*(5x + 6y = 1/6)
40x + 20y = 25/3
40x + 48y = 4/3
Subtract equations
-28y = 7
y = 7/-28
y = -1/4

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


Input: Find the solution to x^3 - 157/70x^2 + 44/35x  = 0

Output:
x^3 - 157/70x^2 + 44/35x  = 0
(x - 11/10)(x - 0)(x - 8/7) = 0
x - 11/10 = 0
x - 0 = 0
x - 8/7 = 0
x = 11/10
x = 0
x = 8/7


Input: What value of x satisfies x^2 - 23/10x + 9/10 = 0

Output:
x^2 - 23/10x + 9/10 = 0
(x - 9/5)(x - 1/2) = 0
x - 9/5 = 0  or  x - 1/2 = 0
x = 9/5
x = 1/2


Input: Compute the solution of x^3 + 22/5x^2 + 9/4x - 63/20 = 0

Output:
x^3 + 22/5x^2 + 9/4x - 63/20 = 0
(x - -7/2)(x - 3/5)(x - -3/2) = 0
x - -7/2 = 0
x - 3/5 = 0
x - -3/2 = 0
x = -7/2
x = 3/5
x = -3/2


Input: Solve x^3 + 5/24x^2 - 101/96x + 5/16 = 0

Output:
x^3 + 5/24x^2 - 101/96x + 5/16 = 0
(x - -5/4)(x - 3/8)(x - 2/3) = 0
x - -5/4 = 0
x - 3/8 = 0
x - 2/3 = 0
x = -5/4
x = 3/8
x = 2/3


Input:
Solve the system:
4x + 3y = -25
9x + 2y = -4

Output:
4x + 3y = -25
9x + 2y = -4

Using elimination
9*(4x + 3y = -25)
4*(9x + 2y = -4)
36x + 27y = -225
36x + 8y = -16
Subtract equations
19y = -209
y = -209/19
y = -11

Substitute y
4x + 3(-11) = -25
4x = 8
x = 8/4
x = 2


Input: Solve quickly: x^3 + 17/5x^2 + 3/5x - 9/5 = 0

Output:
x^3 + 17/5x^2 + 3/5x - 9/5 = 0
(x - -3)(x - -1)(x - 3/5) = 0
x - -3 = 0
x - -1 = 0
x - 3/5 = 0
x = -3
x = -1
x = 3/5


Input:
Solve simultaneously:
1x + 6y = -13
6x + 3y = -1

Output:
1x + 6y = -13
6x + 3y = -1

Using elimination
6*(1x + 6y = -13)
1*(6x + 3y = -1)
6x + 36y = -78
6x + 3y = -1
Subtract equations
33y = -77
y = -77/33
y = -7/3

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


Input: Compute the solution of x^3 + 17/4x^2 + 9/2x  = 0

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


Input:
Find x and y such that
2x + 7y = -663/56
4x + 5y = -885/56

Output:
2x + 7y = -663/56
4x + 5y = -885/56

Using elimination
4*(2x + 7y = -663/56)
2*(4x + 5y = -885/56)
8x + 28y = -663/14
8x + 10y = -885/28
Subtract equations
18y = -63/4
y = -63/4/18
y = -7/8

Substitute y
2x + 7(-7/8) = -663/56
2x = -40/7
x = -40/7/2
x = -20/7


Input: Find x for 10x - 200/9 = 0

Output:
10x - 200/9 = 0
10x = 200/9
x = 200/9 / 10
x = 20/9


Input:
Find x and y such that
7x + 10y = -109/2
9x + 9y = -207/4

Output:
7x + 10y = -109/2
9x + 9y = -207/4

Using elimination
9*(7x + 10y = -109/2)
7*(9x + 9y = -207/4)
63x + 90y = -981/2
63x + 63y = -1449/4
Subtract equations
27y = -513/4
y = -513/4/27
y = -19/4

Substitute y
7x + 10(-19/4) = -109/2
7x = -7
x = -7/7
x = -1


Input:
Solve the equations:
3x + 5y = 25
4x + 10y = 46

Output:
3x + 5y = 25
4x + 10y = 46

Using elimination
4*(3x + 5y = 25)
3*(4x + 10y = 46)
12x + 20y = 100
12x + 30y = 138
Subtract equations
-10y = -38
y = -38/-10
y = 19/5

Substitute y
3x + 5(19/5) = 25
3x = 6
x = 6/3
x = 2


Input:
Solve the equations:
4x + 5y = 785/21
10x + 1y = 433/21

Output:
4x + 5y = 785/21
10x + 1y = 433/21

Using elimination
10*(4x + 5y = 785/21)
4*(10x + 1y = 433/21)
40x + 50y = 7850/21
40x + 4y = 1732/21
Subtract equations
46y = 874/3
y = 874/3/46
y = 19/3

Substitute y
4x + 5(19/3) = 785/21
4x = 40/7
x = 40/7/4
x = 10/7


Input: Compute the solution of x^3 + 37/9x^2 + 10/3x  = 0

Output:
x^3 + 37/9x^2 + 10/3x  = 0
(x - -10/9)(x - 0)(x - -3) = 0
x - -10/9 = 0
x - 0 = 0
x - -3 = 0
x = -10/9
x = 0
x = -3


Input:
Solve the equations:
8x + 7y = -113
5x + 7y = -68

Output:
8x + 7y = -113
5x + 7y = -68

Using elimination
5*(8x + 7y = -113)
8*(5x + 7y = -68)
40x + 35y = -565
40x + 56y = -544
Subtract equations
-21y = -21
y = -21/-21
y = 1

Substitute y
8x + 7(1) = -113
8x = -120
x = -120/8
x = -15


Input: Solve the equation 5x - 55/3 = 0

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


Input:
Solve simultaneously:
1x + 8y = -17/3
6x + 1y = 31/6

Output:
1x + 8y = -17/3
6x + 1y = 31/6

Using elimination
6*(1x + 8y = -17/3)
1*(6x + 1y = 31/6)
6x + 48y = -34
6x + 1y = 31/6
Subtract equations
47y = -235/6
y = -235/6/47
y = -5/6

Substitute y
1x + 8(-5/6) = -17/3
1x = 1
x = 1/1
x = 1


Input:
Solve simultaneously:
9x + 2y = 2
1x + 1y = 1

Output:
9x + 2y = 2
1x + 1y = 1

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

Substitute y
9x + 2(1) = 2
9x = 0
x = 0/9
x = 0


Input:
Solve the system:
4x + 7y = -94/3
10x + 2y = 13/3

Output:
4x + 7y = -94/3
10x + 2y = 13/3

Using elimination
10*(4x + 7y = -94/3)
4*(10x + 2y = 13/3)
40x + 70y = -940/3
40x + 8y = 52/3
Subtract equations
62y = -992/3
y = -992/3/62
y = -16/3

Substitute y
4x + 7(-16/3) = -94/3
4x = 6
x = 6/4
x = 3/2


Input: Determine x in x^3 - 59/35x^2 + 13/28x + 9/140 = 0

Output:
x^3 - 59/35x^2 + 13/28x + 9/140 = 0
(x - 1/2)(x - 9/7)(x - -1/10) = 0
x - 1/2 = 0
x - 9/7 = 0
x - -1/10 = 0
x = 1/2
x = 9/7
x = -1/10


Input: Solve 4x + 68/9 = 0

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


Input:
Solve simultaneously:
9x + 6y = 54
8x + 8y = 196/3

Output:
9x + 6y = 54
8x + 8y = 196/3

Using elimination
8*(9x + 6y = 54)
9*(8x + 8y = 196/3)
72x + 48y = 432
72x + 72y = 588
Subtract equations
-24y = -156
y = -156/-24
y = 13/2

Substitute y
9x + 6(13/2) = 54
9x = 15
x = 15/9
x = 5/3


Input: What value of x satisfies x^3 - 123/35x^2 - 323/35x + 1083/35 = 0

Output:
x^3 - 123/35x^2 - 323/35x + 1083/35 = 0
(x - 19/7)(x - 19/5)(x - -3) = 0
x - 19/7 = 0
x - 19/5 = 0
x - -3 = 0
x = 19/7
x = 19/5
x = -3


Input: Determine x in 10x - 190/3 = 0

Output:
10x - 190/3 = 0
10x = 190/3
x = 190/3 / 10
x = 19/3


Input:
Solve the equations:
10x + 5y = -85/3
3x + 10y = -51

Output:
10x + 5y = -85/3
3x + 10y = -51

Using elimination
3*(10x + 5y = -85/3)
10*(3x + 10y = -51)
30x + 15y = -85
30x + 100y = -510
Subtract equations
-85y = 425
y = 425/-85
y = -5

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


Input: Find the solution to x^2 - 23x + 120 = 0

Output:
x^2 - 23x + 120 = 0
(x - 8)(x - 15) = 0
x - 8 = 0  or  x - 15 = 0
x = 8
x = 15


Input: Solve the equation 5x + 65/9 = 0

Output:
5x + 65/9 = 0
5x = -65/9
x = -65/9 / 5
x = -13/9


Input:
Find x and y such that
8x + 1y = 9
5x + 10y = -45/2

Output:
8x + 1y = 9
5x + 10y = -45/2

Using elimination
5*(8x + 1y = 9)
8*(5x + 10y = -45/2)
40x + 5y = 45
40x + 80y = -180
Subtract equations
-75y = 225
y = 225/-75
y = -3

