Input: Find x in 1x + 17/2 = 0

Output:
1x + 17/2 = 0
1x = -17/2
x = -17/2 / 1
x = -17/2


Input: Compute the solution of x^3 + 26/7x^2 + 95/28x + 25/28 = 0

Output:
x^3 + 26/7x^2 + 95/28x + 25/28 = 0
(x - -1/2)(x - -5/7)(x - -5/2) = 0
x - -1/2 = 0
x - -5/7 = 0
x - -5/2 = 0
x = -1/2
x = -5/7
x = -5/2


Input: Determine x in x^2 + 18/5x + 56/25 = 0

Output:
x^2 + 18/5x + 56/25 = 0
(x - -4/5)(x - -14/5) = 0
x - -4/5 = 0  or  x - -14/5 = 0
x = -4/5
x = -14/5


Input: Find x for 9x + 153 = 0

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


Input:
Find x and y such that
6x + 1y = 21/2
4x + 4y = 2

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

Using elimination
4*(6x + 1y = 21/2)
6*(4x + 4y = 2)
24x + 4y = 42
24x + 24y = 12
Subtract equations
-20y = 30
y = 30/-20
y = -3/2

Substitute y
6x + 1(-3/2) = 21/2
6x = 12
x = 12/6
x = 2


Input: Determine x in 1x + 3/2 = 0

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


Input:
Solve simultaneously:
9x + 8y = 306/35
2x + 3y = -9/35

Output:
9x + 8y = 306/35
2x + 3y = -9/35

Using elimination
2*(9x + 8y = 306/35)
9*(2x + 3y = -9/35)
18x + 16y = 612/35
18x + 27y = -81/35
Subtract equations
-11y = 99/5
y = 99/5/-11
y = -9/5

Substitute y
9x + 8(-9/5) = 306/35
9x = 162/7
x = 162/7/9
x = 18/7


Input: What value of x satisfies x^3 - 303/20x^2 + 89/40x + 3/8 = 0

Output:
x^3 - 303/20x^2 + 89/40x + 3/8 = 0
(x - -1/10)(x - 15)(x - 1/4) = 0
x - -1/10 = 0
x - 15 = 0
x - 1/4 = 0
x = -1/10
x = 15
x = 1/4


Input:
Solve the system:
7x + 6y = -24
1x + 10y = -56/3

Output:
7x + 6y = -24
1x + 10y = -56/3

Using elimination
1*(7x + 6y = -24)
7*(1x + 10y = -56/3)
7x + 6y = -24
7x + 70y = -392/3
Subtract equations
-64y = 320/3
y = 320/3/-64
y = -5/3

Substitute y
7x + 6(-5/3) = -24
7x = -14
x = -14/7
x = -2


Input: Compute the solution of x^3 + 58/5x^2 + 72/5x - 576/5 = 0

Output:
x^3 + 58/5x^2 + 72/5x - 576/5 = 0
(x - -8)(x - 12/5)(x - -6) = 0
x - -8 = 0
x - 12/5 = 0
x - -6 = 0
x = -8
x = 12/5
x = -6


Input: What value of x satisfies x^3 + 659/280x^2 - 71/280x - 9/4 = 0

Output:
x^3 + 659/280x^2 - 71/280x - 9/4 = 0
(x - 7/8)(x - -10/7)(x - -9/5) = 0
x - 7/8 = 0
x - -10/7 = 0
x - -9/5 = 0
x = 7/8
x = -10/7
x = -9/5


Input: Determine x in 5x - 15 = 0

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


Input: Solve quickly: x^3 - 141/14x^2 - 341/14x + 102/7 = 0

Output:
x^3 - 141/14x^2 - 341/14x + 102/7 = 0
(x - -17/7)(x - 12)(x - 1/2) = 0
x - -17/7 = 0
x - 12 = 0
x - 1/2 = 0
x = -17/7
x = 12
x = 1/2


Input:
Solve simultaneously:
1x + 7y = 346/5
8x + 8y = 368/5

Output:
1x + 7y = 346/5
8x + 8y = 368/5

Using elimination
8*(1x + 7y = 346/5)
1*(8x + 8y = 368/5)
8x + 56y = 2768/5
8x + 8y = 368/5
Subtract equations
48y = 480
y = 480/48
y = 10

Substitute y
1x + 7(10) = 346/5
1x = -4/5
x = -4/5/1
x = -4/5


Input: Solve the equation 6x - 6 = 0

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


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 quickly: x^3 - 17/12x^2 + 1/2x  = 0

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


Input:
Solve simultaneously:
8x + 3y = -11
1x + 4y = -5

Output:
8x + 3y = -11
1x + 4y = -5

Using elimination
1*(8x + 3y = -11)
8*(1x + 4y = -5)
8x + 3y = -11
8x + 32y = -40
Subtract equations
-29y = 29
y = 29/-29
y = -1

Substitute y
8x + 3(-1) = -11
8x = -8
x = -8/8
x = -1


Input: Solve x^3 - 9/20x^2 - 71/8x - 63/10 = 0

Output:
x^3 - 9/20x^2 - 71/8x - 63/10 = 0
(x - 7/2)(x - -4/5)(x - -9/4) = 0
x - 7/2 = 0
x - -4/5 = 0
x - -9/4 = 0
x = 7/2
x = -4/5
x = -9/4


Input: Determine x in 3x + 21/4 = 0

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


Input: Find x for x^2 + 53/9x - 140/27 = 0

Output:
x^2 + 53/9x - 140/27 = 0
(x - -20/3)(x - 7/9) = 0
x - -20/3 = 0  or  x - 7/9 = 0
x = -20/3
x = 7/9


Input: Find x in 8x - 44/3 = 0

Output:
8x - 44/3 = 0
8x = 44/3
x = 44/3 / 8
x = 11/6


Input: Find the solution to x^2 - 107/28x - 51/28 = 0

Output:
x^2 - 107/28x - 51/28 = 0
(x - -3/7)(x - 17/4) = 0
x - -3/7 = 0  or  x - 17/4 = 0
x = -3/7
x = 17/4


Input:
Solve the equations:
5x + 2y = 64/9
7x + 10y = -40/9

Output:
5x + 2y = 64/9
7x + 10y = -40/9

Using elimination
7*(5x + 2y = 64/9)
5*(7x + 10y = -40/9)
35x + 14y = 448/9
35x + 50y = -200/9
Subtract equations
-36y = 72
y = 72/-36
y = -2

Substitute y
5x + 2(-2) = 64/9
5x = 100/9
x = 100/9/5
x = 20/9


Input:
Solve simultaneously:
3x + 3y = -150/7
8x + 3y = -155/7

Output:
3x + 3y = -150/7
8x + 3y = -155/7

Using elimination
8*(3x + 3y = -150/7)
3*(8x + 3y = -155/7)
24x + 24y = -1200/7
24x + 9y = -465/7
Subtract equations
15y = -105
y = -105/15
y = -7

Substitute y
3x + 3(-7) = -150/7
3x = -3/7
x = -3/7/3
x = -1/7


Input:
Solve simultaneously:
3x + 3y = 9/2
3x + 5y = 27/10

Output:
3x + 3y = 9/2
3x + 5y = 27/10

Using elimination
3*(3x + 3y = 9/2)
3*(3x + 5y = 27/10)
9x + 9y = 27/2
9x + 15y = 81/10
Subtract equations
-6y = 27/5
y = 27/5/-6
y = -9/10

Substitute y
3x + 3(-9/10) = 9/2
3x = 36/5
x = 36/5/3
x = 12/5


Input:
Solve simultaneously:
4x + 6y = 16
6x + 6y = 19

Output:
4x + 6y = 16
6x + 6y = 19

Using elimination
6*(4x + 6y = 16)
4*(6x + 6y = 19)
24x + 36y = 96
24x + 24y = 76
Subtract equations
12y = 20
y = 20/12
y = 5/3

Substitute y
4x + 6(5/3) = 16
4x = 6
x = 6/4
x = 3/2


Input: Solve the equation x^2 - 115/56x + 25/28 = 0

Output:
x^2 - 115/56x + 25/28 = 0
(x - 5/8)(x - 10/7) = 0
x - 5/8 = 0  or  x - 10/7 = 0
x = 5/8
x = 10/7


Input: Find x in 3x + 9 = 0

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


Input:
Solve simultaneously:
7x + 2y = -89/12
10x + 4y = -73/6

Output:
7x + 2y = -89/12
10x + 4y = -73/6

Using elimination
10*(7x + 2y = -89/12)
7*(10x + 4y = -73/6)
70x + 20y = -445/6
70x + 28y = -511/6
Subtract equations
-8y = 11
y = 11/-8
y = -11/8

Substitute y
7x + 2(-11/8) = -89/12
7x = -14/3
x = -14/3/7
x = -2/3


Input: Find x in 6x - 12 = 0

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


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

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

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

Substitute y
7x + 9(-1) = -9
7x = 0
x = 0/7
x = 0


Input:
Find x and y such that
1x + 6y = -5/6
3x + 8y = -65/18

Output:
1x + 6y = -5/6
3x + 8y = -65/18

Using elimination
3*(1x + 6y = -5/6)
1*(3x + 8y = -65/18)
3x + 18y = -5/2
3x + 8y = -65/18
Subtract equations
10y = 10/9
y = 10/9/10
y = 1/9

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


Input: Solve the equation 7x - 28 = 0

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


Input:
Solve the equations:
9x + 5y = 167/3
2x + 3y = 13

Output:
9x + 5y = 167/3
2x + 3y = 13

Using elimination
2*(9x + 5y = 167/3)
9*(2x + 3y = 13)
18x + 10y = 334/3
18x + 27y = 117
Subtract equations
-17y = -17/3
y = -17/3/-17
y = 1/3

Substitute y
9x + 5(1/3) = 167/3
9x = 54
x = 54/9
x = 6


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

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


Input:
Find x and y such that
3x + 9y = 80/3
2x + 8y = 220/9

Output:
3x + 9y = 80/3
2x + 8y = 220/9

Using elimination
2*(3x + 9y = 80/3)
3*(2x + 8y = 220/9)
6x + 18y = 160/3
6x + 24y = 220/3
Subtract equations
-6y = -20
y = -20/-6
y = 10/3

Substitute y
3x + 9(10/3) = 80/3
3x = -10/3
x = -10/3/3
x = -10/9


Input: Determine x in x^2 + 13x - 68 = 0

Output:
x^2 + 13x - 68 = 0
(x - -17)(x - 4) = 0
x - -17 = 0  or  x - 4 = 0
x = -17
x = 4


Input: Find the solution to x^2 + 12/5x - 13 = 0

Output:
x^2 + 12/5x - 13 = 0
(x - 13/5)(x - -5) = 0
x - 13/5 = 0  or  x - -5 = 0
x = 13/5
x = -5


Input:
Find x and y such that
7x + 8y = 53/5
3x + 8y = -7/5

Output:
7x + 8y = 53/5
3x + 8y = -7/5

Using elimination
3*(7x + 8y = 53/5)
7*(3x + 8y = -7/5)
21x + 24y = 159/5
21x + 56y = -49/5
Subtract equations
-32y = 208/5
y = 208/5/-32
y = -13/10

Substitute y
7x + 8(-13/10) = 53/5
7x = 21
x = 21/7
x = 3


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

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


Input: Find the solution to 8x + 18 = 0

Output:
8x + 18 = 0
8x = -18
x = -18 / 8
x = -9/4


Input: Find x in x^3 - 249/40x^2 + 507/40x - 169/20 = 0

Output:
x^3 - 249/40x^2 + 507/40x - 169/20 = 0
(x - 13/8)(x - 13/5)(x - 2) = 0
x - 13/8 = 0
x - 13/5 = 0
x - 2 = 0
x = 13/8
x = 13/5
x = 2


Input: Solve the equation 7x + 5 = 0

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


Input:
Solve the system:
10x + 5y = -565/63
8x + 5y = -425/63

Output:
10x + 5y = -565/63
8x + 5y = -425/63

Using elimination
8*(10x + 5y = -565/63)
10*(8x + 5y = -425/63)
80x + 40y = -4520/63
80x + 50y = -4250/63
Subtract equations
-10y = -30/7
y = -30/7/-10
y = 3/7

Substitute y
10x + 5(3/7) = -565/63
10x = -100/9
x = -100/9/10
x = -10/9


Input: Find the solution to x^3 - 289/42x^2 - 30/7x + 800/21 = 0

Output:
x^3 - 289/42x^2 - 30/7x + 800/21 = 0
(x - 5/2)(x - 20/3)(x - -16/7) = 0
x - 5/2 = 0
x - 20/3 = 0
x - -16/7 = 0
x = 5/2
x = 20/3
x = -16/7


Input: What value of x satisfies x^3 - 3/2x^2 - 253/64x + 195/32 = 0

Output:
x^3 - 3/2x^2 - 253/64x + 195/32 = 0
(x - -2)(x - 13/8)(x - 15/8) = 0
x - -2 = 0
x - 13/8 = 0
x - 15/8 = 0
x = -2
x = 13/8
x = 15/8


Input: Find x for x^3 + 114/7x^2 + 1532/49x - 72/7 = 0

Output:
x^3 + 114/7x^2 + 1532/49x - 72/7 = 0
(x - 2/7)(x - -18/7)(x - -14) = 0
x - 2/7 = 0
x - -18/7 = 0
x - -14 = 0
x = 2/7
x = -18/7
x = -14


Input: Solve x^3 - 141/28x^2 + 155/28x + 12/7 = 0

Output:
x^3 - 141/28x^2 + 155/28x + 12/7 = 0
(x - 16/7)(x - 3)(x - -1/4) = 0
x - 16/7 = 0
x - 3 = 0
x - -1/4 = 0
x = 16/7
x = 3
x = -1/4


Input: Find x for x^3 - 17/24x^2 - 1325/36x + 3553/72 = 0

Output:
x^3 - 17/24x^2 - 1325/36x + 3553/72 = 0
(x - 17/3)(x - -19/3)(x - 11/8) = 0
x - 17/3 = 0
x - -19/3 = 0
x - 11/8 = 0
x = 17/3
x = -19/3
x = 11/8


Input: What value of x satisfies x^2 + 8/3x - 11/3 = 0

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


Input: Solve quickly: x^2 - 13/6x - 19/6 = 0

Output:
x^2 - 13/6x - 19/6 = 0
(x - -1)(x - 19/6) = 0
x - -1 = 0  or  x - 19/6 = 0
x = -1
x = 19/6


Input: Determine x in x^3 - 563/35x^2 - 556/35x + 204/35 = 0

Output:
x^3 - 563/35x^2 - 556/35x + 204/35 = 0
(x - -6/5)(x - 2/7)(x - 17) = 0
x - -6/5 = 0
x - 2/7 = 0
x - 17 = 0
x = -6/5
x = 2/7
x = 17


Input:
Solve the system:
10x + 3y = -31
9x + 2y = -53/2

Output:
10x + 3y = -31
9x + 2y = -53/2

Using elimination
9*(10x + 3y = -31)
10*(9x + 2y = -53/2)
90x + 27y = -279
90x + 20y = -265
Subtract equations
7y = -14
y = -14/7
y = -2

Substitute y
10x + 3(-2) = -31
10x = -25
x = -25/10
x = -5/2


Input: Solve x^3 + 67/10x^2 + 103/10x + 9/5 = 0

Output:
x^3 + 67/10x^2 + 103/10x + 9/5 = 0
(x - -1/5)(x - -9/2)(x - -2) = 0
x - -1/5 = 0
x - -9/2 = 0
x - -2 = 0
x = -1/5
x = -9/2
x = -2


Input: Determine x in 5x + 15 = 0

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


Input: Solve the equation x^3 + 7/2x^2 - 84x + 216 = 0

Output:
x^3 + 7/2x^2 - 84x + 216 = 0
(x - -12)(x - 9/2)(x - 4) = 0
x - -12 = 0
x - 9/2 = 0
x - 4 = 0
x = -12
x = 9/2
x = 4


Input:
Find x and y such that
5x + 4y = -185/3
5x + 5y = -205/3

Output:
5x + 4y = -185/3
5x + 5y = -205/3

Using elimination
5*(5x + 4y = -185/3)
5*(5x + 5y = -205/3)
25x + 20y = -925/3
25x + 25y = -1025/3
Subtract equations
-5y = 100/3
y = 100/3/-5
y = -20/3

Substitute y
5x + 4(-20/3) = -185/3
5x = -35
x = -35/5
x = -7


Input:
Find x and y such that
9x + 8y = -493/40
10x + 10y = -61/4

Output:
9x + 8y = -493/40
10x + 10y = -61/4

Using elimination
10*(9x + 8y = -493/40)
9*(10x + 10y = -61/4)
90x + 80y = -493/4
90x + 90y = -549/4
Subtract equations
-10y = 14
y = 14/-10
y = -7/5

Substitute y
9x + 8(-7/5) = -493/40
9x = -9/8
x = -9/8/9
x = -1/8


Input: Find the solution to x^3 + 29/6x^2 - 167/16x - 1235/24 = 0

Output:
x^3 + 29/6x^2 - 167/16x - 1235/24 = 0
(x - -10/3)(x - -19/4)(x - 13/4) = 0
x - -10/3 = 0
x - -19/4 = 0
x - 13/4 = 0
x = -10/3
x = -19/4
x = 13/4


Input: Solve the equation x^3 + 19/8x^2 - 57/32x + 9/32 = 0

Output:
x^3 + 19/8x^2 - 57/32x + 9/32 = 0
(x - 1/4)(x - -3)(x - 3/8) = 0
x - 1/4 = 0
x - -3 = 0
x - 3/8 = 0
x = 1/4
x = -3
x = 3/8


Input:
Solve the system:
6x + 4y = -5
6x + 7y = -11

Output:
6x + 4y = -5
6x + 7y = -11

Using elimination
6*(6x + 4y = -5)
6*(6x + 7y = -11)
36x + 24y = -30
36x + 42y = -66
Subtract equations
-18y = 36
y = 36/-18
y = -2

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


Input: Solve quickly: 1x + 18 = 0

Output:
1x + 18 = 0
1x = -18
x = -18 / 1
x = -18


Input:
Solve simultaneously:
2x + 5y = 13/5
1x + 8y = 23/5

Output:
2x + 5y = 13/5
1x + 8y = 23/5

Using elimination
1*(2x + 5y = 13/5)
2*(1x + 8y = 23/5)
2x + 5y = 13/5
2x + 16y = 46/5
Subtract equations
-11y = -33/5
y = -33/5/-11
y = 3/5

Substitute y
2x + 5(3/5) = 13/5
2x = -2/5
x = -2/5/2
x = -1/5


Input: Solve x^2 - 7x - 60 = 0

Output:
x^2 - 7x - 60 = 0
(x - 12)(x - -5) = 0
x - 12 = 0  or  x - -5 = 0
x = 12
x = -5


Input: Solve the equation x^3 + 100/3x^2 + 281x + 90 = 0

Output:
x^3 + 100/3x^2 + 281x + 90 = 0
(x - -1/3)(x - -18)(x - -15) = 0
x - -1/3 = 0
x - -18 = 0
x - -15 = 0
x = -1/3
x = -18
x = -15


Input: Find x for x^2 - 41/10x + 4 = 0

Output:
x^2 - 41/10x + 4 = 0
(x - 5/2)(x - 8/5) = 0
x - 5/2 = 0  or  x - 8/5 = 0
x = 5/2
x = 8/5


Input: Compute the solution of x^3 + 11/5x^2 - 144/25x - 324/125 = 0

Output:
x^3 + 11/5x^2 - 144/25x - 324/125 = 0
(x - -18/5)(x - -2/5)(x - 9/5) = 0
x - -18/5 = 0
x - -2/5 = 0
x - 9/5 = 0
x = -18/5
x = -2/5
x = 9/5


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

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

Using elimination
8*(3x + 5y = -15/8)
3*(8x + 5y = -5)
24x + 40y = -15
24x + 15y = -15
Subtract equations
25y = 0
y = 0/25
y = 0

Substitute y
3x + 5(0) = -15/8
3x = -15/8
x = -15/8/3
x = -5/8


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

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


Input: Solve 7x - 7/8 = 0

Output:
7x - 7/8 = 0
7x = 7/8
x = 7/8 / 7
x = 1/8


Input: Compute the solution of 3x - 27/7 = 0

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


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

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


Input:
Solve simultaneously:
3x + 1y = 85/14
3x + 10y = -115/7

Output:
3x + 1y = 85/14
3x + 10y = -115/7

Using elimination
3*(3x + 1y = 85/14)
3*(3x + 10y = -115/7)
9x + 3y = 255/14
9x + 30y = -345/7
Subtract equations
-27y = 135/2
y = 135/2/-27
y = -5/2

Substitute y
3x + 1(-5/2) = 85/14
3x = 60/7
x = 60/7/3
x = 20/7


Input: Determine x in x^2 + 65/3x + 66 = 0

Output:
x^2 + 65/3x + 66 = 0
(x - -11/3)(x - -18) = 0
x - -11/3 = 0  or  x - -18 = 0
x = -11/3
x = -18


Input:
Solve simultaneously:
3x + 5y = -32
5x + 2y = -157/9

Output:
3x + 5y = -32
5x + 2y = -157/9

Using elimination
5*(3x + 5y = -32)
3*(5x + 2y = -157/9)
15x + 25y = -160
15x + 6y = -157/3
Subtract equations
19y = -323/3
y = -323/3/19
y = -17/3

Substitute y
3x + 5(-17/3) = -32
3x = -11/3
x = -11/3/3
x = -11/9


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

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


Input: Determine x in x^3 + 5/9x^2 - 314/225x + 56/225 = 0

Output:
x^3 + 5/9x^2 - 314/225x + 56/225 = 0
(x - 4/5)(x - 1/5)(x - -14/9) = 0
x - 4/5 = 0
x - 1/5 = 0
x - -14/9 = 0
x = 4/5
x = 1/5
x = -14/9


Input: Find x for 5x - 35 = 0

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


Input:
Solve simultaneously:
10x + 6y = -666/5
4x + 9y = -174/5

Output:
10x + 6y = -666/5
4x + 9y = -174/5

Using elimination
4*(10x + 6y = -666/5)
10*(4x + 9y = -174/5)
40x + 24y = -2664/5
40x + 90y = -348
Subtract equations
-66y = -924/5
y = -924/5/-66
y = 14/5

Substitute y
10x + 6(14/5) = -666/5
10x = -150
x = -150/10
x = -15


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

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


Input: Find x for x^2 + 26/35x - 48/35 = 0

Output:
x^2 + 26/35x - 48/35 = 0
(x - 6/7)(x - -8/5) = 0
x - 6/7 = 0  or  x - -8/5 = 0
x = 6/7
x = -8/5


Input: What value of x satisfies x^2 + 18/7x - 9/7 = 0

Output:
x^2 + 18/7x - 9/7 = 0
(x - 3/7)(x - -3) = 0
x - 3/7 = 0  or  x - -3 = 0
x = 3/7
x = -3


Input: Solve the equation x^3 + 529/56x^2 + 1019/56x + 15/2 = 0

Output:
x^3 + 529/56x^2 + 1019/56x + 15/2 = 0
(x - -7)(x - -15/8)(x - -4/7) = 0
x - -7 = 0
x - -15/8 = 0
x - -4/7 = 0
x = -7
x = -15/8
x = -4/7


Input: Compute the solution of x^2 - 91/20x + 99/20 = 0

Output:
x^2 - 91/20x + 99/20 = 0
(x - 9/5)(x - 11/4) = 0
x - 9/5 = 0  or  x - 11/4 = 0
x = 9/5
x = 11/4


Input:
Solve the system:
5x + 10y = -925/7
6x + 9y = -816/7

Output:
5x + 10y = -925/7
6x + 9y = -816/7

Using elimination
6*(5x + 10y = -925/7)
5*(6x + 9y = -816/7)
30x + 60y = -5550/7
30x + 45y = -4080/7
Subtract equations
15y = -210
y = -210/15
y = -14

Substitute y
5x + 10(-14) = -925/7
5x = 55/7
x = 55/7/5
x = 11/7


Input:
Solve simultaneously:
7x + 1y = -93/4
9x + 9y = -351/4

Output:
7x + 1y = -93/4
9x + 9y = -351/4

Using elimination
9*(7x + 1y = -93/4)
7*(9x + 9y = -351/4)
63x + 9y = -837/4
63x + 63y = -2457/4
Subtract equations
-54y = 405
y = 405/-54
y = -15/2

Substitute y
7x + 1(-15/2) = -93/4
7x = -63/4
x = -63/4/7
x = -9/4


Input:
Solve the equations:
4x + 8y = -16/5
5x + 8y = -24/5

Output:
4x + 8y = -16/5
5x + 8y = -24/5

Using elimination
5*(4x + 8y = -16/5)
4*(5x + 8y = -24/5)
20x + 40y = -16
20x + 32y = -96/5
Subtract equations
8y = 16/5
y = 16/5/8
y = 2/5

Substitute y
4x + 8(2/5) = -16/5
4x = -32/5
x = -32/5/4
x = -8/5


Input: What value of x satisfies x^3 + 19/4x^2 - 9x - 9 = 0

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


Input: What value of x satisfies 4x - 16/3 = 0

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


Input:
Solve simultaneously:
4x + 10y = 164/7
2x + 2y = 242/35

Output:
4x + 10y = 164/7
2x + 2y = 242/35

Using elimination
2*(4x + 10y = 164/7)
4*(2x + 2y = 242/35)
8x + 20y = 328/7
8x + 8y = 968/35
Subtract equations
12y = 96/5
y = 96/5/12
y = 8/5

Substitute y
4x + 10(8/5) = 164/7
4x = 52/7
x = 52/7/4
x = 13/7


Input: Find x for x^3 - 171/35x^2 - 342/35x + 648/35 = 0

Output:
x^3 - 171/35x^2 - 342/35x + 648/35 = 0
(x - 6)(x - -12/5)(x - 9/7) = 0
x - 6 = 0
x - -12/5 = 0
x - 9/7 = 0
x = 6
x = -12/5
x = 9/7


Input: Find x for 8x + 26 = 0

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


Input:
Solve the system:
1x + 3y = -31/18
1x + 5y = -49/18

Output:
1x + 3y = -31/18
1x + 5y = -49/18

Using elimination
1*(1x + 3y = -31/18)
1*(1x + 5y = -49/18)
1x + 3y = -31/18
1x + 5y = -49/18
Subtract equations
-2y = 1
y = 1/-2
y = -1/2

Substitute y
1x + 3(-1/2) = -31/18
1x = -2/9
x = -2/9/1
x = -2/9


Input: Solve the equation x^2 + 43/5x - 14 = 0

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


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

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


Input: Determine x in x^2 + 4/5x - 9/5 = 0

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


Input: Determine x in x^3 + 3/4x^2 - 69/4x - 17 = 0

Output:
x^3 + 3/4x^2 - 69/4x - 17 = 0
(x - -1)(x - -4)(x - 17/4) = 0
x - -1 = 0
x - -4 = 0
x - 17/4 = 0
x = -1
x = -4
x = 17/4


Input: Find x for x^3 - 23/7x^2 + 8/7x + 20/7 = 0

Output:
x^3 - 23/7x^2 + 8/7x + 20/7 = 0
(x - 2)(x - 2)(x - -5/7) = 0
x - 2 = 0
x - 2 = 0
x - -5/7 = 0
x = 2
x = 2
x = -5/7


Input: Find x in x^3 + 49/9x^2 - 374/81x - 208/27 = 0

Output:
x^3 + 49/9x^2 - 374/81x - 208/27 = 0
(x - -6)(x - -8/9)(x - 13/9) = 0
x - -6 = 0
x - -8/9 = 0
x - 13/9 = 0
x = -6
x = -8/9
x = 13/9


Input: What value of x satisfies x^3 + 103/30x^2 - 79/10x - 52/3 = 0

Output:
x^3 + 103/30x^2 - 79/10x - 52/3 = 0
(x - 5/2)(x - -13/3)(x - -8/5) = 0
x - 5/2 = 0
x - -13/3 = 0
x - -8/5 = 0
x = 5/2
x = -13/3
x = -8/5