Substitute y
8x + 1(-3) = 9
8x = 12
x = 12/8
x = 3/2


Input:
Find x and y such that
10x + 10y = -41/3
5x + 4y = -199/30

Output:
10x + 10y = -41/3
5x + 4y = -199/30

Using elimination
5*(10x + 10y = -41/3)
10*(5x + 4y = -199/30)
50x + 50y = -205/3
50x + 40y = -199/3
Subtract equations
10y = -2
y = -2/10
y = -1/5

Substitute y
10x + 10(-1/5) = -41/3
10x = -35/3
x = -35/3/10
x = -7/6


Input: Compute the solution of x^3 + 53/2x^2 + 130x  = 0

Output:
x^3 + 53/2x^2 + 130x  = 0
(x - -13/2)(x - 0)(x - -20) = 0
x - -13/2 = 0
x - 0 = 0
x - -20 = 0
x = -13/2
x = 0
x = -20


Input: Solve the equation x^3 - 23/9x^2 + 40/81x + 100/81 = 0

Output:
x^3 - 23/9x^2 + 40/81x + 100/81 = 0
(x - -5/9)(x - 10/9)(x - 2) = 0
x - -5/9 = 0
x - 10/9 = 0
x - 2 = 0
x = -5/9
x = 10/9
x = 2


Input:
Solve simultaneously:
9x + 3y = 519/10
3x + 7y = 563/10

Output:
9x + 3y = 519/10
3x + 7y = 563/10

Using elimination
3*(9x + 3y = 519/10)
9*(3x + 7y = 563/10)
27x + 9y = 1557/10
27x + 63y = 5067/10
Subtract equations
-54y = -351
y = -351/-54
y = 13/2

Substitute y
9x + 3(13/2) = 519/10
9x = 162/5
x = 162/5/9
x = 18/5


Input:
Find x and y such that
7x + 5y = -98/3
2x + 5y = -53/3

Output:
7x + 5y = -98/3
2x + 5y = -53/3

Using elimination
2*(7x + 5y = -98/3)
7*(2x + 5y = -53/3)
14x + 10y = -196/3
14x + 35y = -371/3
Subtract equations
-25y = 175/3
y = 175/3/-25
y = -7/3

Substitute y
7x + 5(-7/3) = -98/3
7x = -21
x = -21/7
x = -3


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

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


Input: Determine x in x^2 + 7/3x - 16 = 0

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


Input: Solve quickly: 3x + 48 = 0

Output:
3x + 48 = 0
3x = -48
x = -48 / 3
x = -16


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

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


Input:
Solve the equations:
9x + 2y = 32/7
7x + 5y = 23/21

Output:
9x + 2y = 32/7
7x + 5y = 23/21

Using elimination
7*(9x + 2y = 32/7)
9*(7x + 5y = 23/21)
63x + 14y = 32
63x + 45y = 69/7
Subtract equations
-31y = 155/7
y = 155/7/-31
y = -5/7

Substitute y
9x + 2(-5/7) = 32/7
9x = 6
x = 6/9
x = 2/3


Input: Solve 4x + 24/5 = 0

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


Input: What value of x satisfies x^2 + 34/15x + 16/15 = 0

Output:
x^2 + 34/15x + 16/15 = 0
(x - -8/5)(x - -2/3) = 0
x - -8/5 = 0  or  x - -2/3 = 0
x = -8/5
x = -2/3


Input: Solve x^3 + 1/14x^2 - 23/14x - 5/7 = 0

Output:
x^3 + 1/14x^2 - 23/14x - 5/7 = 0
(x - 10/7)(x - -1/2)(x - -1) = 0
x - 10/7 = 0
x - -1/2 = 0
x - -1 = 0
x = 10/7
x = -1/2
x = -1


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

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


Input: Determine x in 7x + 126/5 = 0

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


Input: Solve 4x + 28 = 0

Output:
4x + 28 = 0
4x = -28
x = -28 / 4
x = -7


Input:
Solve simultaneously:
10x + 8y = -1528/21
9x + 8y = -472/7

Output:
10x + 8y = -1528/21
9x + 8y = -472/7

Using elimination
9*(10x + 8y = -1528/21)
10*(9x + 8y = -472/7)
90x + 72y = -4584/7
90x + 80y = -4720/7
Subtract equations
-8y = 136/7
y = 136/7/-8
y = -17/7

Substitute y
10x + 8(-17/7) = -1528/21
10x = -160/3
x = -160/3/10
x = -16/3


Input: Solve 4x - 44/3 = 0

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


Input: Determine x in x^3 + 153/56x^2 - 1151/224x - 765/56 = 0

Output:
x^3 + 153/56x^2 - 1151/224x - 765/56 = 0
(x - 9/4)(x - -20/7)(x - -17/8) = 0
x - 9/4 = 0
x - -20/7 = 0
x - -17/8 = 0
x = 9/4
x = -20/7
x = -17/8


Input: Find x for x^3 - 22/5x^2 - 152/5x + 64/5 = 0

Output:
x^3 - 22/5x^2 - 152/5x + 64/5 = 0
(x - -4)(x - 2/5)(x - 8) = 0
x - -4 = 0
x - 2/5 = 0
x - 8 = 0
x = -4
x = 2/5
x = 8


Input: Determine x in 5x - 45 = 0

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


Input:
Solve the equations:
1x + 3y = -127/35
3x + 8y = -341/35

Output:
1x + 3y = -127/35
3x + 8y = -341/35

Using elimination
3*(1x + 3y = -127/35)
1*(3x + 8y = -341/35)
3x + 9y = -381/35
3x + 8y = -341/35
Subtract equations
1y = -8/7
y = -8/7/1
y = -8/7

Substitute y
1x + 3(-8/7) = -127/35
1x = -1/5
x = -1/5/1
x = -1/5


Input: Find x in x^2 + 5/36x - 2/3 = 0

Output:
x^2 + 5/36x - 2/3 = 0
(x - 3/4)(x - -8/9) = 0
x - 3/4 = 0  or  x - -8/9 = 0
x = 3/4
x = -8/9


Input:
Solve the equations:
2x + 1y = 81/5
7x + 9y = 289/5

Output:
2x + 1y = 81/5
7x + 9y = 289/5

Using elimination
7*(2x + 1y = 81/5)
2*(7x + 9y = 289/5)
14x + 7y = 567/5
14x + 18y = 578/5
Subtract equations
-11y = -11/5
y = -11/5/-11
y = 1/5

Substitute y
2x + 1(1/5) = 81/5
2x = 16
x = 16/2
x = 8


Input: Find x in 5x - 11/2 = 0

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


Input: Solve quickly: x^2 + 43/30x - 91/30 = 0

Output:
x^2 + 43/30x - 91/30 = 0
(x - -13/5)(x - 7/6) = 0
x - -13/5 = 0  or  x - 7/6 = 0
x = -13/5
x = 7/6


Input:
Solve the equations:
2x + 8y = 986/35
7x + 3y = 1201/35

Output:
2x + 8y = 986/35
7x + 3y = 1201/35

Using elimination
7*(2x + 8y = 986/35)
2*(7x + 3y = 1201/35)
14x + 56y = 986/5
14x + 6y = 2402/35
Subtract equations
50y = 900/7
y = 900/7/50
y = 18/7

Substitute y
2x + 8(18/7) = 986/35
2x = 38/5
x = 38/5/2
x = 19/5


Input: Solve quickly: x^3 - 187/10x^2 + 123/10x + 27/5 = 0

Output:
x^3 - 187/10x^2 + 123/10x + 27/5 = 0
(x - 1)(x - 18)(x - -3/10) = 0
x - 1 = 0
x - 18 = 0
x - -3/10 = 0
x = 1
x = 18
x = -3/10


Input:
Solve simultaneously:
7x + 8y = 341/10
5x + 8y = 271/10

Output:
7x + 8y = 341/10
5x + 8y = 271/10

Using elimination
5*(7x + 8y = 341/10)
7*(5x + 8y = 271/10)
35x + 40y = 341/2
35x + 56y = 1897/10
Subtract equations
-16y = -96/5
y = -96/5/-16
y = 6/5

Substitute y
7x + 8(6/5) = 341/10
7x = 49/2
x = 49/2/7
x = 7/2


Input:
Solve the system:
6x + 1y = -92/5
7x + 3y = -611/30

Output:
6x + 1y = -92/5
7x + 3y = -611/30

Using elimination
7*(6x + 1y = -92/5)
6*(7x + 3y = -611/30)
42x + 7y = -644/5
42x + 18y = -611/5
Subtract equations
-11y = -33/5
y = -33/5/-11
y = 3/5

Substitute y
6x + 1(3/5) = -92/5
6x = -19
x = -19/6
x = -19/6


Input: Find x for x^2 + 1/4x - 15/8 = 0

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


Input: Solve quickly: x^3 - 14/5x^2 + 71/100x + 1/10 = 0

Output:
x^3 - 14/5x^2 + 71/100x + 1/10 = 0
(x - 2/5)(x - -1/10)(x - 5/2) = 0
x - 2/5 = 0
x - -1/10 = 0
x - 5/2 = 0
x = 2/5
x = -1/10
x = 5/2


Input: Solve x^3 + 11/8x^2 - 185/32x - 475/64 = 0

Output:
x^3 + 11/8x^2 - 185/32x - 475/64 = 0
(x - 19/8)(x - -5/4)(x - -5/2) = 0
x - 19/8 = 0
x - -5/4 = 0
x - -5/2 = 0
x = 19/8
x = -5/4
x = -5/2


Input: Determine x in x^3 + 101/5x^2 + 16/5x - 16 = 0

Output:
x^3 + 101/5x^2 + 16/5x - 16 = 0
(x - 4/5)(x - -1)(x - -20) = 0
x - 4/5 = 0
x - -1 = 0
x - -20 = 0
x = 4/5
x = -1
x = -20


Input: Determine x in 7x + 35 = 0

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


Input: Determine x in x^3 - 23/15x^2 - 304/15x  = 0

Output:
x^3 - 23/15x^2 - 304/15x  = 0
(x - -19/5)(x - 0)(x - 16/3) = 0
x - -19/5 = 0
x - 0 = 0
x - 16/3 = 0
x = -19/5
x = 0
x = 16/3


Input: Determine x in x^2 + 13/4x - 15/8 = 0

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


Input: Determine x in x^2 - 11/5x + 28/25 = 0

Output:
x^2 - 11/5x + 28/25 = 0
(x - 7/5)(x - 4/5) = 0
x - 7/5 = 0  or  x - 4/5 = 0
x = 7/5
x = 4/5


Input: Solve x^2 - 1/18x - 1/27 = 0

Output:
x^2 - 1/18x - 1/27 = 0
(x - 2/9)(x - -1/6) = 0
x - 2/9 = 0  or  x - -1/6 = 0
x = 2/9
x = -1/6


Input: What value of x satisfies x^2 + 2/5x - 8/25 = 0

Output:
x^2 + 2/5x - 8/25 = 0
(x - -4/5)(x - 2/5) = 0
x - -4/5 = 0  or  x - 2/5 = 0
x = -4/5
x = 2/5


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

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


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

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


Input: Find the solution to 9x + 27/2 = 0

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


Input: Solve quickly: 2x + 1 = 0

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


Input: Find the solution to x^3 + 40/21x^2 - 92/21x - 48/7 = 0

Output:
x^3 + 40/21x^2 - 92/21x - 48/7 = 0
(x - -18/7)(x - -4/3)(x - 2) = 0
x - -18/7 = 0
x - -4/3 = 0
x - 2 = 0
x = -18/7
x = -4/3
x = 2


Input: Find x for x^3 + 133/10x^2 + 261/5x + 567/10 = 0

Output:
x^3 + 133/10x^2 + 261/5x + 567/10 = 0
(x - -9/2)(x - -7)(x - -9/5) = 0
x - -9/2 = 0
x - -7 = 0
x - -9/5 = 0
x = -9/2
x = -7
x = -9/5


Input:
Find x and y such that
2x + 3y = 1/2
4x + 8y = -5

Output:
2x + 3y = 1/2
4x + 8y = -5

Using elimination
4*(2x + 3y = 1/2)
2*(4x + 8y = -5)
8x + 12y = 2
8x + 16y = -10
Subtract equations
-4y = 12
y = 12/-4
y = -3

Substitute y
2x + 3(-3) = 1/2
2x = 19/2
x = 19/2/2
x = 19/4


Input: Find x for x^2 + 9/4x - 13/4 = 0

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


Input:
Solve simultaneously:
4x + 1y = -46/5
5x + 5y = -17/2

Output:
4x + 1y = -46/5
5x + 5y = -17/2

Using elimination
5*(4x + 1y = -46/5)
4*(5x + 5y = -17/2)
20x + 5y = -46
20x + 20y = -34
Subtract equations
-15y = -12
y = -12/-15
y = 4/5

Substitute y
4x + 1(4/5) = -46/5
4x = -10
x = -10/4
x = -5/2


Input: Solve x^3 + 181/45x^2 + 2891/540x + 637/270 = 0

Output:
x^3 + 181/45x^2 + 2891/540x + 637/270 = 0
(x - -13/10)(x - -7/6)(x - -14/9) = 0
x - -13/10 = 0
x - -7/6 = 0
x - -14/9 = 0
x = -13/10
x = -7/6
x = -14/9


Input:
Solve the equations:
2x + 1y = -35/6
2x + 6y = -25/2

Output:
2x + 1y = -35/6
2x + 6y = -25/2

Using elimination
2*(2x + 1y = -35/6)
2*(2x + 6y = -25/2)
4x + 2y = -35/3
4x + 12y = -25
Subtract equations
-10y = 40/3
y = 40/3/-10
y = -4/3

Substitute y
2x + 1(-4/3) = -35/6
2x = -9/2
x = -9/2/2
x = -9/4


Input: What value of x satisfies 9x + 9 = 0

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


Input: Solve quickly: 1x + 13/3 = 0

Output:
1x + 13/3 = 0
1x = -13/3
x = -13/3 / 1
x = -13/3


Input:
Solve the equations:
7x + 10y = 278/45
10x + 10y = 88/9

Output:
7x + 10y = 278/45
10x + 10y = 88/9

Using elimination
10*(7x + 10y = 278/45)
7*(10x + 10y = 88/9)
70x + 100y = 556/9
70x + 70y = 616/9
Subtract equations
30y = -20/3
y = -20/3/30
y = -2/9

Substitute y
7x + 10(-2/9) = 278/45
7x = 42/5
x = 42/5/7
x = 6/5


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

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


Input: Solve the equation x^2 - 23/10x - 21/10 = 0

Output:
x^2 - 23/10x - 21/10 = 0
(x - 3)(x - -7/10) = 0
x - 3 = 0  or  x - -7/10 = 0
x = 3
x = -7/10


Input: Determine x in 6x - 9/2 = 0

Output:
6x - 9/2 = 0
6x = 9/2
x = 9/2 / 6
x = 3/4


Input: Compute the solution of 2x - 12/5 = 0

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


Input: What value of x satisfies 8x - 9 = 0

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


Input: Solve quickly: 3x - 6 = 0

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


Input:
Find x and y such that
3x + 3y = -19/3
2x + 10y = 98/9

Output:
3x + 3y = -19/3
2x + 10y = 98/9

Using elimination
2*(3x + 3y = -19/3)
3*(2x + 10y = 98/9)
6x + 6y = -38/3
6x + 30y = 98/3
Subtract equations
-24y = -136/3
y = -136/3/-24
y = 17/9

Substitute y
3x + 3(17/9) = -19/3
3x = -12
x = -12/3
x = -4


Input: Solve x^3 - 88/15x^2 + 39/5x - 4/3 = 0

Output:
x^3 - 88/15x^2 + 39/5x - 4/3 = 0
(x - 5/3)(x - 1/5)(x - 4) = 0
x - 5/3 = 0
x - 1/5 = 0
x - 4 = 0
x = 5/3
x = 1/5
x = 4


Input: Solve quickly: 9x - 54/5 = 0

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


Input: Find x in x^3 - 13/4x^2 - 9/8x + 45/8 = 0

Output:
x^3 - 13/4x^2 - 9/8x + 45/8 = 0
(x - 3)(x - -5/4)(x - 3/2) = 0
x - 3 = 0
x - -5/4 = 0
x - 3/2 = 0
x = 3
x = -5/4
x = 3/2


Input:
Solve simultaneously:
8x + 4y = 56/3
7x + 2y = 53/6

Output:
8x + 4y = 56/3
7x + 2y = 53/6

Using elimination
7*(8x + 4y = 56/3)
8*(7x + 2y = 53/6)
56x + 28y = 392/3
56x + 16y = 212/3
Subtract equations
12y = 60
y = 60/12
y = 5

Substitute y
8x + 4(5) = 56/3
8x = -4/3
x = -4/3/8
x = -1/6


Input: Solve quickly: x^3 - 353/15x^2 + 1076/15x - 64/3 = 0

Output:
x^3 - 353/15x^2 + 1076/15x - 64/3 = 0
(x - 20)(x - 1/3)(x - 16/5) = 0
x - 20 = 0
x - 1/3 = 0
x - 16/5 = 0
x = 20
x = 1/3
x = 16/5


Input: Solve quickly: x^3 - 29/8x^2 - 7/16x + 49/16 = 0

Output:
x^3 - 29/8x^2 - 7/16x + 49/16 = 0
(x - 7/2)(x - 1)(x - -7/8) = 0
x - 7/2 = 0
x - 1 = 0
x - -7/8 = 0
x = 7/2
x = 1
x = -7/8


Input: What value of x satisfies 4x - 20/7 = 0

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


Input:
Solve simultaneously:
3x + 4y = 40/9
8x + 7y = 9

Output:
3x + 4y = 40/9
8x + 7y = 9

Using elimination
8*(3x + 4y = 40/9)
3*(8x + 7y = 9)
24x + 32y = 320/9
24x + 21y = 27
Subtract equations
11y = 77/9
y = 77/9/11
y = 7/9

Substitute y
3x + 4(7/9) = 40/9
3x = 4/3
x = 4/3/3
x = 4/9


Input: Compute the solution of 10x + 70/3 = 0

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


Input: Find x for 9x + 45 = 0

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


Input: Solve x^2 - 85/36x - 26/9 = 0

Output:
x^2 - 85/36x - 26/9 = 0
(x - 13/4)(x - -8/9) = 0
x - 13/4 = 0  or  x - -8/9 = 0
x = 13/4
x = -8/9


Input:
Find x and y such that
5x + 1y = -16/9
10x + 9y = 346/9

Output:
5x + 1y = -16/9
10x + 9y = 346/9

Using elimination
10*(5x + 1y = -16/9)
5*(10x + 9y = 346/9)
50x + 10y = -160/9
50x + 45y = 1730/9
Subtract equations
-35y = -210
y = -210/-35
y = 6