Input:
Solve the system:
5x + 9y = -193/2
10x + 9y = -323/2

Output:
5x + 9y = -193/2
10x + 9y = -323/2

Using elimination
10*(5x + 9y = -193/2)
5*(10x + 9y = -323/2)
50x + 90y = -965
50x + 45y = -1615/2
Subtract equations
45y = -315/2
y = -315/2/45
y = -7/2

Substitute y
5x + 9(-7/2) = -193/2
5x = -65
x = -65/5
x = -13


Input: What value of x satisfies x^3 + 107/21x^2 + 10/7x - 8/3 = 0

Output:
x^3 + 107/21x^2 + 10/7x - 8/3 = 0
(x - -1)(x - 4/7)(x - -14/3) = 0
x - -1 = 0
x - 4/7 = 0
x - -14/3 = 0
x = -1
x = 4/7
x = -14/3


Input: Find x in 6x + 22 = 0

Output:
6x + 22 = 0
6x = -22
x = -22 / 6
x = -11/3


Input: Find the solution to x^3 + 15/8x^2 + 11/16x  = 0

Output:
x^3 + 15/8x^2 + 11/16x  = 0
(x - -1/2)(x - 0)(x - -11/8) = 0
x - -1/2 = 0
x - 0 = 0
x - -11/8 = 0
x = -1/2
x = 0
x = -11/8


Input:
Solve the system:
5x + 7y = 56/9
2x + 10y = 80/9

Output:
5x + 7y = 56/9
2x + 10y = 80/9

Using elimination
2*(5x + 7y = 56/9)
5*(2x + 10y = 80/9)
10x + 14y = 112/9
10x + 50y = 400/9
Subtract equations
-36y = -32
y = -32/-36
y = 8/9

Substitute y
5x + 7(8/9) = 56/9
5x = 0
x = 0/5
x = 0


Input:
Find x and y such that
2x + 2y = -67/9
2x + 10y = -247/9

Output:
2x + 2y = -67/9
2x + 10y = -247/9

Using elimination
2*(2x + 2y = -67/9)
2*(2x + 10y = -247/9)
4x + 4y = -134/9
4x + 20y = -494/9
Subtract equations
-16y = 40
y = 40/-16
y = -5/2

Substitute y
2x + 2(-5/2) = -67/9
2x = -22/9
x = -22/9/2
x = -11/9


Input: Determine x in x^2 - 87/35x + 54/35 = 0

Output:
x^2 - 87/35x + 54/35 = 0
(x - 6/5)(x - 9/7) = 0
x - 6/5 = 0  or  x - 9/7 = 0
x = 6/5
x = 9/7


Input: What value of x satisfies x^3 - 24/5x^2 + 16/5x  = 0

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


Input: Find the solution to x^3 - 40/21x^2 - 199/21x + 110/7 = 0

Output:
x^3 - 40/21x^2 - 199/21x + 110/7 = 0
(x - 10/3)(x - -3)(x - 11/7) = 0
x - 10/3 = 0
x - -3 = 0
x - 11/7 = 0
x = 10/3
x = -3
x = 11/7


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

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


Input: Find x in x^2 + 77/15x - 38/5 = 0

Output:
x^2 + 77/15x - 38/5 = 0
(x - -19/3)(x - 6/5) = 0
x - -19/3 = 0  or  x - 6/5 = 0
x = -19/3
x = 6/5


Input: Find x for x^3 + 1151/360x^2 - 209/120x - 21/20 = 0

Output:
x^3 + 1151/360x^2 - 209/120x - 21/20 = 0
(x - -3/8)(x - 7/9)(x - -18/5) = 0
x - -3/8 = 0
x - 7/9 = 0
x - -18/5 = 0
x = -3/8
x = 7/9
x = -18/5


Input: Solve the equation x^2 - 81/14x - 90/7 = 0

Output:
x^2 - 81/14x - 90/7 = 0
(x - 15/2)(x - -12/7) = 0
x - 15/2 = 0  or  x - -12/7 = 0
x = 15/2
x = -12/7


Input:
Solve the system:
4x + 2y = 90/7
6x + 9y = 153/7

Output:
4x + 2y = 90/7
6x + 9y = 153/7

Using elimination
6*(4x + 2y = 90/7)
4*(6x + 9y = 153/7)
24x + 12y = 540/7
24x + 36y = 612/7
Subtract equations
-24y = -72/7
y = -72/7/-24
y = 3/7

Substitute y
4x + 2(3/7) = 90/7
4x = 12
x = 12/4
x = 3


Input: What value of x satisfies x^2 - 2x + 1 = 0

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


Input: Find x for x^2 - 26/15x + 8/15 = 0

Output:
x^2 - 26/15x + 8/15 = 0
(x - 2/5)(x - 4/3) = 0
x - 2/5 = 0  or  x - 4/3 = 0
x = 2/5
x = 4/3


Input: Compute the solution of x^2 - 13/5x + 22/25 = 0

Output:
x^2 - 13/5x + 22/25 = 0
(x - 11/5)(x - 2/5) = 0
x - 11/5 = 0  or  x - 2/5 = 0
x = 11/5
x = 2/5


Input: What value of x satisfies 6x - 54/5 = 0

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


Input: Determine x in x^3 - 4x^2 - 185/4x - 57 = 0

Output:
x^3 - 4x^2 - 185/4x - 57 = 0
(x - 19/2)(x - -3/2)(x - -4) = 0
x - 19/2 = 0
x - -3/2 = 0
x - -4 = 0
x = 19/2
x = -3/2
x = -4


Input: Find the solution to x^2 - 4/3x - 11/12 = 0

Output:
x^2 - 4/3x - 11/12 = 0
(x - 11/6)(x - -1/2) = 0
x - 11/6 = 0  or  x - -1/2 = 0
x = 11/6
x = -1/2


Input: Find x for 6x + 102/7 = 0

Output:
6x + 102/7 = 0
6x = -102/7
x = -102/7 / 6
x = -17/7


Input: Compute the solution of x^3 - 26/5x^2 + 12/5x + 1512/125 = 0

Output:
x^3 - 26/5x^2 + 12/5x + 1512/125 = 0
(x - -6/5)(x - 14/5)(x - 18/5) = 0
x - -6/5 = 0
x - 14/5 = 0
x - 18/5 = 0
x = -6/5
x = 14/5
x = 18/5


Input: Find the solution to x^3 + 113/24x^2 + 2x - 10/3 = 0

Output:
x^3 + 113/24x^2 + 2x - 10/3 = 0
(x - 5/8)(x - -4)(x - -4/3) = 0
x - 5/8 = 0
x - -4 = 0
x - -4/3 = 0
x = 5/8
x = -4
x = -4/3


Input: What value of x satisfies 7x + 21/4 = 0

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


Input: Find x for x^3 + 203/9x^2 + 1420/27x + 800/27 = 0

Output:
x^3 + 203/9x^2 + 1420/27x + 800/27 = 0
(x - -8/9)(x - -5/3)(x - -20) = 0
x - -8/9 = 0
x - -5/3 = 0
x - -20 = 0
x = -8/9
x = -5/3
x = -20


Input: Solve x^3 + 21/2x^2 + 1739/64x + 1197/64 = 0

Output:
x^3 + 21/2x^2 + 1739/64x + 1197/64 = 0
(x - -19/8)(x - -7)(x - -9/8) = 0
x - -19/8 = 0
x - -7 = 0
x - -9/8 = 0
x = -19/8
x = -7
x = -9/8


Input: What value of x satisfies x^2 + 23/7x + 16/7 = 0

Output:
x^2 + 23/7x + 16/7 = 0
(x - -16/7)(x - -1) = 0
x - -16/7 = 0  or  x - -1 = 0
x = -16/7
x = -1


Input: Solve quickly: x^3 + 13/3x^2 - 10/3x  = 0

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


Input: Find x for x^3 + 15/8x^2 - 225/16x + 125/16 = 0

Output:
x^3 + 15/8x^2 - 225/16x + 125/16 = 0
(x - -5)(x - 5/8)(x - 5/2) = 0
x - -5 = 0
x - 5/8 = 0
x - 5/2 = 0
x = -5
x = 5/8
x = 5/2


Input:
Solve the equations:
5x + 5y = 155/8
8x + 9y = 34

Output:
5x + 5y = 155/8
8x + 9y = 34

Using elimination
8*(5x + 5y = 155/8)
5*(8x + 9y = 34)
40x + 40y = 155
40x + 45y = 170
Subtract equations
-5y = -15
y = -15/-5
y = 3

Substitute y
5x + 5(3) = 155/8
5x = 35/8
x = 35/8/5
x = 7/8


Input:
Solve the system:
5x + 7y = -19/2
3x + 9y = -21/2

Output:
5x + 7y = -19/2
3x + 9y = -21/2

Using elimination
3*(5x + 7y = -19/2)
5*(3x + 9y = -21/2)
15x + 21y = -57/2
15x + 45y = -105/2
Subtract equations
-24y = 24
y = 24/-24
y = -1

Substitute y
5x + 7(-1) = -19/2
5x = -5/2
x = -5/2/5
x = -1/2


Input: Solve 8x + 72/5 = 0

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


Input: What value of x satisfies x^3 - 17/2x^2 + 19x - 15/2 = 0

Output:
x^3 - 17/2x^2 + 19x - 15/2 = 0
(x - 1/2)(x - 3)(x - 5) = 0
x - 1/2 = 0
x - 3 = 0
x - 5 = 0
x = 1/2
x = 3
x = 5


Input:
Find x and y such that
3x + 2y = 17/4
5x + 7y = 181/24

Output:
3x + 2y = 17/4
5x + 7y = 181/24

Using elimination
5*(3x + 2y = 17/4)
3*(5x + 7y = 181/24)
15x + 10y = 85/4
15x + 21y = 181/8
Subtract equations
-11y = -11/8
y = -11/8/-11
y = 1/8

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


Input: Determine x in 6x - 57/4 = 0

Output:
6x - 57/4 = 0
6x = 57/4
x = 57/4 / 6
x = 19/8


Input:
Solve simultaneously:
1x + 10y = 0
6x + 3y = 57/2

Output:
1x + 10y = 0
6x + 3y = 57/2

Using elimination
6*(1x + 10y = 0)
1*(6x + 3y = 57/2)
6x + 60y = 0
6x + 3y = 57/2
Subtract equations
57y = -57/2
y = -57/2/57
y = -1/2

Substitute y
1x + 10(-1/2) = 0
1x = 5
x = 5/1
x = 5


Input: Determine x in x^2 + 157/70x + 44/35 = 0

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


Input: What value of x satisfies x^3 - 5/7x^2 - 554/49x - 360/49 = 0

Output:
x^3 - 5/7x^2 - 554/49x - 360/49 = 0
(x - 4)(x - -18/7)(x - -5/7) = 0
x - 4 = 0
x - -18/7 = 0
x - -5/7 = 0
x = 4
x = -18/7
x = -5/7


Input: Find x for x^3 + 137/24x^2 + 1039/96x + 1309/192 = 0

Output:
x^3 + 137/24x^2 + 1039/96x + 1309/192 = 0
(x - -11/6)(x - -17/8)(x - -7/4) = 0
x - -11/6 = 0
x - -17/8 = 0
x - -7/4 = 0
x = -11/6
x = -17/8
x = -7/4


Input: Find x for x^3 + 95/6x^2 + 109/3x - 13/2 = 0

Output:
x^3 + 95/6x^2 + 109/3x - 13/2 = 0
(x - -3)(x - -13)(x - 1/6) = 0
x - -3 = 0
x - -13 = 0
x - 1/6 = 0
x = -3
x = -13
x = 1/6


Input: Determine x in x^3 + 134/15x^2 - 843/5x + 1292/3 = 0

Output:
x^3 + 134/15x^2 - 843/5x + 1292/3 = 0
(x - -19)(x - 20/3)(x - 17/5) = 0
x - -19 = 0
x - 20/3 = 0
x - 17/5 = 0
x = -19
x = 20/3
x = 17/5


Input: Solve the equation 3x + 57/2 = 0

Output:
3x + 57/2 = 0
3x = -57/2
x = -57/2 / 3
x = -19/2


Input: Solve the equation x^2 + 1x - 6 = 0

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


Input: Solve x^3 + 29/30x^2 - 1061/75x + 364/25 = 0

Output:
x^3 + 29/30x^2 - 1061/75x + 364/25 = 0
(x - 13/10)(x - 12/5)(x - -14/3) = 0
x - 13/10 = 0
x - 12/5 = 0
x - -14/3 = 0
x = 13/10
x = 12/5
x = -14/3


Input: Find x for 8x + 76/5 = 0

Output:
8x + 76/5 = 0
8x = -76/5
x = -76/5 / 8
x = -19/10


Input: Solve x^3 - 241/28x^2 - 815/28x + 429/14 = 0

Output:
x^3 - 241/28x^2 - 815/28x + 429/14 = 0
(x - -13/4)(x - 11)(x - 6/7) = 0
x - -13/4 = 0
x - 11 = 0
x - 6/7 = 0
x = -13/4
x = 11
x = 6/7


Input: Solve x^3 - 47/5x^2 + 343/20x + 221/20 = 0

Output:
x^3 - 47/5x^2 + 343/20x + 221/20 = 0
(x - 17/5)(x - 13/2)(x - -1/2) = 0
x - 17/5 = 0
x - 13/2 = 0
x - -1/2 = 0
x = 17/5
x = 13/2
x = -1/2


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

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


Input: Find x for 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: Compute the solution of 6x - 39 = 0

Output:
6x - 39 = 0
6x = 39
x = 39 / 6
x = 13/2


Input:
Solve the system:
9x + 7y = 157/4
2x + 8y = 2/3

Output:
9x + 7y = 157/4
2x + 8y = 2/3

Using elimination
2*(9x + 7y = 157/4)
9*(2x + 8y = 2/3)
18x + 14y = 157/2
18x + 72y = 6
Subtract equations
-58y = 145/2
y = 145/2/-58
y = -5/4

Substitute y
9x + 7(-5/4) = 157/4
9x = 48
x = 48/9
x = 16/3


Input:
Solve simultaneously:
6x + 3y = 231/4
6x + 4y = 307/4

Output:
6x + 3y = 231/4
6x + 4y = 307/4

Using elimination
6*(6x + 3y = 231/4)
6*(6x + 4y = 307/4)
36x + 18y = 693/2
36x + 24y = 921/2
Subtract equations
-6y = -114
y = -114/-6
y = 19