Substitute y
5x + 1(6) = -16/9
5x = -70/9
x = -70/9/5
x = -14/9


Input: Find x for x^3 + 439/168x^2 - 151/56x - 143/21 = 0

Output:
x^3 + 439/168x^2 - 151/56x - 143/21 = 0
(x - -8/3)(x - 13/8)(x - -11/7) = 0
x - -8/3 = 0
x - 13/8 = 0
x - -11/7 = 0
x = -8/3
x = 13/8
x = -11/7


Input: Solve quickly: 8x + 15 = 0

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


Input:
Solve the equations:
9x + 5y = -15/2
5x + 9y = -27/2

Output:
9x + 5y = -15/2
5x + 9y = -27/2

Using elimination
5*(9x + 5y = -15/2)
9*(5x + 9y = -27/2)
45x + 25y = -75/2
45x + 81y = -243/2
Subtract equations
-56y = 84
y = 84/-56
y = -3/2

Substitute y
9x + 5(-3/2) = -15/2
9x = 0
x = 0/9
x = 0


Input: Find the solution to x^2 + 29/5x - 6/5 = 0

Output:
x^2 + 29/5x - 6/5 = 0
(x - 1/5)(x - -6) = 0
x - 1/5 = 0  or  x - -6 = 0
x = 1/5
x = -6


Input: What value of x satisfies x^3 - 47/4x^2 + 213/8x + 27 = 0

Output:
x^3 - 47/4x^2 + 213/8x + 27 = 0
(x - 9/2)(x - -3/4)(x - 8) = 0
x - 9/2 = 0
x - -3/4 = 0
x - 8 = 0
x = 9/2
x = -3/4
x = 8


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

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


Input:
Find x and y such that
4x + 10y = 137/3
1x + 9y = 122/3

Output:
4x + 10y = 137/3
1x + 9y = 122/3

Using elimination
1*(4x + 10y = 137/3)
4*(1x + 9y = 122/3)
4x + 10y = 137/3
4x + 36y = 488/3
Subtract equations
-26y = -117
y = -117/-26
y = 9/2

Substitute y
4x + 10(9/2) = 137/3
4x = 2/3
x = 2/3/4
x = 1/6


Input: Find x for x^2 - 9/8x - 9/16 = 0

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


Input:
Solve simultaneously:
9x + 5y = 381/4
3x + 6y = 48

Output:
9x + 5y = 381/4
3x + 6y = 48

Using elimination
3*(9x + 5y = 381/4)
9*(3x + 6y = 48)
27x + 15y = 1143/4
27x + 54y = 432
Subtract equations
-39y = -585/4
y = -585/4/-39
y = 15/4

Substitute y
9x + 5(15/4) = 381/4
9x = 153/2
x = 153/2/9
x = 17/2


Input: Solve the equation 5x + 15 = 0

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


Input: Find the solution to x^2 - 100/21x - 64/21 = 0

Output:
x^2 - 100/21x - 64/21 = 0
(x - 16/3)(x - -4/7) = 0
x - 16/3 = 0  or  x - -4/7 = 0
x = 16/3
x = -4/7


Input:
Find x and y such that
2x + 2y = 64/15
1x + 4y = 137/15

Output:
2x + 2y = 64/15
1x + 4y = 137/15

Using elimination
1*(2x + 2y = 64/15)
2*(1x + 4y = 137/15)
2x + 2y = 64/15
2x + 8y = 274/15
Subtract equations
-6y = -14
y = -14/-6
y = 7/3

Substitute y
2x + 2(7/3) = 64/15
2x = -2/5
x = -2/5/2
x = -1/5


Input: Solve quickly: x^3 - 3/5x^2 - 225/49x + 135/49 = 0

Output:
x^3 - 3/5x^2 - 225/49x + 135/49 = 0
(x - 15/7)(x - 3/5)(x - -15/7) = 0
x - 15/7 = 0
x - 3/5 = 0
x - -15/7 = 0
x = 15/7
x = 3/5
x = -15/7


Input: Solve the equation x^3 + 79/6x^2 - 571/18x - 190/3 = 0

Output:
x^3 + 79/6x^2 - 571/18x - 190/3 = 0
(x - -15)(x - -4/3)(x - 19/6) = 0
x - -15 = 0
x - -4/3 = 0
x - 19/6 = 0
x = -15
x = -4/3
x = 19/6


Input: What value of x satisfies x^3 - 22/45x^2 - 404/45x - 8 = 0

Output:
x^3 - 22/45x^2 - 404/45x - 8 = 0
(x - -2)(x - -10/9)(x - 18/5) = 0
x - -2 = 0
x - -10/9 = 0
x - 18/5 = 0
x = -2
x = -10/9
x = 18/5


Input:
Solve the system:
8x + 7y = 98/9
8x + 2y = 956/63

Output:
8x + 7y = 98/9
8x + 2y = 956/63

Using elimination
8*(8x + 7y = 98/9)
8*(8x + 2y = 956/63)
64x + 56y = 784/9
64x + 16y = 7648/63
Subtract equations
40y = -240/7
y = -240/7/40
y = -6/7

Substitute y
8x + 7(-6/7) = 98/9
8x = 152/9
x = 152/9/8
x = 19/9


Input: What value of x satisfies x^2 - 51/14x + 1/2 = 0

Output:
x^2 - 51/14x + 1/2 = 0
(x - 1/7)(x - 7/2) = 0
x - 1/7 = 0  or  x - 7/2 = 0
x = 1/7
x = 7/2


Input: Solve 5x + 75/7 = 0

Output:
5x + 75/7 = 0
5x = -75/7
x = -75/7 / 5
x = -15/7


Input: Determine x in x^3 + 7x^2 - 1665/16x + 3825/16 = 0

Output:
x^3 + 7x^2 - 1665/16x + 3825/16 = 0
(x - 17/4)(x - -15)(x - 15/4) = 0
x - 17/4 = 0
x - -15 = 0
x - 15/4 = 0
x = 17/4
x = -15
x = 15/4


Input: Solve quickly: 7x - 56/9 = 0

Output:
7x - 56/9 = 0
7x = 56/9
x = 56/9 / 7
x = 8/9


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

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


Input:
Solve the equations:
6x + 10y = 0
7x + 5y = 0

Output:
6x + 10y = 0
7x + 5y = 0

Using elimination
7*(6x + 10y = 0)
6*(7x + 5y = 0)
42x + 70y = 0
42x + 30y = 0
Subtract equations
40y = 0
y = 0/40
y = 0

Substitute y
6x + 10(0) = 0
6x = 0
x = 0/6
x = 0


Input: Determine x in x^2 + 145/28x + 57/28 = 0

Output:
x^2 + 145/28x + 57/28 = 0
(x - -19/4)(x - -3/7) = 0
x - -19/4 = 0  or  x - -3/7 = 0
x = -19/4
x = -3/7


Input: What value of x satisfies 7x - 63/2 = 0

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


Input:
Solve the equations:
1x + 8y = 62/9
2x + 10y = 64/9

Output:
1x + 8y = 62/9
2x + 10y = 64/9

Using elimination
2*(1x + 8y = 62/9)
1*(2x + 10y = 64/9)
2x + 16y = 124/9
2x + 10y = 64/9
Subtract equations
6y = 20/3
y = 20/3/6
y = 10/9

Substitute y
1x + 8(10/9) = 62/9
1x = -2
x = -2/1
x = -2


Input: Solve the equation x^3 + 101/15x^2 - 466/15x + 16 = 0

Output:
x^3 + 101/15x^2 - 466/15x + 16 = 0
(x - 8/3)(x - 3/5)(x - -10) = 0
x - 8/3 = 0
x - 3/5 = 0
x - -10 = 0
x = 8/3
x = 3/5
x = -10


Input: Determine x in x^3 - 35/6x^2 - 213/4x + 4199/24 = 0

Output:
x^3 - 35/6x^2 - 213/4x + 4199/24 = 0
(x - -13/2)(x - 17/6)(x - 19/2) = 0
x - -13/2 = 0
x - 17/6 = 0
x - 19/2 = 0
x = -13/2
x = 17/6
x = 19/2


Input: Solve the equation 3x - 57/4 = 0

Output:
3x - 57/4 = 0
3x = 57/4
x = 57/4 / 3
x = 19/4


Input:
Solve the system:
3x + 6y = -27/2
7x + 2y = -33/2

Output:
3x + 6y = -27/2
7x + 2y = -33/2

Using elimination
7*(3x + 6y = -27/2)
3*(7x + 2y = -33/2)
21x + 42y = -189/2
21x + 6y = -99/2
Subtract equations
36y = -45
y = -45/36
y = -5/4

Substitute y
3x + 6(-5/4) = -27/2
3x = -6
x = -6/3
x = -2


Input:
Solve the equations:
1x + 8y = -295/24
10x + 8y = -323/12

Output:
1x + 8y = -295/24
10x + 8y = -323/12

Using elimination
10*(1x + 8y = -295/24)
1*(10x + 8y = -323/12)
10x + 80y = -1475/12
10x + 8y = -323/12
Subtract equations
72y = -96
y = -96/72
y = -4/3

Substitute y
1x + 8(-4/3) = -295/24
1x = -13/8
x = -13/8/1
x = -13/8


Input:
Find x and y such that
9x + 1y = -45/8
10x + 1y = -469/72

Output:
9x + 1y = -45/8
10x + 1y = -469/72

Using elimination
10*(9x + 1y = -45/8)
9*(10x + 1y = -469/72)
90x + 10y = -225/4
90x + 9y = -469/8
Subtract equations
1y = 19/8
y = 19/8/1
y = 19/8