Substitute y
6x + 3(19) = 231/4
6x = 3/4
x = 3/4/6
x = 1/8


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

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


Input: Find x in x^3 + 13/70x^2 - 157/350x - 3/25 = 0

Output:
x^3 + 13/70x^2 - 157/350x - 3/25 = 0
(x - -3/5)(x - 7/10)(x - -2/7) = 0
x - -3/5 = 0
x - 7/10 = 0
x - -2/7 = 0
x = -3/5
x = 7/10
x = -2/7


Input:
Solve simultaneously:
8x + 2y = 179/6
4x + 4y = 83/3

Output:
8x + 2y = 179/6
4x + 4y = 83/3

Using elimination
4*(8x + 2y = 179/6)
8*(4x + 4y = 83/3)
32x + 8y = 358/3
32x + 32y = 664/3
Subtract equations
-24y = -102
y = -102/-24
y = 17/4

Substitute y
8x + 2(17/4) = 179/6
8x = 64/3
x = 64/3/8
x = 8/3


Input: Solve quickly: x^2 - 29/10x - 63/25 = 0

Output:
x^2 - 29/10x - 63/25 = 0
(x - 18/5)(x - -7/10) = 0
x - 18/5 = 0  or  x - -7/10 = 0
x = 18/5
x = -7/10


Input: What value of x satisfies 8x + 16 = 0

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


Input:
Solve simultaneously:
4x + 2y = 9/4
1x + 6y = 5/4

Output:
4x + 2y = 9/4
1x + 6y = 5/4

Using elimination
1*(4x + 2y = 9/4)
4*(1x + 6y = 5/4)
4x + 2y = 9/4
4x + 24y = 5
Subtract equations
-22y = -11/4
y = -11/4/-22
y = 1/8

Substitute y
4x + 2(1/8) = 9/4
4x = 2
x = 2/4
x = 1/2


Input:
Solve the system:
5x + 7y = 23/2
7x + 4y = 8/5

Output:
5x + 7y = 23/2
7x + 4y = 8/5

Using elimination
7*(5x + 7y = 23/2)
5*(7x + 4y = 8/5)
35x + 49y = 161/2
35x + 20y = 8
Subtract equations
29y = 145/2
y = 145/2/29
y = 5/2

Substitute y
5x + 7(5/2) = 23/2
5x = -6
x = -6/5
x = -6/5


Input: Solve the equation x^2 - 17/6x + 5/6 = 0

Output:
x^2 - 17/6x + 5/6 = 0
(x - 1/3)(x - 5/2) = 0
x - 1/3 = 0  or  x - 5/2 = 0
x = 1/3
x = 5/2


Input: Solve the equation 6x + 120/7 = 0

Output:
6x + 120/7 = 0
6x = -120/7
x = -120/7 / 6
x = -20/7


Input: Find x for x^2 - 13/3x + 10/3 = 0

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


Input: Find the solution to x^2 + 35/12x - 19/24 = 0

Output:
x^2 + 35/12x - 19/24 = 0
(x - -19/6)(x - 1/4) = 0
x - -19/6 = 0  or  x - 1/4 = 0
x = -19/6
x = 1/4


Input:
Solve simultaneously:
6x + 2y = 102
6x + 3y = 99

Output:
6x + 2y = 102
6x + 3y = 99

Using elimination
6*(6x + 2y = 102)
6*(6x + 3y = 99)
36x + 12y = 612
36x + 18y = 594
Subtract equations
-6y = 18
y = 18/-6
y = -3

Substitute y
6x + 2(-3) = 102
6x = 108
x = 108/6
x = 18


Input: Determine x in 10x - 5 = 0

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


Input: Find x for x^2 - 13/20x - 21/20 = 0

Output:
x^2 - 13/20x - 21/20 = 0
(x - 7/5)(x - -3/4) = 0
x - 7/5 = 0  or  x - -3/4 = 0
x = 7/5
x = -3/4


Input: Determine x in x^3 - 35/4x^2 + 109/8x + 187/8 = 0

Output:
x^3 - 35/4x^2 + 109/8x + 187/8 = 0
(x - 11/2)(x - 17/4)(x - -1) = 0
x - 11/2 = 0
x - 17/4 = 0
x - -1 = 0
x = 11/2
x = 17/4
x = -1


Input: Solve x^2 - 17/10x + 13/25 = 0

Output:
x^2 - 17/10x + 13/25 = 0
(x - 13/10)(x - 2/5) = 0
x - 13/10 = 0  or  x - 2/5 = 0
x = 13/10
x = 2/5


Input:
Solve simultaneously:
1x + 5y = 187/5
10x + 5y = 59

Output:
1x + 5y = 187/5
10x + 5y = 59

Using elimination
10*(1x + 5y = 187/5)
1*(10x + 5y = 59)
10x + 50y = 374
10x + 5y = 59
Subtract equations
45y = 315
y = 315/45
y = 7

Substitute y
1x + 5(7) = 187/5
1x = 12/5
x = 12/5/1
x = 12/5


Input:
Solve the system:
6x + 8y = -22
1x + 3y = -88/9

Output:
6x + 8y = -22
1x + 3y = -88/9

Using elimination
1*(6x + 8y = -22)
6*(1x + 3y = -88/9)
6x + 8y = -22
6x + 18y = -176/3
Subtract equations
-10y = 110/3
y = 110/3/-10
y = -11/3

Substitute y
6x + 8(-11/3) = -22
6x = 22/3
x = 22/3/6
x = 11/9


Input:
Solve simultaneously:
2x + 1y = 5
4x + 9y = 10

Output:
2x + 1y = 5
4x + 9y = 10

Using elimination
4*(2x + 1y = 5)
2*(4x + 9y = 10)
8x + 4y = 20
8x + 18y = 20
Subtract equations
-14y = 0
y = 0/-14
y = 0

Substitute y
2x + 1(0) = 5
2x = 5
x = 5/2
x = 5/2


Input: Find x for x^3 + 6x^2 + 17/4x - 15/4 = 0

Output:
x^3 + 6x^2 + 17/4x - 15/4 = 0
(x - -3/2)(x - -5)(x - 1/2) = 0
x - -3/2 = 0
x - -5 = 0
x - 1/2 = 0
x = -3/2
x = -5
x = 1/2


Input: Determine x in 10x - 32 = 0

Output:
10x - 32 = 0
10x = 32
x = 32 / 10
x = 16/5


Input: What value of x satisfies x^3 - 141/20x^2 + 127/20x + 39/2 = 0

Output:
x^3 - 141/20x^2 + 127/20x + 39/2 = 0
(x - 13/4)(x - -6/5)(x - 5) = 0
x - 13/4 = 0
x - -6/5 = 0
x - 5 = 0
x = 13/4
x = -6/5
x = 5


Input:
Solve simultaneously:
4x + 5y = -99/2
6x + 2y = -33

Output:
4x + 5y = -99/2
6x + 2y = -33

Using elimination
6*(4x + 5y = -99/2)
4*(6x + 2y = -33)
24x + 30y = -297
24x + 8y = -132
Subtract equations
22y = -165
y = -165/22
y = -15/2

Substitute y
4x + 5(-15/2) = -99/2
4x = -12
x = -12/4
x = -3


Input: What value of x satisfies x^3 + 115/12x^2 + 359/12x + 91/3 = 0

Output:
x^3 + 115/12x^2 + 359/12x + 91/3 = 0
(x - -4)(x - -13/4)(x - -7/3) = 0
x - -4 = 0
x - -13/4 = 0
x - -7/3 = 0
x = -4
x = -13/4
x = -7/3


Input:
Solve simultaneously:
9x + 6y = 234/5
3x + 7y = 123/5

Output:
9x + 6y = 234/5
3x + 7y = 123/5

Using elimination
3*(9x + 6y = 234/5)
9*(3x + 7y = 123/5)
27x + 18y = 702/5
27x + 63y = 1107/5
Subtract equations
-45y = -81
y = -81/-45
y = 9/5

Substitute y
9x + 6(9/5) = 234/5
9x = 36
x = 36/9
x = 4


Input:
Solve simultaneously:
7x + 2y = 438/5
3x + 7y = 243/5

Output:
7x + 2y = 438/5
3x + 7y = 243/5

Using elimination
3*(7x + 2y = 438/5)
7*(3x + 7y = 243/5)
21x + 6y = 1314/5
21x + 49y = 1701/5
Subtract equations
-43y = -387/5
y = -387/5/-43
y = 9/5

Substitute y
7x + 2(9/5) = 438/5
7x = 84
x = 84/7
x = 12


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

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


Input:
Solve simultaneously:
3x + 7y = -311/30
3x + 3y = -77/10

Output:
3x + 7y = -311/30
3x + 3y = -77/10

Using elimination
3*(3x + 7y = -311/30)
3*(3x + 3y = -77/10)
9x + 21y = -311/10
9x + 9y = -231/10
Subtract equations
12y = -8
y = -8/12
y = -2/3

Substitute y
3x + 7(-2/3) = -311/30
3x = -57/10
x = -57/10/3
x = -19/10


Input:
Solve the equations:
8x + 3y = -26
5x + 8y = 37/3

Output:
8x + 3y = -26
5x + 8y = 37/3

Using elimination
5*(8x + 3y = -26)
8*(5x + 8y = 37/3)
40x + 15y = -130
40x + 64y = 296/3
Subtract equations
-49y = -686/3
y = -686/3/-49
y = 14/3

Substitute y
8x + 3(14/3) = -26
8x = -40
x = -40/8
x = -5


Input: What value of x satisfies 10x  = 0

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


Input: Find the solution to 6x - 30/7 = 0

Output:
6x - 30/7 = 0
6x = 30/7
x = 30/7 / 6
x = 5/7


Input: Compute the solution of x^3 + 5/7x^2   = 0

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


Input: Determine x in x^3 - 7/9x^2 - 100/27x + 100/27 = 0

Output:
x^3 - 7/9x^2 - 100/27x + 100/27 = 0
(x - 5/3)(x - 10/9)(x - -2) = 0
x - 5/3 = 0
x - 10/9 = 0
x - -2 = 0
x = 5/3
x = 10/9
x = -2


Input: Compute the solution of x^2 + 101/18x - 52/9 = 0

Output:
x^2 + 101/18x - 52/9 = 0
(x - -13/2)(x - 8/9) = 0
x - -13/2 = 0  or  x - 8/9 = 0
x = -13/2
x = 8/9


Input: Determine x in x^2 - 25/2x + 77/2 = 0

Output:
x^2 - 25/2x + 77/2 = 0
(x - 11/2)(x - 7) = 0
x - 11/2 = 0  or  x - 7 = 0
x = 11/2
x = 7


Input: What value of x satisfies x^3 + 1/8x^2 - 61/32x + 15/64 = 0

Output:
x^3 + 1/8x^2 - 61/32x + 15/64 = 0
(x - 5/4)(x - -3/2)(x - 1/8) = 0
x - 5/4 = 0
x - -3/2 = 0
x - 1/8 = 0
x = 5/4
x = -3/2
x = 1/8


Input: Solve x^3 - 31/18x^2 - 181/225x + 133/150 = 0

Output:
x^3 - 31/18x^2 - 181/225x + 133/150 = 0
(x - -7/9)(x - 19/10)(x - 3/5) = 0
x - -7/9 = 0
x - 19/10 = 0
x - 3/5 = 0
x = -7/9
x = 19/10
x = 3/5


Input:
Find x and y such that
3x + 3y = 72/7
5x + 9y = 160/7

Output:
3x + 3y = 72/7
5x + 9y = 160/7

Using elimination
5*(3x + 3y = 72/7)
3*(5x + 9y = 160/7)
15x + 15y = 360/7
15x + 27y = 480/7
Subtract equations
-12y = -120/7
y = -120/7/-12
y = 10/7

Substitute y
3x + 3(10/7) = 72/7
3x = 6
x = 6/3
x = 2


Input: Find x for x^2 - 47/9x - 14/3 = 0

Output:
x^2 - 47/9x - 14/3 = 0
(x - -7/9)(x - 6) = 0
x - -7/9 = 0  or  x - 6 = 0
x = -7/9
x = 6


Input: Solve 2x + 13/5 = 0

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


Input:
Solve the equations:
6x + 7y = 43/6
2x + 8y = 10/3

Output:
6x + 7y = 43/6
2x + 8y = 10/3

Using elimination
2*(6x + 7y = 43/6)
6*(2x + 8y = 10/3)
12x + 14y = 43/3
12x + 48y = 20
Subtract equations
-34y = -17/3
y = -17/3/-34
y = 1/6

Substitute y
6x + 7(1/6) = 43/6
6x = 6
x = 6/6
x = 1


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

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

Using elimination
1*(2x + 10y = -1)
2*(1x + 2y = 10)
2x + 10y = -1
2x + 4y = 20
Subtract equations
6y = -21
y = -21/6
y = -7/2

Substitute y
2x + 10(-7/2) = -1
2x = 34
x = 34/2
x = 17


Input: Solve 1x + 13/9 = 0

Output:
1x + 13/9 = 0
1x = -13/9
x = -13/9 / 1
x = -13/9


Input:
Solve simultaneously:
10x + 9y = 23/8
9x + 9y = 27/8

Output:
10x + 9y = 23/8
9x + 9y = 27/8

Using elimination
9*(10x + 9y = 23/8)
10*(9x + 9y = 27/8)
90x + 81y = 207/8
90x + 90y = 135/4
Subtract equations
-9y = -63/8
y = -63/8/-9
y = 7/8

Substitute y
10x + 9(7/8) = 23/8
10x = -5
x = -5/10
x = -1/2


Input: Find x in x^3 - 881/210x^2 - 1/7x + 323/30 = 0

Output:
x^3 - 881/210x^2 - 1/7x + 323/30 = 0
(x - -7/5)(x - 17/7)(x - 19/6) = 0
x - -7/5 = 0
x - 17/7 = 0
x - 19/6 = 0
x = -7/5
x = 17/7
x = 19/6


Input:
Solve the system:
1x + 1y = 29/7
10x + 5y = 150/7

Output:
1x + 1y = 29/7
10x + 5y = 150/7

Using elimination
10*(1x + 1y = 29/7)
1*(10x + 5y = 150/7)
10x + 10y = 290/7
10x + 5y = 150/7
Subtract equations
5y = 20
y = 20/5
y = 4

Substitute y
1x + 1(4) = 29/7
1x = 1/7
x = 1/7/1
x = 1/7


Input: Solve the equation 1x - 5/4 = 0

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


Input: Solve 6x + 9 = 0

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


Input: What value of x satisfies x^2 - 13/20x - 18/5 = 0

Output:
x^2 - 13/20x - 18/5 = 0
(x - 9/4)(x - -8/5) = 0
x - 9/4 = 0  or  x - -8/5 = 0
x = 9/4
x = -8/5


Input:
Solve simultaneously:
7x + 3y = 170
5x + 1y = 110

Output:
7x + 3y = 170
5x + 1y = 110

Using elimination
5*(7x + 3y = 170)
7*(5x + 1y = 110)
35x + 15y = 850
35x + 7y = 770
Subtract equations
8y = 80
y = 80/8
y = 10

Substitute y
7x + 3(10) = 170
7x = 140
x = 140/7
x = 20


Input: Find the solution to x^2 + 43/7x + 6/7 = 0

Output:
x^2 + 43/7x + 6/7 = 0
(x - -6)(x - -1/7) = 0
x - -6 = 0  or  x - -1/7 = 0
x = -6
x = -1/7


Input: Determine x in 8x - 16/7 = 0

Output:
8x - 16/7 = 0
8x = 16/7
x = 16/7 / 8
x = 2/7


Input: Find x in x^2 - 46/21x - 80/21 = 0

Output:
x^2 - 46/21x - 80/21 = 0
(x - 10/3)(x - -8/7) = 0
x - 10/3 = 0  or  x - -8/7 = 0
x = 10/3
x = -8/7


Input:
Solve the system:
3x + 6y = 19
5x + 4y = 29/3

Output:
3x + 6y = 19
5x + 4y = 29/3

Using elimination
5*(3x + 6y = 19)
3*(5x + 4y = 29/3)
15x + 30y = 95
15x + 12y = 29
Subtract equations
18y = 66
y = 66/18
y = 11/3

Substitute y
3x + 6(11/3) = 19
3x = -3
x = -3/3
x = -1


Input: Find x for x^2 + 46/5x + 96/5 = 0

Output:
x^2 + 46/5x + 96/5 = 0
(x - -16/5)(x - -6) = 0
x - -16/5 = 0  or  x - -6 = 0
x = -16/5
x = -6


Input: Compute the solution of x^3 - 23/3x^2 - 41x + 143/3 = 0

Output:
x^3 - 23/3x^2 - 41x + 143/3 = 0
(x - 1)(x - 11)(x - -13/3) = 0
x - 1 = 0
x - 11 = 0
x - -13/3 = 0
x = 1
x = 11
x = -13/3


Input:
Solve the equations:
1x + 7y = -149/12
5x + 7y = -157/12

Output:
1x + 7y = -149/12
5x + 7y = -157/12

Using elimination
5*(1x + 7y = -149/12)
1*(5x + 7y = -157/12)
5x + 35y = -745/12
5x + 7y = -157/12
Subtract equations
28y = -49
y = -49/28
y = -7/4

Substitute y
1x + 7(-7/4) = -149/12
1x = -1/6
x = -1/6/1
x = -1/6


Input:
Find x and y such that
2x + 6y = 198/7
6x + 4y = 410/21

Output:
2x + 6y = 198/7
6x + 4y = 410/21

Using elimination
6*(2x + 6y = 198/7)
2*(6x + 4y = 410/21)
12x + 36y = 1188/7
12x + 8y = 820/21
Subtract equations
28y = 392/3
y = 392/3/28
y = 14/3

Substitute y
2x + 6(14/3) = 198/7
2x = 2/7
x = 2/7/2
x = 1/7


Input: Solve the equation x^3 + 3x^2 - 9/16x - 55/16 = 0

Output:
x^3 + 3x^2 - 9/16x - 55/16 = 0
(x - -5/4)(x - -11/4)(x - 1) = 0
x - -5/4 = 0
x - -11/4 = 0
x - 1 = 0
x = -5/4
x = -11/4
x = 1


Input: Solve x^3 + 119/24x^2 - 1535/144x + 175/36 = 0

Output:
x^3 + 119/24x^2 - 1535/144x + 175/36 = 0
(x - 5/6)(x - -20/3)(x - 7/8) = 0
x - 5/6 = 0
x - -20/3 = 0
x - 7/8 = 0
x = 5/6
x = -20/3
x = 7/8


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

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


Input: Solve quickly: x^2 - 41/8x - 21/4 = 0

Output:
x^2 - 41/8x - 21/4 = 0
(x - -7/8)(x - 6) = 0
x - -7/8 = 0  or  x - 6 = 0
x = -7/8
x = 6


Input:
Solve the system:
6x + 7y = -105
10x + 8y = -1258/7

Output:
6x + 7y = -105
10x + 8y = -1258/7

Using elimination
10*(6x + 7y = -105)
6*(10x + 8y = -1258/7)
60x + 70y = -1050
60x + 48y = -7548/7
Subtract equations
22y = 198/7
y = 198/7/22
y = 9/7

Substitute y
6x + 7(9/7) = -105
6x = -114
x = -114/6
x = -19


Input: Compute the solution of x^2 + 39/20x + 9/10 = 0

Output:
x^2 + 39/20x + 9/10 = 0
(x - -3/4)(x - -6/5) = 0
x - -3/4 = 0  or  x - -6/5 = 0
x = -3/4
x = -6/5


Input: Solve quickly: 6x - 11 = 0

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


Input: Find x for x^2 - 46/5x - 8 = 0

Output:
x^2 - 46/5x - 8 = 0
(x - -4/5)(x - 10) = 0
x - -4/5 = 0  or  x - 10 = 0
x = -4/5
x = 10


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

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


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

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


Input:
Solve the equations:
4x + 3y = -1/5
10x + 2y = -8/5

Output:
4x + 3y = -1/5
10x + 2y = -8/5

Using elimination
10*(4x + 3y = -1/5)
4*(10x + 2y = -8/5)
40x + 30y = -2
40x + 8y = -32/5
Subtract equations
22y = 22/5
y = 22/5/22
y = 1/5

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


Input:
Find x and y such that
3x + 8y = -18
1x + 9y = -169/6

Output:
3x + 8y = -18
1x + 9y = -169/6

Using elimination
1*(3x + 8y = -18)
3*(1x + 9y = -169/6)
3x + 8y = -18
3x + 27y = -169/2
Subtract equations
-19y = 133/2
y = 133/2/-19
y = -7/2

Substitute y
3x + 8(-7/2) = -18
3x = 10
x = 10/3
x = 10/3


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

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


Input: Solve 5x - 35 = 0

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


Input:
Solve the system:
4x + 7y = -70/3
6x + 3y = -5

Output:
4x + 7y = -70/3
6x + 3y = -5

Using elimination
6*(4x + 7y = -70/3)
4*(6x + 3y = -5)
24x + 42y = -140
24x + 12y = -20
Subtract equations
30y = -120
y = -120/30
y = -4

Substitute y
4x + 7(-4) = -70/3
4x = 14/3
x = 14/3/4
x = 7/6


Input: Solve x^3 - 31/3x^2 + 535/36x + 221/36 = 0

Output:
x^3 - 31/3x^2 + 535/36x + 221/36 = 0
(x - -1/3)(x - 13/6)(x - 17/2) = 0
x - -1/3 = 0
x - 13/6 = 0
x - 17/2 = 0
x = -1/3
x = 13/6
x = 17/2


Input: What value of x satisfies x^3 - 77/20x^2 - 49/10x + 68/5 = 0

Output:
x^3 - 77/20x^2 - 49/10x + 68/5 = 0
(x - 8/5)(x - 17/4)(x - -2) = 0
x - 8/5 = 0
x - 17/4 = 0
x - -2 = 0
x = 8/5
x = 17/4
x = -2


Input:
Solve simultaneously:
7x + 4y = -72/5
7x + 10y = -21

Output:
7x + 4y = -72/5
7x + 10y = -21

Using elimination
7*(7x + 4y = -72/5)
7*(7x + 10y = -21)
49x + 28y = -504/5
49x + 70y = -147
Subtract equations
-42y = 231/5
y = 231/5/-42
y = -11/10

Substitute y
7x + 4(-11/10) = -72/5
7x = -10
x = -10/7
x = -10/7


Input: What value of x satisfies 1x - 16/7 = 0

Output:
1x - 16/7 = 0
1x = 16/7
x = 16/7 / 1
x = 16/7


Input: Find x for 5x - 25/3 = 0

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


Input: What value of x satisfies x^3 + 55/18x^2 - 137/18x - 5 = 0

Output:
x^3 + 55/18x^2 - 137/18x - 5 = 0
(x - 2)(x - -5/9)(x - -9/2) = 0
x - 2 = 0
x - -5/9 = 0
x - -9/2 = 0
x = 2
x = -5/9
x = -9/2


Input: Compute the solution of x^2 + 57/20x - 27/8 = 0

Output:
x^2 + 57/20x - 27/8 = 0
(x - -15/4)(x - 9/10) = 0
x - -15/4 = 0  or  x - 9/10 = 0
x = -15/4
x = 9/10


Input: Solve the equation 5x - 45/8 = 0

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


Input: Find x for 5x - 60/7 = 0

Output:
5x - 60/7 = 0
5x = 60/7
x = 60/7 / 5
x = 12/7


Input:
Find x and y such that
9x + 6y = -99/4
7x + 8y = -18

Output:
9x + 6y = -99/4
7x + 8y = -18

Using elimination
7*(9x + 6y = -99/4)
9*(7x + 8y = -18)
63x + 42y = -693/4
63x + 72y = -162
Subtract equations
-30y = -45/4
y = -45/4/-30
y = 3/8

Substitute y
9x + 6(3/8) = -99/4
9x = -27
x = -27/9
x = -3


Input: Solve quickly: 1x + 2/3 = 0

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


Input: Find x in x^3 - 259/20x^2 + 601/20x - 11/2 = 0

Output:
x^3 - 259/20x^2 + 601/20x - 11/2 = 0
(x - 1/5)(x - 11/4)(x - 10) = 0
x - 1/5 = 0
x - 11/4 = 0
x - 10 = 0
x = 1/5
x = 11/4
x = 10


Input: Find x in x^3 + 109/30x^2 - 38/15x - 21/2 = 0

Output:
x^3 + 109/30x^2 - 38/15x - 21/2 = 0
(x - 5/3)(x - -7/2)(x - -9/5) = 0
x - 5/3 = 0
x - -7/2 = 0
x - -9/5 = 0
x = 5/3
x = -7/2
x = -9/5


Input: What value of x satisfies x^3 + 41/40x^2 - 179/200x + 13/100 = 0

Output:
x^3 + 41/40x^2 - 179/200x + 13/100 = 0
(x - 2/5)(x - 1/5)(x - -13/8) = 0
x - 2/5 = 0
x - 1/5 = 0
x - -13/8 = 0
x = 2/5
x = 1/5
x = -13/8


Input: Find the solution to x^2 + 163/21x + 272/21 = 0

Output:
x^2 + 163/21x + 272/21 = 0
(x - -16/3)(x - -17/7) = 0
x - -16/3 = 0  or  x - -17/7 = 0
x = -16/3
x = -17/7


Input: Solve quickly: x^3 + 23/10x^2 - 2x + 3/10 = 0

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


Input: Find the solution to 9x + 135/7 = 0

Output:
9x + 135/7 = 0
9x = -135/7
x = -135/7 / 9
x = -15/7


Input: Solve quickly: x^3 - 233/60x^2 + 521/120x - 3/2 = 0

Output:
x^3 - 233/60x^2 + 521/120x - 3/2 = 0
(x - 4/5)(x - 9/4)(x - 5/6) = 0
x - 4/5 = 0
x - 9/4 = 0
x - 5/6 = 0
x = 4/5
x = 9/4
x = 5/6


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

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


Input: Determine x in 6x + 66 = 0

Output:
6x + 66 = 0
6x = -66
x = -66 / 6
x = -11


Input:
Solve the system:
4x + 3y = -22/3
5x + 10y = -65/3

Output:
4x + 3y = -22/3
5x + 10y = -65/3

Using elimination
5*(4x + 3y = -22/3)
4*(5x + 10y = -65/3)
20x + 15y = -110/3
20x + 40y = -260/3
Subtract equations
-25y = 50
y = 50/-25
y = -2

Substitute y
4x + 3(-2) = -22/3
4x = -4/3
x = -4/3/4
x = -1/3


Input:
Solve the system:
8x + 4y = -74/7
1x + 5y = -113/14

Output:
8x + 4y = -74/7
1x + 5y = -113/14

Using elimination
1*(8x + 4y = -74/7)
8*(1x + 5y = -113/14)
8x + 4y = -74/7
8x + 40y = -452/7
Subtract equations
-36y = 54
y = 54/-36
y = -3/2

Substitute y
8x + 4(-3/2) = -74/7
8x = -32/7
x = -32/7/8
x = -4/7


Input:
Find x and y such that
8x + 8y = -4/5
7x + 9y = 29/10

Output:
8x + 8y = -4/5
7x + 9y = 29/10

Using elimination
7*(8x + 8y = -4/5)
8*(7x + 9y = 29/10)
56x + 56y = -28/5
56x + 72y = 116/5
Subtract equations
-16y = -144/5
y = -144/5/-16
y = 9/5

Substitute y
8x + 8(9/5) = -4/5
8x = -76/5
x = -76/5/8
x = -19/10


Input: Solve the equation x^2 - 28/15x - 32/15 = 0

Output:
x^2 - 28/15x - 32/15 = 0
(x - 8/3)(x - -4/5) = 0
x - 8/3 = 0  or  x - -4/5 = 0
x = 8/3
x = -4/5