Substitute y
9x + 1(19/8) = -45/8
9x = -8
x = -8/9
x = -8/9


Input:
Find x and y such that
2x + 3y = 59/14
7x + 4y = 5

Output:
2x + 3y = 59/14
7x + 4y = 5

Using elimination
7*(2x + 3y = 59/14)
2*(7x + 4y = 5)
14x + 21y = 59/2
14x + 8y = 10
Subtract equations
13y = 39/2
y = 39/2/13
y = 3/2

Substitute y
2x + 3(3/2) = 59/14
2x = -2/7
x = -2/7/2
x = -1/7


Input: Compute the solution of x^2 + 9/2x + 5 = 0

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


Input:
Find x and y such that
4x + 3y = 41
4x + 8y = 86

Output:
4x + 3y = 41
4x + 8y = 86

Using elimination
4*(4x + 3y = 41)
4*(4x + 8y = 86)
16x + 12y = 164
16x + 32y = 344
Subtract equations
-20y = -180
y = -180/-20
y = 9

Substitute y
4x + 3(9) = 41
4x = 14
x = 14/4
x = 7/2


Input: Determine x in 8x + 128/7 = 0

Output:
8x + 128/7 = 0
8x = -128/7
x = -128/7 / 8
x = -16/7


Input: Compute the solution of x^2 - 1/2x - 35/18 = 0

Output:
x^2 - 1/2x - 35/18 = 0
(x - -7/6)(x - 5/3) = 0
x - -7/6 = 0  or  x - 5/3 = 0
x = -7/6
x = 5/3


Input: Find the solution to x^2 - 11/5x + 6/5 = 0

Output:
x^2 - 11/5x + 6/5 = 0
(x - 1)(x - 6/5) = 0
x - 1 = 0  or  x - 6/5 = 0
x = 1
x = 6/5


Input: Find x for x^2 + 16x - 57 = 0

Output:
x^2 + 16x - 57 = 0
(x - 3)(x - -19) = 0
x - 3 = 0  or  x - -19 = 0
x = 3
x = -19


Input: Find x in 10x - 22 = 0

Output:
10x - 22 = 0
10x = 22
x = 22 / 10
x = 11/5


Input: Find x in 8x - 8 = 0

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


Input: Determine x in x^3 - 19/12x^2 - 37/8x + 91/12 = 0

Output:
x^3 - 19/12x^2 - 37/8x + 91/12 = 0
(x - 7/4)(x - 2)(x - -13/6) = 0
x - 7/4 = 0
x - 2 = 0
x - -13/6 = 0
x = 7/4
x = 2
x = -13/6


Input:
Solve the equations:
9x + 9y = 291/8
1x + 3y = 59/8

Output:
9x + 9y = 291/8
1x + 3y = 59/8

Using elimination
1*(9x + 9y = 291/8)
9*(1x + 3y = 59/8)
9x + 9y = 291/8
9x + 27y = 531/8
Subtract equations
-18y = -30
y = -30/-18
y = 5/3

Substitute y
9x + 9(5/3) = 291/8
9x = 171/8
x = 171/8/9
x = 19/8


Input:
Solve simultaneously:
1x + 10y = 655/12
9x + 6y = 173/4

Output:
1x + 10y = 655/12
9x + 6y = 173/4

Using elimination
9*(1x + 10y = 655/12)
1*(9x + 6y = 173/4)
9x + 90y = 1965/4
9x + 6y = 173/4
Subtract equations
84y = 448
y = 448/84
y = 16/3

Substitute y
1x + 10(16/3) = 655/12
1x = 5/4
x = 5/4/1
x = 5/4


Input: Find x in 9x - 9/10 = 0

Output:
9x - 9/10 = 0
9x = 9/10
x = 9/10 / 9
x = 1/10


Input:
Solve simultaneously:
5x + 10y = 125/4
10x + 7y = 99/2

Output:
5x + 10y = 125/4
10x + 7y = 99/2

Using elimination
10*(5x + 10y = 125/4)
5*(10x + 7y = 99/2)
50x + 100y = 625/2
50x + 35y = 495/2
Subtract equations
65y = 65
y = 65/65
y = 1

Substitute y
5x + 10(1) = 125/4
5x = 85/4
x = 85/4/5
x = 17/4


Input: Find x for x^2 + 11/10x - 7/2 = 0

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


Input:
Find x and y such that
10x + 2y = 13/2
5x + 9y = 117/4

Output:
10x + 2y = 13/2
5x + 9y = 117/4

Using elimination
5*(10x + 2y = 13/2)
10*(5x + 9y = 117/4)
50x + 10y = 65/2
50x + 90y = 585/2
Subtract equations
-80y = -260
y = -260/-80
y = 13/4

Substitute y
10x + 2(13/4) = 13/2
10x = 0
x = 0/10
x = 0


Input: Find x for 6x + 9/4 = 0

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


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

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


Input: What value of x satisfies x^2 - 38/15x - 39/5 = 0

Output:
x^2 - 38/15x - 39/5 = 0
(x - 13/3)(x - -9/5) = 0
x - 13/3 = 0  or  x - -9/5 = 0
x = 13/3
x = -9/5


Input: Find x in x^3 + 223/120x^2 + 27/40x - 27/160 = 0

Output:
x^3 + 223/120x^2 + 27/40x - 27/160 = 0
(x - 1/6)(x - -9/8)(x - -9/10) = 0
x - 1/6 = 0
x - -9/8 = 0
x - -9/10 = 0
x = 1/6
x = -9/8
x = -9/10


Input: Solve quickly: x^3 - 131/120x^2 - 121/240x + 21/40 = 0

Output:
x^3 - 131/120x^2 - 121/240x + 21/40 = 0
(x - -7/10)(x - 2/3)(x - 9/8) = 0
x - -7/10 = 0
x - 2/3 = 0
x - 9/8 = 0
x = -7/10
x = 2/3
x = 9/8


Input: Solve quickly: x^3 + 225/7x^2 + 1574/7x - 3744/7 = 0

Output:
x^3 + 225/7x^2 + 1574/7x - 3744/7 = 0
(x - 13/7)(x - -16)(x - -18) = 0
x - 13/7 = 0
x - -16 = 0
x - -18 = 0
x = 13/7
x = -16
x = -18


Input: Find x for x^2 + 16/5x - 36/25 = 0

Output:
x^2 + 16/5x - 36/25 = 0
(x - -18/5)(x - 2/5) = 0
x - -18/5 = 0  or  x - 2/5 = 0
x = -18/5
x = 2/5


Input: What value of x satisfies x^3 - 9/2x^2 - 99/2x + 81 = 0

Output:
x^3 - 9/2x^2 - 99/2x + 81 = 0
(x - 9)(x - -6)(x - 3/2) = 0
x - 9 = 0
x - -6 = 0
x - 3/2 = 0
x = 9
x = -6
x = 3/2


Input:
Solve simultaneously:
6x + 9y = 177/7
7x + 3y = 199/7

Output:
6x + 9y = 177/7
7x + 3y = 199/7

Using elimination
7*(6x + 9y = 177/7)
6*(7x + 3y = 199/7)
42x + 63y = 177
42x + 18y = 1194/7
Subtract equations
45y = 45/7
y = 45/7/45
y = 1/7

Substitute y
6x + 9(1/7) = 177/7
6x = 24
x = 24/6
x = 4


Input: Solve quickly: x^2 - 34/5x + 9 = 0

Output:
x^2 - 34/5x + 9 = 0
(x - 5)(x - 9/5) = 0
x - 5 = 0  or  x - 9/5 = 0
x = 5
x = 9/5


Input: Find x in x^3 + 37/8x^2 + 17/8x - 3/2 = 0

Output:
x^3 + 37/8x^2 + 17/8x - 3/2 = 0
(x - -1)(x - -4)(x - 3/8) = 0
x - -1 = 0
x - -4 = 0
x - 3/8 = 0
x = -1
x = -4
x = 3/8


Input: Solve quickly: 3x - 19 = 0

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


Input: Solve quickly: x^3 + 749/90x^2 + 343/18x + 110/9 = 0

Output:
x^3 + 749/90x^2 + 343/18x + 110/9 = 0
(x - -5)(x - -20/9)(x - -11/10) = 0
x - -5 = 0
x - -20/9 = 0
x - -11/10 = 0
x = -5
x = -20/9
x = -11/10


Input: What value of x satisfies x^2 + 31/7x - 20/7 = 0

Output:
x^2 + 31/7x - 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 4x - 14/3 = 0

Output:
4x - 14/3 = 0
4x = 14/3
x = 14/3 / 4
x = 7/6


Input:
Solve simultaneously:
1x + 3y = 35/2
4x + 9y = 53

Output:
1x + 3y = 35/2
4x + 9y = 53

Using elimination
4*(1x + 3y = 35/2)
1*(4x + 9y = 53)
4x + 12y = 70
4x + 9y = 53
Subtract equations
3y = 17
y = 17/3
y = 17/3

Substitute y
1x + 3(17/3) = 35/2
1x = 1/2
x = 1/2/1
x = 1/2


Input:
Find x and y such that
1x + 8y = -149/7
9x + 10y = -783/7

Output:
1x + 8y = -149/7
9x + 10y = -783/7

Using elimination
9*(1x + 8y = -149/7)
1*(9x + 10y = -783/7)
9x + 72y = -1341/7
9x + 10y = -783/7
Subtract equations
62y = -558/7
y = -558/7/62
y = -9/7