Input: What value of x satisfies x^2 - 8x - 9 = 0

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


Input: Solve quickly: 8x - 128 = 0

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


Input:
Solve simultaneously:
7x + 4y = -80/7
3x + 3y = -51/7

Output:
7x + 4y = -80/7
3x + 3y = -51/7

Using elimination
3*(7x + 4y = -80/7)
7*(3x + 3y = -51/7)
21x + 12y = -240/7
21x + 21y = -51
Subtract equations
-9y = 117/7
y = 117/7/-9
y = -13/7

Substitute y
7x + 4(-13/7) = -80/7
7x = -4
x = -4/7
x = -4/7


Input: Find x for x^3 + 4x^2 - 135/4x - 225/4 = 0

Output:
x^3 + 4x^2 - 135/4x - 225/4 = 0
(x - -15/2)(x - -3/2)(x - 5) = 0
x - -15/2 = 0
x - -3/2 = 0
x - 5 = 0
x = -15/2
x = -3/2
x = 5


Input: Solve quickly: 3x + 6 = 0

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


Input: Determine x in x^2 - 17/5x - 99/20 = 0

Output:
x^2 - 17/5x - 99/20 = 0
(x - -11/10)(x - 9/2) = 0
x - -11/10 = 0  or  x - 9/2 = 0
x = -11/10
x = 9/2


Input:
Solve simultaneously:
8x + 4y = -200/7
2x + 4y = -86/7

Output:
8x + 4y = -200/7
2x + 4y = -86/7

Using elimination
2*(8x + 4y = -200/7)
8*(2x + 4y = -86/7)
16x + 8y = -400/7
16x + 32y = -688/7
Subtract equations
-24y = 288/7
y = 288/7/-24
y = -12/7

Substitute y
8x + 4(-12/7) = -200/7
8x = -152/7
x = -152/7/8
x = -19/7


Input:
Find x and y such that
9x + 1y = -157/15
2x + 3y = -7/5

Output:
9x + 1y = -157/15
2x + 3y = -7/5

Using elimination
2*(9x + 1y = -157/15)
9*(2x + 3y = -7/5)
18x + 2y = -314/15
18x + 27y = -63/5
Subtract equations
-25y = -25/3
y = -25/3/-25
y = 1/3

Substitute y
9x + 1(1/3) = -157/15
9x = -54/5
x = -54/5/9
x = -6/5


Input: Solve 3x - 9/2 = 0

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


Input: Solve the equation 10x + 20/7 = 0

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


Input: Find x for x^2 - 37/9x + 38/9 = 0

Output:
x^2 - 37/9x + 38/9 = 0
(x - 19/9)(x - 2) = 0
x - 19/9 = 0  or  x - 2 = 0
x = 19/9
x = 2


Input: Find the solution to x^3 + 487/140x^2 - 379/56x - 969/280 = 0

Output:
x^3 + 487/140x^2 - 379/56x - 969/280 = 0
(x - 17/10)(x - -19/4)(x - -3/7) = 0
x - 17/10 = 0
x - -19/4 = 0
x - -3/7 = 0
x = 17/10
x = -19/4
x = -3/7


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

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


Input:
Solve the system:
9x + 10y = 123/4
5x + 5y = 1135/72

Output:
9x + 10y = 123/4
5x + 5y = 1135/72

Using elimination
5*(9x + 10y = 123/4)
9*(5x + 5y = 1135/72)
45x + 50y = 615/4
45x + 45y = 1135/8
Subtract equations
5y = 95/8
y = 95/8/5
y = 19/8

Substitute y
9x + 10(19/8) = 123/4
9x = 7
x = 7/9
x = 7/9


Input: Solve quickly: x^2 + 11/2x + 68/9 = 0

Output:
x^2 + 11/2x + 68/9 = 0
(x - -17/6)(x - -8/3) = 0
x - -17/6 = 0  or  x - -8/3 = 0
x = -17/6
x = -8/3


Input:
Solve the equations:
1x + 3y = 4
9x + 6y = 36

Output:
1x + 3y = 4
9x + 6y = 36

Using elimination
9*(1x + 3y = 4)
1*(9x + 6y = 36)
9x + 27y = 36
9x + 6y = 36
Subtract equations
21y = 0
y = 0/21
y = 0

Substitute y
1x + 3(0) = 4
1x = 4
x = 4/1
x = 4


Input:
Find x and y such that
9x + 2y = 141
10x + 9y = 177

Output:
9x + 2y = 141
10x + 9y = 177

Using elimination
10*(9x + 2y = 141)
9*(10x + 9y = 177)
90x + 20y = 1410
90x + 81y = 1593
Subtract equations
-61y = -183
y = -183/-61
y = 3

Substitute y
9x + 2(3) = 141
9x = 135
x = 135/9
x = 15


Input: Solve 2x - 3 = 0

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


Input: Solve 1x  = 0

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


Input:
Find x and y such that
3x + 3y = 57/8
2x + 9y = 143/8

Output:
3x + 3y = 57/8
2x + 9y = 143/8

Using elimination
2*(3x + 3y = 57/8)
3*(2x + 9y = 143/8)
6x + 6y = 57/4
6x + 27y = 429/8
Subtract equations
-21y = -315/8
y = -315/8/-21
y = 15/8

Substitute y
3x + 3(15/8) = 57/8
3x = 3/2
x = 3/2/3
x = 1/2


Input:
Solve simultaneously:
9x + 8y = 286/35
5x + 4y = 30/7

Output:
9x + 8y = 286/35
5x + 4y = 30/7

Using elimination
5*(9x + 8y = 286/35)
9*(5x + 4y = 30/7)
45x + 40y = 286/7
45x + 36y = 270/7
Subtract equations
4y = 16/7
y = 16/7/4
y = 4/7

Substitute y
9x + 8(4/7) = 286/35
9x = 18/5
x = 18/5/9
x = 2/5


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

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

Using elimination
3*(7x + 3y = 1/3)
7*(3x + 4y = 11)
21x + 9y = 1
21x + 28y = 77
Subtract equations
-19y = -76
y = -76/-19
y = 4

Substitute y
7x + 3(4) = 1/3
7x = -35/3
x = -35/3/7
x = -5/3


Input:
Solve simultaneously:
9x + 10y = -311/8
7x + 7y = -231/8

Output:
9x + 10y = -311/8
7x + 7y = -231/8

Using elimination
7*(9x + 10y = -311/8)
9*(7x + 7y = -231/8)
63x + 70y = -2177/8
63x + 63y = -2079/8
Subtract equations
7y = -49/4
y = -49/4/7
y = -7/4

Substitute y
9x + 10(-7/4) = -311/8
9x = -171/8
x = -171/8/9
x = -19/8


Input: Solve x^2 - 4/5x - 28/5 = 0

Output:
x^2 - 4/5x - 28/5 = 0
(x - -2)(x - 14/5) = 0
x - -2 = 0  or  x - 14/5 = 0
x = -2
x = 14/5


Input: Find the solution to x^3 - 281/30x^2 + 43/3x - 5/2 = 0

Output:
x^3 - 281/30x^2 + 43/3x - 5/2 = 0
(x - 15/2)(x - 5/3)(x - 1/5) = 0
x - 15/2 = 0
x - 5/3 = 0
x - 1/5 = 0
x = 15/2
x = 5/3
x = 1/5


Input: Find the solution to x^3 - 19/35x^2 - 99/35x - 9/7 = 0

Output:
x^3 - 19/35x^2 - 99/35x - 9/7 = 0
(x - 15/7)(x - -1)(x - -3/5) = 0
x - 15/7 = 0
x - -1 = 0
x - -3/5 = 0
x = 15/7
x = -1
x = -3/5


Input: Compute the solution of 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 x in x^2 + 200/63x + 128/63 = 0

Output:
x^2 + 200/63x + 128/63 = 0
(x - -8/9)(x - -16/7) = 0
x - -8/9 = 0  or  x - -16/7 = 0
x = -8/9
x = -16/7


Input: Solve the equation x^3 - 849/40x^2 + 199/8x - 15/2 = 0

Output:
x^3 - 849/40x^2 + 199/8x - 15/2 = 0
(x - 3/5)(x - 5/8)(x - 20) = 0
x - 3/5 = 0
x - 5/8 = 0
x - 20 = 0
x = 3/5
x = 5/8
x = 20


Input: What value of x satisfies 8x + 80/3 = 0

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


Input:
Solve the system:
5x + 2y = -1175/72
1x + 10y = -1771/72

Output:
5x + 2y = -1175/72
1x + 10y = -1771/72

Using elimination
1*(5x + 2y = -1175/72)
5*(1x + 10y = -1771/72)
5x + 2y = -1175/72
5x + 50y = -8855/72
Subtract equations
-48y = 320/3
y = 320/3/-48
y = -20/9

Substitute y
5x + 2(-20/9) = -1175/72
5x = -95/8
x = -95/8/5
x = -19/8


Input: What value of x satisfies x^3 + 335/72x^2 + 1121/288x - 13/6 = 0

Output:
x^3 + 335/72x^2 + 1121/288x - 13/6 = 0
(x - -13/4)(x - 3/8)(x - -16/9) = 0
x - -13/4 = 0
x - 3/8 = 0
x - -16/9 = 0
x = -13/4
x = 3/8
x = -16/9


Input:
Find x and y such that
2x + 7y = 97/45
10x + 3y = 773/45

Output:
2x + 7y = 97/45
10x + 3y = 773/45

Using elimination
10*(2x + 7y = 97/45)
2*(10x + 3y = 773/45)
20x + 70y = 194/9
20x + 6y = 1546/45
Subtract equations
64y = -64/5
y = -64/5/64
y = -1/5

Substitute y
2x + 7(-1/5) = 97/45
2x = 32/9
x = 32/9/2
x = 16/9


Input: What value of x satisfies x^3 - 263/60x^2 + 44/15x + 21/5 = 0

Output:
x^3 - 263/60x^2 + 44/15x + 21/5 = 0
(x - -2/3)(x - 9/4)(x - 14/5) = 0
x - -2/3 = 0
x - 9/4 = 0
x - 14/5 = 0
x = -2/3
x = 9/4
x = 14/5


Input: Find x for x^3 - 71/8x^2 + 2891/144x - 19/3 = 0

Output:
x^3 - 71/8x^2 + 2891/144x - 19/3 = 0
(x - 16/3)(x - 19/6)(x - 3/8) = 0
x - 16/3 = 0
x - 19/6 = 0
x - 3/8 = 0
x = 16/3
x = 19/6
x = 3/8


Input:
Solve the equations:
4x + 10y = 19
7x + 6y = 57/5

Output:
4x + 10y = 19
7x + 6y = 57/5

Using elimination
7*(4x + 10y = 19)
4*(7x + 6y = 57/5)
28x + 70y = 133
28x + 24y = 228/5
Subtract equations
46y = 437/5
y = 437/5/46
y = 19/10

Substitute y
4x + 10(19/10) = 19
4x = 0
x = 0/4
x = 0


Input: Find x in 8x + 40 = 0

Output:
8x + 40 = 0
8x = -40
x = -40 / 8
x = -5


Input: Find x for 10x - 45 = 0

Output:
10x - 45 = 0
10x = 45
x = 45 / 10
x = 9/2


Input: Find the solution to 1x + 4 = 0

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


Input: Solve quickly: x^3 + 1/2x^2 - 71/16x - 9/8 = 0

Output:
x^3 + 1/2x^2 - 71/16x - 9/8 = 0
(x - -1/4)(x - 2)(x - -9/4) = 0
x - -1/4 = 0
x - 2 = 0
x - -9/4 = 0
x = -1/4
x = 2
x = -9/4


Input: Find x for 4x + 76/3 = 0

Output:
4x + 76/3 = 0
4x = -76/3
x = -76/3 / 4
x = -19/3


Input: Find x for x^2 - 23/63x - 22/21 = 0

Output:
x^2 - 23/63x - 22/21 = 0
(x - -6/7)(x - 11/9) = 0
x - -6/7 = 0  or  x - 11/9 = 0
x = -6/7
x = 11/9


Input:
Solve simultaneously:
8x + 9y = -157/10
10x + 5y = -33/2

Output:
8x + 9y = -157/10
10x + 5y = -33/2

Using elimination
10*(8x + 9y = -157/10)
8*(10x + 5y = -33/2)
80x + 90y = -157
80x + 40y = -132
Subtract equations
50y = -25
y = -25/50
y = -1/2

Substitute y
8x + 9(-1/2) = -157/10
8x = -56/5
x = -56/5/8
x = -7/5


Input: Solve quickly: x^3 - 271/72x^2 - 535/54x - 119/24 = 0

Output:
x^3 - 271/72x^2 - 535/54x - 119/24 = 0
(x - 17/3)(x - -7/9)(x - -9/8) = 0
x - 17/3 = 0
x - -7/9 = 0
x - -9/8 = 0
x = 17/3
x = -7/9
x = -9/8


Input:
Solve the equations:
1x + 3y = -9
6x + 3y = 31

Output:
1x + 3y = -9
6x + 3y = 31

Using elimination
6*(1x + 3y = -9)
1*(6x + 3y = 31)
6x + 18y = -54
6x + 3y = 31
Subtract equations
15y = -85
y = -85/15
y = -17/3

Substitute y
1x + 3(-17/3) = -9
1x = 8
x = 8/1
x = 8


Input: What value of x satisfies x^2 + 26/3x + 40/3 = 0

Output:
x^2 + 26/3x + 40/3 = 0
(x - -20/3)(x - -2) = 0
x - -20/3 = 0  or  x - -2 = 0
x = -20/3
x = -2


Input: Determine x in x^2 + 15/4x - 25/4 = 0

Output:
x^2 + 15/4x - 25/4 = 0
(x - -5)(x - 5/4) = 0
x - -5 = 0  or  x - 5/4 = 0
x = -5
x = 5/4


Input: What value of x satisfies x^2 + 10/3x + 1 = 0

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


Input:
Find x and y such that
9x + 9y = -9/8
10x + 8y = -21/4

Output:
9x + 9y = -9/8
10x + 8y = -21/4

Using elimination
10*(9x + 9y = -9/8)
9*(10x + 8y = -21/4)
90x + 90y = -45/4
90x + 72y = -189/4
Subtract equations
18y = 36
y = 36/18
y = 2

Substitute y
9x + 9(2) = -9/8
9x = -153/8
x = -153/8/9
x = -17/8


Input: What value of x satisfies x^3 + 7/4x^2 - 69/8x - 135/8 = 0

Output:
x^3 + 7/4x^2 - 69/8x - 135/8 = 0
(x - -9/4)(x - 3)(x - -5/2) = 0
x - -9/4 = 0
x - 3 = 0
x - -5/2 = 0
x = -9/4
x = 3
x = -5/2


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

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


Input: Find x for 2x + 8/5 = 0

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


Input: Find the solution to x^2 + 117/10x - 18/5 = 0

Output:
x^2 + 117/10x - 18/5 = 0
(x - -12)(x - 3/10) = 0
x - -12 = 0  or  x - 3/10 = 0
x = -12
x = 3/10


Input: Determine x in x^3 - 29/9x^2 + 85/27x - 25/27 = 0

Output:
x^3 - 29/9x^2 + 85/27x - 25/27 = 0
(x - 5/3)(x - 1)(x - 5/9) = 0
x - 5/3 = 0
x - 1 = 0
x - 5/9 = 0
x = 5/3
x = 1
x = 5/9


Input:
Find x and y such that
10x + 1y = 801/35
2x + 7y = -173/35

Output:
10x + 1y = 801/35
2x + 7y = -173/35

Using elimination
2*(10x + 1y = 801/35)
10*(2x + 7y = -173/35)
20x + 2y = 1602/35
20x + 70y = -346/7
Subtract equations
-68y = 476/5
y = 476/5/-68
y = -7/5

Substitute y
10x + 1(-7/5) = 801/35
10x = 170/7
x = 170/7/10
x = 17/7


Input:
Solve simultaneously:
4x + 6y = -116/21
4x + 1y = -628/63

Output:
4x + 6y = -116/21
4x + 1y = -628/63

Using elimination
4*(4x + 6y = -116/21)
4*(4x + 1y = -628/63)
16x + 24y = -464/21
16x + 4y = -2512/63
Subtract equations
20y = 160/9
y = 160/9/20
y = 8/9

Substitute y
4x + 6(8/9) = -116/21
4x = -76/7
x = -76/7/4
x = -19/7


Input: Find the solution to 6x + 12 = 0

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


Input:
Solve the equations:
5x + 6y = 23
3x + 9y = 96/5

Output:
5x + 6y = 23
3x + 9y = 96/5

Using elimination
3*(5x + 6y = 23)
5*(3x + 9y = 96/5)
15x + 18y = 69
15x + 45y = 96
Subtract equations
-27y = -27
y = -27/-27
y = 1

Substitute y
5x + 6(1) = 23
5x = 17
x = 17/5
x = 17/5


Input:
Find x and y such that
3x + 5y = -79/2
4x + 3y = -16

Output:
3x + 5y = -79/2
4x + 3y = -16

Using elimination
4*(3x + 5y = -79/2)
3*(4x + 3y = -16)
12x + 20y = -158
12x + 9y = -48
Subtract equations
11y = -110
y = -110/11
y = -10

Substitute y
3x + 5(-10) = -79/2
3x = 21/2
x = 21/2/3
x = 7/2


Input: Find the solution to 10x - 70/9 = 0

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


Input:
Solve the system:
6x + 1y = -67/2
6x + 8y = -179/2

Output:
6x + 1y = -67/2
6x + 8y = -179/2

Using elimination
6*(6x + 1y = -67/2)
6*(6x + 8y = -179/2)
36x + 6y = -201
36x + 48y = -537
Subtract equations
-42y = 336
y = 336/-42
y = -8

Substitute y
6x + 1(-8) = -67/2
6x = -51/2
x = -51/2/6
x = -17/4


Input: Solve the equation x^3 - 43/5x^2 - 771/20x - 27 = 0

Output:
x^3 - 43/5x^2 - 771/20x - 27 = 0
(x - -5/2)(x - -9/10)(x - 12) = 0
x - -5/2 = 0
x - -9/10 = 0
x - 12 = 0
x = -5/2
x = -9/10
x = 12


Input: Find x in x^2 + 37/8x + 165/32 = 0

Output:
x^2 + 37/8x + 165/32 = 0
(x - -15/8)(x - -11/4) = 0
x - -15/8 = 0  or  x - -11/4 = 0
x = -15/8
x = -11/4


Input: Solve the equation 10x + 50 = 0

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


Input: Solve the equation x^3 - 50/9x^2 - 997/9x + 182 = 0

Output:
x^3 - 50/9x^2 - 997/9x + 182 = 0
(x - 14/9)(x - 13)(x - -9) = 0
x - 14/9 = 0
x - 13 = 0
x - -9 = 0
x = 14/9
x = 13
x = -9


Input: Compute the solution of 2x + 8/9 = 0

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


Input: What value of x satisfies x^2 + 29/8x + 51/16 = 0

Output:
x^2 + 29/8x + 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 5x - 5/7 = 0

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


Input: Find x for x^2 - 11/15x - 4/5 = 0

Output:
x^2 - 11/15x - 4/5 = 0
(x - -3/5)(x - 4/3) = 0
x - -3/5 = 0  or  x - 4/3 = 0
x = -3/5
x = 4/3


Input: Determine x in 1x - 7/4 = 0

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


Input:
Solve the system:
1x + 7y = 59/3
1x + 1y = 11/3

Output:
1x + 7y = 59/3
1x + 1y = 11/3

Using elimination
1*(1x + 7y = 59/3)
1*(1x + 1y = 11/3)
1x + 7y = 59/3
1x + 1y = 11/3
Subtract equations
6y = 16
y = 16/6
y = 8/3

Substitute y
1x + 7(8/3) = 59/3
1x = 1
x = 1/1
x = 1


Input: What value of x satisfies 2x - 16/9 = 0

Output:
2x - 16/9 = 0
2x = 16/9
x = 16/9 / 2
x = 8/9


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

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


Input: Solve quickly: x^2 - 37/12x - 95/12 = 0

Output:
x^2 - 37/12x - 95/12 = 0
(x - -5/3)(x - 19/4) = 0
x - -5/3 = 0  or  x - 19/4 = 0
x = -5/3
x = 19/4


Input:
Solve simultaneously:
10x + 2y = -28
8x + 2y = -25

Output:
10x + 2y = -28
8x + 2y = -25

Using elimination
8*(10x + 2y = -28)
10*(8x + 2y = -25)
80x + 16y = -224
80x + 20y = -250
Subtract equations
-4y = 26
y = 26/-4
y = -13/2

Substitute y
10x + 2(-13/2) = -28
10x = -15
x = -15/10
x = -3/2


Input: Determine x in x^2 - 121/18x - 35/6 = 0

Output:
x^2 - 121/18x - 35/6 = 0
(x - 15/2)(x - -7/9) = 0
x - 15/2 = 0  or  x - -7/9 = 0
x = 15/2
x = -7/9


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

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


Input: Find x for 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: Compute the solution of x^3 + 49/18x^2 + 7/6x + 10/81 = 0

Output:
x^3 + 49/18x^2 + 7/6x + 10/81 = 0
(x - -1/6)(x - -20/9)(x - -1/3) = 0
x - -1/6 = 0
x - -20/9 = 0
x - -1/3 = 0
x = -1/6
x = -20/9
x = -1/3


Input: Solve 10x - 45/2 = 0

Output:
10x - 45/2 = 0
10x = 45/2
x = 45/2 / 10
x = 9/4


Input: Solve x^2 - 2x + 1 = 0

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


Input: Find x in x^2 - 25/6x + 19/6 = 0

Output:
x^2 - 25/6x + 19/6 = 0
(x - 1)(x - 19/6) = 0
x - 1 = 0  or  x - 19/6 = 0
x = 1
x = 19/6


Input:
Solve the equations:
6x + 2y = -62/3
4x + 8y = -16

Output:
6x + 2y = -62/3
4x + 8y = -16

Using elimination
4*(6x + 2y = -62/3)
6*(4x + 8y = -16)
24x + 8y = -248/3
24x + 48y = -96
Subtract equations
-40y = 40/3
y = 40/3/-40
y = -1/3

Substitute y
6x + 2(-1/3) = -62/3
6x = -20
x = -20/6
x = -10/3


Input: Solve the equation x^3 + 134/15x^2 + 347/15x + 52/3 = 0

Output:
x^3 + 134/15x^2 + 347/15x + 52/3 = 0
(x - -5)(x - -4/3)(x - -13/5) = 0
x - -5 = 0
x - -4/3 = 0
x - -13/5 = 0
x = -5
x = -4/3
x = -13/5


Input:
Solve the system:
1x + 10y = 37/2
4x + 8y = 10

Output:
1x + 10y = 37/2
4x + 8y = 10

Using elimination
4*(1x + 10y = 37/2)
1*(4x + 8y = 10)
4x + 40y = 74
4x + 8y = 10
Subtract equations
32y = 64
y = 64/32
y = 2

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


Input: Solve x^2 + 13x  = 0

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


Input:
Solve simultaneously:
1x + 8y = -104/15
9x + 4y = -256/15

Output:
1x + 8y = -104/15
9x + 4y = -256/15

Using elimination
9*(1x + 8y = -104/15)
1*(9x + 4y = -256/15)
9x + 72y = -312/5
9x + 4y = -256/15
Subtract equations
68y = -136/3
y = -136/3/68
y = -2/3

Substitute y
1x + 8(-2/3) = -104/15
1x = -8/5
x = -8/5/1
x = -8/5


Input: What value of x satisfies x^3 + 129/8x^2 + 993/16x + 1001/16 = 0

Output:
x^3 + 129/8x^2 + 993/16x + 1001/16 = 0
(x - -13/8)(x - -7/2)(x - -11) = 0
x - -13/8 = 0
x - -7/2 = 0
x - -11 = 0
x = -13/8
x = -7/2
x = -11


Input:
Solve simultaneously:
9x + 5y = -117/4
2x + 3y = -13/2

Output:
9x + 5y = -117/4
2x + 3y = -13/2

Using elimination
2*(9x + 5y = -117/4)
9*(2x + 3y = -13/2)
18x + 10y = -117/2
18x + 27y = -117/2
Subtract equations
-17y = 0
y = 0/-17
y = 0

Substitute y
9x + 5(0) = -117/4
9x = -117/4
x = -117/4/9
x = -13/4


Input: Solve quickly: 1x + 11/5 = 0

Output:
1x + 11/5 = 0
1x = -11/5
x = -11/5 / 1
x = -11/5


Input: Solve quickly: x^2 - 47/28x + 5/14 = 0

Output:
x^2 - 47/28x + 5/14 = 0
(x - 10/7)(x - 1/4) = 0
x - 10/7 = 0  or  x - 1/4 = 0
x = 10/7
x = 1/4


Input:
Solve the equations:
1x + 7y = -107/12
10x + 4y = -271/6

Output:
1x + 7y = -107/12
10x + 4y = -271/6

Using elimination
10*(1x + 7y = -107/12)
1*(10x + 4y = -271/6)
10x + 70y = -535/6
10x + 4y = -271/6
Subtract equations
66y = -44
y = -44/66
y = -2/3

Substitute y
1x + 7(-2/3) = -107/12
1x = -17/4
x = -17/4/1
x = -17/4


Input: Find x for 6x + 24 = 0

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


Input: What value of x satisfies 5x + 25/4 = 0

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


Input: Find the solution to x^2 + 32/3x - 91/3 = 0

Output:
x^2 + 32/3x - 91/3 = 0
(x - -13)(x - 7/3) = 0
x - -13 = 0  or  x - 7/3 = 0
x = -13
x = 7/3


Input: What value of x satisfies 7x - 126/5 = 0

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


Input: Determine x in x^3 - 1x^2 - 16x + 16 = 0

Output:
x^3 - 1x^2 - 16x + 16 = 0
(x - -4)(x - 4)(x - 1) = 0
x - -4 = 0
x - 4 = 0
x - 1 = 0
x = -4
x = 4
x = 1


Input: Solve the equation x^3 + 113/35x^2 - 16/35x - 204/35 = 0

Output:
x^3 + 113/35x^2 - 16/35x - 204/35 = 0
(x - -17/7)(x - 6/5)(x - -2) = 0
x - -17/7 = 0
x - 6/5 = 0
x - -2 = 0
x = -17/7
x = 6/5
x = -2


Input: Solve the equation x^2 - 99/5x + 162/5 = 0

Output:
x^2 - 99/5x + 162/5 = 0
(x - 9/5)(x - 18) = 0
x - 9/5 = 0  or  x - 18 = 0
x = 9/5
x = 18


Input: Find x for 7x + 70/9 = 0

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


Input: Solve x^2 + 123/40x + 9/4 = 0

Output:
x^2 + 123/40x + 9/4 = 0
(x - -6/5)(x - -15/8) = 0
x - -6/5 = 0  or  x - -15/8 = 0
x = -6/5
x = -15/8


Input: Find x in 5x - 25/7 = 0

Output:
5x - 25/7 = 0
5x = 25/7
x = 25/7 / 5
x = 5/7


Input: Find x in x^3 - 67/6x^2 + 27x - 40/3 = 0

Output:
x^3 - 67/6x^2 + 27x - 40/3 = 0
(x - 8)(x - 5/2)(x - 2/3) = 0
x - 8 = 0
x - 5/2 = 0
x - 2/3 = 0
x = 8
x = 5/2
x = 2/3


Input:
Solve the system:
1x + 2y = 48/5
6x + 8y = 322/5

Output:
1x + 2y = 48/5
6x + 8y = 322/5

Using elimination
6*(1x + 2y = 48/5)
1*(6x + 8y = 322/5)
6x + 12y = 288/5
6x + 8y = 322/5
Subtract equations
4y = -34/5
y = -34/5/4
y = -17/10

Substitute y
1x + 2(-17/10) = 48/5
1x = 13
x = 13/1
x = 13


Input: Solve quickly: 10x + 11 = 0

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


Input: What value of x satisfies 6x + 3 = 0

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


Input: Find x in 8x + 13 = 0

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


Input: Find x in x^2 + 35/24x - 25/4 = 0

Output:
x^2 + 35/24x - 25/4 = 0
(x - -10/3)(x - 15/8) = 0
x - -10/3 = 0  or  x - 15/8 = 0
x = -10/3
x = 15/8