Substitute y
1x + 8(-9/7) = -149/7
1x = -11
x = -11/1
x = -11


Input: Compute the solution of 7x - 28/3 = 0

Output:
7x - 28/3 = 0
7x = 28/3
x = 28/3 / 7
x = 4/3


Input: Solve the equation x^3 + 1/9x^2 - 2125/36x + 3757/36 = 0

Output:
x^3 + 1/9x^2 - 2125/36x + 3757/36 = 0
(x - -17/2)(x - 13/2)(x - 17/9) = 0
x - -17/2 = 0
x - 13/2 = 0
x - 17/9 = 0
x = -17/2
x = 13/2
x = 17/9


Input: Find the solution to x^2 + 23/3x - 85/12 = 0

Output:
x^2 + 23/3x - 85/12 = 0
(x - -17/2)(x - 5/6) = 0
x - -17/2 = 0  or  x - 5/6 = 0
x = -17/2
x = 5/6


Input: Find x for x^3 + 47/36x^2 - 19/3x - 15/4 = 0

Output:
x^3 + 47/36x^2 - 19/3x - 15/4 = 0
(x - -5/9)(x - -3)(x - 9/4) = 0
x - -5/9 = 0
x - -3 = 0
x - 9/4 = 0
x = -5/9
x = -3
x = 9/4


Input: Compute the solution of x^3 + 169/36x^2 - 91/6x + 245/36 = 0

Output:
x^3 + 169/36x^2 - 91/6x + 245/36 = 0
(x - 7/4)(x - 5/9)(x - -7) = 0
x - 7/4 = 0
x - 5/9 = 0
x - -7 = 0
x = 7/4
x = 5/9
x = -7


Input: What value of x satisfies 8x - 12 = 0

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


Input: Compute the solution of x^2 + 136/7x + 180/7 = 0

Output:
x^2 + 136/7x + 180/7 = 0
(x - -18)(x - -10/7) = 0
x - -18 = 0  or  x - -10/7 = 0
x = -18
x = -10/7


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

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


Input: Solve the equation 7x - 112/5 = 0

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


Input:
Solve the system:
3x + 5y = -2/3
2x + 3y = -23/45

Output:
3x + 5y = -2/3
2x + 3y = -23/45

Using elimination
2*(3x + 5y = -2/3)
3*(2x + 3y = -23/45)
6x + 10y = -4/3
6x + 9y = -23/15
Subtract equations
1y = 1/5
y = 1/5/1
y = 1/5

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


Input: Determine x in x^2 + 35/2x + 117/2 = 0

Output:
x^2 + 35/2x + 117/2 = 0
(x - -13)(x - -9/2) = 0
x - -13 = 0  or  x - -9/2 = 0
x = -13
x = -9/2


Input: Solve the equation 3x + 21 = 0

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


Input:
Solve the system:
5x + 4y = 133/6
3x + 8y = 49/2

Output:
5x + 4y = 133/6
3x + 8y = 49/2

Using elimination
3*(5x + 4y = 133/6)
5*(3x + 8y = 49/2)
15x + 12y = 133/2
15x + 40y = 245/2
Subtract equations
-28y = -56
y = -56/-28
y = 2

Substitute y
5x + 4(2) = 133/6
5x = 85/6
x = 85/6/5
x = 17/6


Input: Find x for x^2 - 1/6x - 5/2 = 0

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


Input: Solve quickly: x^3 + 2/5x^2 - 279/25x + 324/25 = 0

Output:
x^3 + 2/5x^2 - 279/25x + 324/25 = 0
(x - 9/5)(x - 9/5)(x - -4) = 0
x - 9/5 = 0
x - 9/5 = 0
x - -4 = 0
x = 9/5
x = 9/5
x = -4


Input: Solve x^3 + 127/6x^2 + 305/3x + 275/2 = 0

Output:
x^3 + 127/6x^2 + 305/3x + 275/2 = 0
(x - -5/2)(x - -11/3)(x - -15) = 0
x - -5/2 = 0
x - -11/3 = 0
x - -15 = 0
x = -5/2
x = -11/3
x = -15


Input: Solve the equation x^2 - 17/3x  = 0

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


Input:
Find x and y such that
4x + 1y = 7/4
4x + 6y = 21/2

Output:
4x + 1y = 7/4
4x + 6y = 21/2

Using elimination
4*(4x + 1y = 7/4)
4*(4x + 6y = 21/2)
16x + 4y = 7
16x + 24y = 42
Subtract equations
-20y = -35
y = -35/-20
y = 7/4

Substitute y
4x + 1(7/4) = 7/4
4x = 0
x = 0/4
x = 0


Input: Find x for 10x - 140/3 = 0

Output:
10x - 140/3 = 0
10x = 140/3
x = 140/3 / 10
x = 14/3


Input:
Solve the equations:
5x + 4y = -27/2
3x + 6y = -333/20

Output:
5x + 4y = -27/2
3x + 6y = -333/20

Using elimination
3*(5x + 4y = -27/2)
5*(3x + 6y = -333/20)
15x + 12y = -81/2
15x + 30y = -333/4
Subtract equations
-18y = 171/4
y = 171/4/-18
y = -19/8

Substitute y
5x + 4(-19/8) = -27/2
5x = -4
x = -4/5
x = -4/5


Input:
Find x and y such that
9x + 7y = -247/3
7x + 3y = -51

Output:
9x + 7y = -247/3
7x + 3y = -51

Using elimination
7*(9x + 7y = -247/3)
9*(7x + 3y = -51)
63x + 49y = -1729/3
63x + 27y = -459
Subtract equations
22y = -352/3
y = -352/3/22
y = -16/3

Substitute y
9x + 7(-16/3) = -247/3
9x = -45
x = -45/9
x = -5


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

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


Input: Solve x^3 + 16/3x^2 - 80/9x  = 0

Output:
x^3 + 16/3x^2 - 80/9x  = 0
(x - 4/3)(x - 0)(x - -20/3) = 0
x - 4/3 = 0
x - 0 = 0
x - -20/3 = 0
x = 4/3
x = 0
x = -20/3


Input: Compute the solution of x^3 - 67/30x^2 - 149/30x + 28/15 = 0

Output:
x^3 - 67/30x^2 - 149/30x + 28/15 = 0
(x - -8/5)(x - 7/2)(x - 1/3) = 0
x - -8/5 = 0
x - 7/2 = 0
x - 1/3 = 0
x = -8/5
x = 7/2
x = 1/3


Input:
Solve the system:
2x + 7y = -327/28
6x + 2y = -25/14

Output:
2x + 7y = -327/28
6x + 2y = -25/14

Using elimination
6*(2x + 7y = -327/28)
2*(6x + 2y = -25/14)
12x + 42y = -981/14
12x + 4y = -25/7
Subtract equations
38y = -133/2
y = -133/2/38
y = -7/4

Substitute y
2x + 7(-7/4) = -327/28
2x = 4/7
x = 4/7/2
x = 2/7


Input: Solve the equation x^2 - 20/3x - 187/12 = 0

Output:
x^2 - 20/3x - 187/12 = 0
(x - 17/2)(x - -11/6) = 0
x - 17/2 = 0  or  x - -11/6 = 0
x = 17/2
x = -11/6


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

Output:
9x - 3/2 = 0
9x = 3/2
x = 3/2 / 9
x = 1/6


Input:
Solve the equations:
3x + 2y = -123/10
9x + 9y = -963/20

Output:
3x + 2y = -123/10
9x + 9y = -963/20

Using elimination
9*(3x + 2y = -123/10)
3*(9x + 9y = -963/20)
27x + 18y = -1107/10
27x + 27y = -2889/20
Subtract equations
-9y = 135/4
y = 135/4/-9
y = -15/4

Substitute y
3x + 2(-15/4) = -123/10
3x = -24/5
x = -24/5/3
x = -8/5


Input:
Find x and y such that
9x + 9y = -39/2
3x + 4y = -23/3

Output:
9x + 9y = -39/2
3x + 4y = -23/3

Using elimination
3*(9x + 9y = -39/2)
9*(3x + 4y = -23/3)
27x + 27y = -117/2
27x + 36y = -69
Subtract equations
-9y = 21/2
y = 21/2/-9
y = -7/6

Substitute y
9x + 9(-7/6) = -39/2
9x = -9
x = -9/9
x = -1


Input:
Solve the equations:
4x + 9y = -37
10x + 8y = -109/4

Output:
4x + 9y = -37
10x + 8y = -109/4

Using elimination
10*(4x + 9y = -37)
4*(10x + 8y = -109/4)
40x + 90y = -370
40x + 32y = -109
Subtract equations
58y = -261
y = -261/58
y = -9/2

Substitute y
4x + 9(-9/2) = -37
4x = 7/2
x = 7/2/4
x = 7/8


Input: Find x in 8x - 24 = 0

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


Input:
Solve the equations:
4x + 5y = -141/8
8x + 9y = -289/8

Output:
4x + 5y = -141/8
8x + 9y = -289/8

Using elimination
8*(4x + 5y = -141/8)
4*(8x + 9y = -289/8)
32x + 40y = -141
32x + 36y = -289/2
Subtract equations
4y = 7/2
y = 7/2/4
y = 7/8

Substitute y
4x + 5(7/8) = -141/8
4x = -22
x = -22/4
x = -11/2


Input: Solve the equation 4x - 48 = 0

Output:
4x - 48 = 0
4x = 48
x = 48 / 4
x = 12


Input: Compute the solution of x^2 + 133/8x - 51/8 = 0

Output:
x^2 + 133/8x - 51/8 = 0
(x - -17)(x - 3/8) = 0
x - -17 = 0  or  x - 3/8 = 0
x = -17
x = 3/8


Input: What value of x satisfies x^2 + 43/7x + 40/7 = 0

Output:
x^2 + 43/7x + 40/7 = 0
(x - -8/7)(x - -5) = 0
x - -8/7 = 0  or  x - -5 = 0
x = -8/7
x = -5


Input: What value of x satisfies 1x + 8/7 = 0

Output:
1x + 8/7 = 0
1x = -8/7
x = -8/7 / 1
x = -8/7


Input: Compute the solution of x^2 - 5x + 6 = 0

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


Input:
Solve simultaneously:
8x + 8y = 116/5
2x + 9y = -19/10

Output:
8x + 8y = 116/5
2x + 9y = -19/10

Using elimination
2*(8x + 8y = 116/5)
8*(2x + 9y = -19/10)
16x + 16y = 232/5
16x + 72y = -76/5
Subtract equations
-56y = 308/5
y = 308/5/-56
y = -11/10

Substitute y
8x + 8(-11/10) = 116/5
8x = 32
x = 32/8
x = 4


Input: Determine x in x^2 + 3/8x - 119/32 = 0

Output:
x^2 + 3/8x - 119/32 = 0
(x - -17/8)(x - 7/4) = 0
x - -17/8 = 0  or  x - 7/4 = 0
x = -17/8
x = 7/4


Input:
Solve the system:
8x + 4y = 110/3
2x + 6y = 5

Output:
8x + 4y = 110/3
2x + 6y = 5

Using elimination
2*(8x + 4y = 110/3)
8*(2x + 6y = 5)
16x + 8y = 220/3
16x + 48y = 40
Subtract equations
-40y = 100/3
y = 100/3/-40
y = -5/6

Substitute y
8x + 4(-5/6) = 110/3
8x = 40
x = 40/8
x = 5


Input: Find x for 1x + 11/8 = 0

Output:
1x + 11/8 = 0
1x = -11/8
x = -11/8 / 1
x = -11/8


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

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


Input: What value of x satisfies x^3 - 407/24x^2 + 359/12x - 65/8 = 0

Output:
x^3 - 407/24x^2 + 359/12x - 65/8 = 0
(x - 15)(x - 1/3)(x - 13/8) = 0
x - 15 = 0
x - 1/3 = 0
x - 13/8 = 0
x = 15
x = 1/3
x = 13/8


Input: What value of x satisfies x^3 + 201/35x^2 + 19/5x + 3/7 = 0

Output:
x^3 + 201/35x^2 + 19/5x + 3/7 = 0
(x - -3/5)(x - -5)(x - -1/7) = 0
x - -3/5 = 0
x - -5 = 0
x - -1/7 = 0
x = -3/5
x = -5
x = -1/7


Input:
Solve simultaneously:
4x + 3y = -25/14
7x + 3y = -373/56

Output:
4x + 3y = -25/14
7x + 3y = -373/56

Using elimination
7*(4x + 3y = -25/14)
4*(7x + 3y = -373/56)
28x + 21y = -25/2
28x + 12y = -373/14
Subtract equations
9y = 99/7
y = 99/7/9
y = 11/7

Substitute y
4x + 3(11/7) = -25/14
4x = -13/2
x = -13/2/4
x = -13/8


Input: Compute the solution of x^3 - 8x^2 + 1367/81x - 760/81 = 0

Output:
x^3 - 8x^2 + 1367/81x - 760/81 = 0
(x - 8/9)(x - 5)(x - 19/9) = 0
x - 8/9 = 0
x - 5 = 0
x - 19/9 = 0
x = 8/9
x = 5
x = 19/9


Input: What value of x satisfies x^2 - 55/12x - 4 = 0

Output:
x^2 - 55/12x - 4 = 0
(x - -3/4)(x - 16/3) = 0
x - -3/4 = 0  or  x - 16/3 = 0
x = -3/4
x = 16/3


Input:
Solve simultaneously:
6x + 10y = -400/3
10x + 1y = -604/3

Output:
6x + 10y = -400/3
10x + 1y = -604/3

Using elimination
10*(6x + 10y = -400/3)
6*(10x + 1y = -604/3)
60x + 100y = -4000/3
60x + 6y = -1208
Subtract equations
94y = -376/3
y = -376/3/94
y = -4/3

Substitute y
6x + 10(-4/3) = -400/3
6x = -120
x = -120/6
x = -20


Input: Find x in 8x + 76 = 0

Output:
8x + 76 = 0
8x = -76
x = -76 / 8
x = -19/2


Input:
Solve the system:
2x + 4y = 79/6
8x + 5y = 703/24

Output:
2x + 4y = 79/6
8x + 5y = 703/24

Using elimination
8*(2x + 4y = 79/6)
2*(8x + 5y = 703/24)
16x + 32y = 316/3
16x + 10y = 703/12
Subtract equations
22y = 187/4
y = 187/4/22
y = 17/8

Substitute y
2x + 4(17/8) = 79/6
2x = 14/3
x = 14/3/2
x = 7/3


Input: What value of x satisfies x^3 + 67/15x^2 + 4x - 28/15 = 0

Output:
x^3 + 67/15x^2 + 4x - 28/15 = 0
(x - 1/3)(x - -14/5)(x - -2) = 0
x - 1/3 = 0
x - -14/5 = 0
x - -2 = 0
x = 1/3
x = -14/5
x = -2


Input: Determine x in 9x + 45/4 = 0

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


Input: Find the solution to x^2 - 77/30x - 17/6 = 0

Output:
x^2 - 77/30x - 17/6 = 0
(x - 17/5)(x - -5/6) = 0
x - 17/5 = 0  or  x - -5/6 = 0
x = 17/5
x = -5/6


Input: Solve quickly: x^2 + 9x + 17/4 = 0

Output:
x^2 + 9x + 17/4 = 0
(x - -1/2)(x - -17/2) = 0
x - -1/2 = 0  or  x - -17/2 = 0
x = -1/2
x = -17/2


Input:
Solve the equations:
5x + 2y = 81/28
2x + 6y = -15/14

Output:
5x + 2y = 81/28
2x + 6y = -15/14

Using elimination
2*(5x + 2y = 81/28)
5*(2x + 6y = -15/14)
10x + 4y = 81/14
10x + 30y = -75/14
Subtract equations
-26y = 78/7
y = 78/7/-26
y = -3/7

Substitute y
5x + 2(-3/7) = 81/28
5x = 15/4
x = 15/4/5
x = 3/4


Input: What value of x satisfies x^3 + 139/72x^2 - 479/27x + 4199/216 = 0

Output:
x^3 + 139/72x^2 - 479/27x + 4199/216 = 0
(x - 19/9)(x - -17/3)(x - 13/8) = 0
x - 19/9 = 0
x - -17/3 = 0
x - 13/8 = 0
x = 19/9
x = -17/3
x = 13/8


Input: Determine x in x^3 - 77/18x^2 - 1x  = 0

Output:
x^3 - 77/18x^2 - 1x  = 0
(x - -2/9)(x - 0)(x - 9/2) = 0
x - -2/9 = 0
x - 0 = 0
x - 9/2 = 0
x = -2/9
x = 0
x = 9/2


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

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


Input: Compute the solution of x^3 - 3x^2 - 46x - 72 = 0

Output:
x^3 - 3x^2 - 46x - 72 = 0
(x - -2)(x - 9)(x - -4) = 0
x - -2 = 0
x - 9 = 0
x - -4 = 0
x = -2
x = 9
x = -4


Input: Find the solution to x^3 + 17/6x^2 + 325/162x + 34/81 = 0

Output:
x^3 + 17/6x^2 + 325/162x + 34/81 = 0
(x - -1/2)(x - -4/9)(x - -17/9) = 0
x - -1/2 = 0
x - -4/9 = 0
x - -17/9 = 0
x = -1/2
x = -4/9
x = -17/9


Input: Determine x in 9x + 12 = 0

Output:
9x + 12 = 0
9x = -12
x = -12 / 9
x = -4/3


Input: Find the solution to 10x + 80/9 = 0

Output:
10x + 80/9 = 0
10x = -80/9
x = -80/9 / 10
x = -8/9


Input: Compute the solution of x^3 - 151/18x^2 + 40/9x + 50/3 = 0

Output:
x^3 - 151/18x^2 + 40/9x + 50/3 = 0
(x - 15/2)(x - -10/9)(x - 2) = 0
x - 15/2 = 0
x - -10/9 = 0
x - 2 = 0
x = 15/2
x = -10/9
x = 2


Input: Find x in x^2 + 12/5x  = 0

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


Input: Solve quickly: x^3 + 175/12x^2 + 1279/24x + 95/2 = 0

Output:
x^3 + 175/12x^2 + 1279/24x + 95/2 = 0
(x - -4/3)(x - -15/4)(x - -19/2) = 0
x - -4/3 = 0
x - -15/4 = 0
x - -19/2 = 0
x = -4/3
x = -15/4
x = -19/2


Input: Solve the equation x^2 + 29/2x + 39/2 = 0

Output:
x^2 + 29/2x + 39/2 = 0
(x - -13)(x - -3/2) = 0
x - -13 = 0  or  x - -3/2 = 0
x = -13
x = -3/2


Input: Solve the equation x^3 - 6x^2 + 323/36x  = 0

Output:
x^3 - 6x^2 + 323/36x  = 0
(x - 0)(x - 19/6)(x - 17/6) = 0
x - 0 = 0
x - 19/6 = 0
x - 17/6 = 0
x = 0
x = 19/6
x = 17/6


Input: Solve quickly: x^3 - 152/21x^2 + 148/9x - 80/7 = 0

Output:
x^3 - 152/21x^2 + 148/9x - 80/7 = 0
(x - 10/3)(x - 18/7)(x - 4/3) = 0
x - 10/3 = 0
x - 18/7 = 0
x - 4/3 = 0
x = 10/3
x = 18/7
x = 4/3


Input:
Solve the equations:
3x + 5y = -37/4
7x + 5y = -33/4

Output:
3x + 5y = -37/4
7x + 5y = -33/4

Using elimination
7*(3x + 5y = -37/4)
3*(7x + 5y = -33/4)
21x + 35y = -259/4
21x + 15y = -99/4
Subtract equations
20y = -40
y = -40/20
y = -2

Substitute y
3x + 5(-2) = -37/4
3x = 3/4
x = 3/4/3
x = 1/4


Input:
Find x and y such that
5x + 2y = 18/5
10x + 6y = 49/5

Output:
5x + 2y = 18/5
10x + 6y = 49/5

Using elimination
10*(5x + 2y = 18/5)
5*(10x + 6y = 49/5)
50x + 20y = 36
50x + 30y = 49
Subtract equations
-10y = -13
y = -13/-10
y = 13/10

Substitute y
5x + 2(13/10) = 18/5
5x = 1
x = 1/5
x = 1/5


Input:
Solve simultaneously:
10x + 2y = -29/9
9x + 8y = -6

Output:
10x + 2y = -29/9
9x + 8y = -6

Using elimination
9*(10x + 2y = -29/9)
10*(9x + 8y = -6)
90x + 18y = -29
90x + 80y = -60
Subtract equations
-62y = 31
y = 31/-62
y = -1/2

Substitute y
10x + 2(-1/2) = -29/9
10x = -20/9
x = -20/9/10
x = -2/9


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

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


Input: Find the solution to x^2 - 6x - 7 = 0

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


Input:
Solve the equations:
9x + 10y = 241
6x + 5y = 129

Output:
9x + 10y = 241
6x + 5y = 129

Using elimination
6*(9x + 10y = 241)
9*(6x + 5y = 129)
54x + 60y = 1446
54x + 45y = 1161
Subtract equations
15y = 285
y = 285/15
y = 19

Substitute y
9x + 10(19) = 241
9x = 51
x = 51/9
x = 17/3


Input: Solve quickly: 8x - 160/9 = 0

Output:
8x - 160/9 = 0
8x = 160/9
x = 160/9 / 8
x = 20/9


Input: What value of x satisfies 5x - 10/7 = 0

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


Input: Determine x in 9x - 18 = 0

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


Input: Determine x in 10x + 20/7 = 0

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


Input: What value of x satisfies x^2 - 1x - 12 = 0

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


Input: Find x in x^2 + 139/40x + 3 = 0

Output:
x^2 + 139/40x + 3 = 0
(x - -8/5)(x - -15/8) = 0
x - -8/5 = 0  or  x - -15/8 = 0
x = -8/5
x = -15/8


Input: Find the solution to x^3 - 211/30x^2 + 182/15x - 33/10 = 0

Output:
x^3 - 211/30x^2 + 182/15x - 33/10 = 0
(x - 11/5)(x - 9/2)(x - 1/3) = 0
x - 11/5 = 0
x - 9/2 = 0
x - 1/3 = 0
x = 11/5
x = 9/2
x = 1/3


Input:
Find x and y such that
5x + 6y = -263/9
2x + 6y = -251/9

Output:
5x + 6y = -263/9
2x + 6y = -251/9

Using elimination
2*(5x + 6y = -263/9)
5*(2x + 6y = -251/9)
10x + 12y = -526/9
10x + 30y = -1255/9
Subtract equations
-18y = 81
y = 81/-18
y = -9/2

Substitute y
5x + 6(-9/2) = -263/9
5x = -20/9
x = -20/9/5
x = -4/9


Input: Find x in 6x - 30 = 0

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


Input: Find the solution to 8x  = 0

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


Input: What value of x satisfies x^3 - 121/30x^2 - 977/150x - 56/25 = 0

Output:
x^3 - 121/30x^2 - 977/150x - 56/25 = 0
(x - 16/3)(x - -3/5)(x - -7/10) = 0
x - 16/3 = 0
x - -3/5 = 0
x - -7/10 = 0
x = 16/3
x = -3/5
x = -7/10


Input:
Solve simultaneously:
4x + 5y = 10
3x + 10y = 65/4

Output:
4x + 5y = 10
3x + 10y = 65/4

Using elimination
3*(4x + 5y = 10)
4*(3x + 10y = 65/4)
12x + 15y = 30
12x + 40y = 65
Subtract equations
-25y = -35
y = -35/-25
y = 7/5

Substitute y
4x + 5(7/5) = 10
4x = 3
x = 3/4
x = 3/4


Input: Solve x^2 - 2x - 24 = 0

Output:
x^2 - 2x - 24 = 0
(x - 6)(x - -4) = 0
x - 6 = 0  or  x - -4 = 0
x = 6
x = -4


Input: Solve the equation x^3 - 26/5x^2 + 24/5x  = 0

Output:
x^3 - 26/5x^2 + 24/5x  = 0
(x - 0)(x - 6/5)(x - 4) = 0
x - 0 = 0
x - 6/5 = 0
x - 4 = 0
x = 0
x = 6/5
x = 4


Input:
Solve the system:
10x + 5y = -26
10x + 9y = -34

Output:
10x + 5y = -26
10x + 9y = -34

Using elimination
10*(10x + 5y = -26)
10*(10x + 9y = -34)
100x + 50y = -260
100x + 90y = -340
Subtract equations
-40y = 80
y = 80/-40
y = -2

Substitute y
10x + 5(-2) = -26
10x = -16
x = -16/10
x = -8/5


Input:
Find x and y such that
5x + 6y = -151/9
4x + 2y = -83/9

Output:
5x + 6y = -151/9
4x + 2y = -83/9

Using elimination
4*(5x + 6y = -151/9)
5*(4x + 2y = -83/9)
20x + 24y = -604/9
20x + 10y = -415/9
Subtract equations
14y = -21
y = -21/14
y = -3/2

Substitute y
5x + 6(-3/2) = -151/9
5x = -70/9
x = -70/9/5
x = -14/9


Input:
Find x and y such that
8x + 10y = 752/45
10x + 7y = 232/9

Output:
8x + 10y = 752/45
10x + 7y = 232/9

Using elimination
10*(8x + 10y = 752/45)
8*(10x + 7y = 232/9)
80x + 100y = 1504/9
80x + 56y = 1856/9
Subtract equations
44y = -352/9
y = -352/9/44
y = -8/9

Substitute y
8x + 10(-8/9) = 752/45
8x = 128/5
x = 128/5/8
x = 16/5


Input:
Solve the system:
1x + 6y = 96/7
6x + 4y = 64/7

Output:
1x + 6y = 96/7
6x + 4y = 64/7

Using elimination
6*(1x + 6y = 96/7)
1*(6x + 4y = 64/7)
6x + 36y = 576/7
6x + 4y = 64/7
Subtract equations
32y = 512/7
y = 512/7/32
y = 16/7

Substitute y
1x + 6(16/7) = 96/7
1x = 0
x = 0/1
x = 0


Input:
Solve simultaneously:
1x + 5y = 20/3
6x + 2y = 8/3

Output:
1x + 5y = 20/3
6x + 2y = 8/3

Using elimination
6*(1x + 5y = 20/3)
1*(6x + 2y = 8/3)
6x + 30y = 40
6x + 2y = 8/3
Subtract equations
28y = 112/3
y = 112/3/28
y = 4/3

Substitute y
1x + 5(4/3) = 20/3
1x = 0
x = 0/1
x = 0


Input: Find the solution to 6x - 60/7 = 0

Output:
6x - 60/7 = 0
6x = 60/7
x = 60/7 / 6
x = 10/7


Input: Find x for x^3 + 41/12x^2 - 85/2x - 1463/12 = 0

Output:
x^3 + 41/12x^2 - 85/2x - 1463/12 = 0
(x - -11/4)(x - -7)(x - 19/3) = 0
x - -11/4 = 0
x - -7 = 0
x - 19/3 = 0
x = -11/4
x = -7
x = 19/3


Input: Solve quickly: x^3 + 41/7x^2 + 313/28x + 195/28 = 0

Output:
x^3 + 41/7x^2 + 313/28x + 195/28 = 0
(x - -5/2)(x - -13/7)(x - -3/2) = 0
x - -5/2 = 0
x - -13/7 = 0
x - -3/2 = 0
x = -5/2
x = -13/7
x = -3/2


Input: Determine x in x^2 + 8/9x  = 0

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


Input:
Solve simultaneously:
8x + 6y = 37
10x + 2y = 103/3

Output:
8x + 6y = 37
10x + 2y = 103/3

Using elimination
10*(8x + 6y = 37)
8*(10x + 2y = 103/3)
80x + 60y = 370
80x + 16y = 824/3
Subtract equations
44y = 286/3
y = 286/3/44
y = 13/6

Substitute y
8x + 6(13/6) = 37
8x = 24
x = 24/8
x = 3


Input: Find x for 4x + 26/3 = 0

Output:
4x + 26/3 = 0
4x = -26/3
x = -26/3 / 4
x = -13/6


Input: Solve x^2 - 21/2x + 17 = 0

Output:
x^2 - 21/2x + 17 = 0
(x - 2)(x - 17/2) = 0
x - 2 = 0  or  x - 17/2 = 0
x = 2
x = 17/2


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

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