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

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


Input: Determine x in 10x - 110/7 = 0

Output:
10x - 110/7 = 0
10x = 110/7
x = 110/7 / 10
x = 11/7


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

Output:
x^2 + 8/3x - 35/3 = 0
(x - 7/3)(x - -5) = 0
x - 7/3 = 0  or  x - -5 = 0
x = 7/3
x = -5


Input: Solve the equation x^2 + 29/8x + 13/4 = 0

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


Input: Solve 10x - 5 = 0

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


Input: Solve the equation x^3 - 16/15x^2 - 289/45x + 364/45 = 0

Output:
x^3 - 16/15x^2 - 289/45x + 364/45 = 0
(x - -13/5)(x - 4/3)(x - 7/3) = 0
x - -13/5 = 0
x - 4/3 = 0
x - 7/3 = 0
x = -13/5
x = 4/3
x = 7/3


Input: Find x in 7x - 91 = 0

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


Input:
Solve the equations:
3x + 3y = 18
9x + 4y = 122/3

Output:
3x + 3y = 18
9x + 4y = 122/3

Using elimination
9*(3x + 3y = 18)
3*(9x + 4y = 122/3)
27x + 27y = 162
27x + 12y = 122
Subtract equations
15y = 40
y = 40/15
y = 8/3

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


Input:
Solve simultaneously:
8x + 1y = 133/6
3x + 2y = 14

Output:
8x + 1y = 133/6
3x + 2y = 14

Using elimination
3*(8x + 1y = 133/6)
8*(3x + 2y = 14)
24x + 3y = 133/2
24x + 16y = 112
Subtract equations
-13y = -91/2
y = -91/2/-13
y = 7/2

Substitute y
8x + 1(7/2) = 133/6
8x = 56/3
x = 56/3/8
x = 7/3


Input: What value of x satisfies x^2 + 13x + 12 = 0

Output:
x^2 + 13x + 12 = 0
(x - -12)(x - -1) = 0
x - -12 = 0  or  x - -1 = 0
x = -12
x = -1


Input: Find x in x^3 + 11/10x^2 - 587/80x - 143/16 = 0

Output:
x^3 + 11/10x^2 - 587/80x - 143/16 = 0
(x - -13/5)(x - 11/4)(x - -5/4) = 0
x - -13/5 = 0
x - 11/4 = 0
x - -5/4 = 0
x = -13/5
x = 11/4
x = -5/4


Input: Find the solution to x^3 - 1147/504x^2 + 181/504x + 143/126 = 0

Output:
x^3 - 1147/504x^2 + 181/504x + 143/126 = 0
(x - 13/8)(x - 11/9)(x - -4/7) = 0
x - 13/8 = 0
x - 11/9 = 0
x - -4/7 = 0
x = 13/8
x = 11/9
x = -4/7


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

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


Input:
Solve the equations:
3x + 7y = -25/2
5x + 5y = -25/6

Output:
3x + 7y = -25/2
5x + 5y = -25/6

Using elimination
5*(3x + 7y = -25/2)
3*(5x + 5y = -25/6)
15x + 35y = -125/2
15x + 15y = -25/2
Subtract equations
20y = -50
y = -50/20
y = -5/2

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


Input: Solve quickly: x^3 + 19x^2 + 86x + 104 = 0

Output:
x^3 + 19x^2 + 86x + 104 = 0
(x - -2)(x - -13)(x - -4) = 0
x - -2 = 0
x - -13 = 0
x - -4 = 0
x = -2
x = -13
x = -4


Input:
Solve the system:
2x + 7y = 365/21
4x + 4y = 380/21

Output:
2x + 7y = 365/21
4x + 4y = 380/21

Using elimination
4*(2x + 7y = 365/21)
2*(4x + 4y = 380/21)
8x + 28y = 1460/21
8x + 8y = 760/21
Subtract equations
20y = 100/3
y = 100/3/20
y = 5/3

Substitute y
2x + 7(5/3) = 365/21
2x = 40/7
x = 40/7/2
x = 20/7


Input: Solve the equation x^2 - 8/5x - 153/25 = 0

Output:
x^2 - 8/5x - 153/25 = 0
(x - 17/5)(x - -9/5) = 0
x - 17/5 = 0  or  x - -9/5 = 0
x = 17/5
x = -9/5


Input: What value of x satisfies x^3 - 173/42x^2 - 344/21x + 247/42 = 0

Output:
x^3 - 173/42x^2 - 344/21x + 247/42 = 0
(x - 1/3)(x - 13/2)(x - -19/7) = 0
x - 1/3 = 0
x - 13/2 = 0
x - -19/7 = 0
x = 1/3
x = 13/2
x = -19/7


Input:
Find x and y such that
7x + 5y = -43/3
8x + 1y = -46/3

Output:
7x + 5y = -43/3
8x + 1y = -46/3

Using elimination
8*(7x + 5y = -43/3)
7*(8x + 1y = -46/3)
56x + 40y = -344/3
56x + 7y = -322/3
Subtract equations
33y = -22/3
y = -22/3/33
y = -2/9

Substitute y
7x + 5(-2/9) = -43/3
7x = -119/9
x = -119/9/7
x = -17/9


Input: Compute the solution of x^3 - 1x^2 - 5x - 3 = 0

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


Input: Compute the solution of x^3 + 25/8x^2 - 17/2x + 35/8 = 0

Output:
x^3 + 25/8x^2 - 17/2x + 35/8 = 0
(x - -5)(x - 1)(x - 7/8) = 0
x - -5 = 0
x - 1 = 0
x - 7/8 = 0
x = -5
x = 1
x = 7/8


Input:
Find x and y such that
4x + 7y = -248/9
3x + 8y = -241/9

Output:
4x + 7y = -248/9
3x + 8y = -241/9

Using elimination
3*(4x + 7y = -248/9)
4*(3x + 8y = -241/9)
12x + 21y = -248/3
12x + 32y = -964/9
Subtract equations
-11y = 220/9
y = 220/9/-11
y = -20/9

Substitute y
4x + 7(-20/9) = -248/9
4x = -12
x = -12/4
x = -3


Input:
Solve the system:
9x + 1y = -143/70
6x + 7y = -43/5

Output:
9x + 1y = -143/70
6x + 7y = -43/5

Using elimination
6*(9x + 1y = -143/70)
9*(6x + 7y = -43/5)
54x + 6y = -429/35
54x + 63y = -387/5
Subtract equations
-57y = 456/7
y = 456/7/-57
y = -8/7

Substitute y
9x + 1(-8/7) = -143/70
9x = -9/10
x = -9/10/9
x = -1/10


Input: Solve x^3 + 71/8x^2 - 253/32x - 1197/64 = 0

Output:
x^3 + 71/8x^2 - 253/32x - 1197/64 = 0
(x - 7/4)(x - -19/2)(x - -9/8) = 0
x - 7/4 = 0
x - -19/2 = 0
x - -9/8 = 0
x = 7/4
x = -19/2
x = -9/8


Input: Find the solution to x^2 + 89/20x - 57/40 = 0

Output:
x^2 + 89/20x - 57/40 = 0
(x - 3/10)(x - -19/4) = 0
x - 3/10 = 0  or  x - -19/4 = 0
x = 3/10
x = -19/4


Input: Solve quickly: x^3 + 3/8x^2 - 35/32x - 9/32 = 0

Output:
x^3 + 3/8x^2 - 35/32x - 9/32 = 0
(x - -1/4)(x - 1)(x - -9/8) = 0
x - -1/4 = 0
x - 1 = 0
x - -9/8 = 0
x = -1/4
x = 1
x = -9/8


Input: Solve the equation x^3 - 31/8x^2 - 29/8x + 1105/128 = 0

Output:
x^3 - 31/8x^2 - 29/8x + 1105/128 = 0
(x - 17/4)(x - -13/8)(x - 5/4) = 0
x - 17/4 = 0
x - -13/8 = 0
x - 5/4 = 0
x = 17/4
x = -13/8
x = 5/4


Input: What value of x satisfies 9x - 54/7 = 0

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


Input: Solve x^2 - 29/4x - 171/8 = 0

Output:
x^2 - 29/4x - 171/8 = 0
(x - -9/4)(x - 19/2) = 0
x - -9/4 = 0  or  x - 19/2 = 0
x = -9/4
x = 19/2


Input: Find x in 7x + 21/10 = 0

Output:
7x + 21/10 = 0
7x = -21/10
x = -21/10 / 7
x = -3/10


Input: Solve quickly: x^2 + 13/3x + 14/3 = 0

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


Input:
Solve the system:
9x + 10y = -43
6x + 9y = -69/2

Output:
9x + 10y = -43
6x + 9y = -69/2

Using elimination
6*(9x + 10y = -43)
9*(6x + 9y = -69/2)
54x + 60y = -258
54x + 81y = -621/2
Subtract equations
-21y = 105/2
y = 105/2/-21
y = -5/2

Substitute y
9x + 10(-5/2) = -43
9x = -18
x = -18/9
x = -2


Input: Solve x^3 + 313/35x^2 + 165/7x + 135/7 = 0

Output:
x^3 + 313/35x^2 + 165/7x + 135/7 = 0
(x - -15/7)(x - -5)(x - -9/5) = 0
x - -15/7 = 0
x - -5 = 0
x - -9/5 = 0
x = -15/7
x = -5
x = -9/5


Input: Find x for x^2 + 55/6x + 50/3 = 0

Output:
x^2 + 55/6x + 50/3 = 0
(x - -20/3)(x - -5/2) = 0
x - -20/3 = 0  or  x - -5/2 = 0
x = -20/3
x = -5/2


Input: Find x for x^2 - 3/4x - 7/4 = 0

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


Input:
Solve the system:
2x + 7y = 64/9
9x + 9y = 17

Output:
2x + 7y = 64/9
9x + 9y = 17

Using elimination
9*(2x + 7y = 64/9)
2*(9x + 9y = 17)
18x + 63y = 64
18x + 18y = 34
Subtract equations
45y = 30
y = 30/45
y = 2/3

Substitute y
2x + 7(2/3) = 64/9
2x = 22/9
x = 22/9/2
x = 11/9


Input: Solve quickly: x^3 - 32/5x^2 + 29/5x + 6 = 0

Output:
x^3 - 32/5x^2 + 29/5x + 6 = 0
(x - -3/5)(x - 2)(x - 5) = 0
x - -3/5 = 0
x - 2 = 0
x - 5 = 0
x = -3/5
x = 2
x = 5


Input: Find x for x^2 + 1/45x - 28/45 = 0

Output:
x^2 + 1/45x - 28/45 = 0
(x - 7/9)(x - -4/5) = 0
x - 7/9 = 0  or  x - -4/5 = 0
x = 7/9
x = -4/5


Input:
Solve the system:
5x + 8y = 26
8x + 5y = 26

Output:
5x + 8y = 26
8x + 5y = 26

Using elimination
8*(5x + 8y = 26)
5*(8x + 5y = 26)
40x + 64y = 208
40x + 25y = 130
Subtract equations
39y = 78
y = 78/39
y = 2

Substitute y
5x + 8(2) = 26
5x = 10
x = 10/5
x = 2


Input:
Solve the system:
10x + 1y = -348/5
8x + 1y = -278/5

Output:
10x + 1y = -348/5
8x + 1y = -278/5

Using elimination
8*(10x + 1y = -348/5)
10*(8x + 1y = -278/5)
80x + 8y = -2784/5
80x + 10y = -556
Subtract equations
-2y = -4/5
y = -4/5/-2
y = 2/5

Substitute y
10x + 1(2/5) = -348/5
10x = -70
x = -70/10
x = -7


Input: Determine x in 10x - 7 = 0

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


Input: Solve quickly: 10x - 10 = 0

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


Input: Compute the solution of x^3 + 41/3x^2 + 52/3x - 32 = 0

Output:
x^3 + 41/3x^2 + 52/3x - 32 = 0
(x - -12)(x - -8/3)(x - 1) = 0
x - -12 = 0
x - -8/3 = 0
x - 1 = 0
x = -12
x = -8/3
x = 1


Input: Find the solution to x^2 - 43/63x - 88/63 = 0

Output:
x^2 - 43/63x - 88/63 = 0
(x - 11/7)(x - -8/9) = 0
x - 11/7 = 0  or  x - -8/9 = 0
x = 11/7
x = -8/9


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

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


Input:
Solve the system:
1x + 4y = -77
7x + 10y = -197

Output:
1x + 4y = -77
7x + 10y = -197

Using elimination
7*(1x + 4y = -77)
1*(7x + 10y = -197)
7x + 28y = -539
7x + 10y = -197
Subtract equations
18y = -342
y = -342/18
y = -19

Substitute y
1x + 4(-19) = -77
1x = -1
x = -1/1
x = -1


Input: Find the solution to x^2 + 4/3x + 5/12 = 0

Output:
x^2 + 4/3x + 5/12 = 0
(x - -5/6)(x - -1/2) = 0
x - -5/6 = 0  or  x - -1/2 = 0
x = -5/6
x = -1/2


Input: Find x for 9x + 9 = 0

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


Input: Solve quickly: 7x + 14 = 0

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


Input: Find x for 1x - 16 = 0

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


Input: Find the solution to 8x - 8 = 0

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


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

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


Input:
Solve simultaneously:
5x + 1y = -339/56
8x + 6y = -81/7

Output:
5x + 1y = -339/56
8x + 6y = -81/7

Using elimination
8*(5x + 1y = -339/56)
5*(8x + 6y = -81/7)
40x + 8y = -339/7
40x + 30y = -405/7
Subtract equations
-22y = 66/7
y = 66/7/-22
y = -3/7

Substitute y
5x + 1(-3/7) = -339/56
5x = -45/8
x = -45/8/5
x = -9/8


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

Output:
6x + 10/3 = 0
6x = -10/3
x = -10/3 / 6
x = -5/9


Input:
Solve the system:
10x + 10y = -6
7x + 10y = -81/5

Output:
10x + 10y = -6
7x + 10y = -81/5

Using elimination
7*(10x + 10y = -6)
10*(7x + 10y = -81/5)
70x + 70y = -42
70x + 100y = -162
Subtract equations
-30y = 120
y = 120/-30
y = -4

Substitute y
10x + 10(-4) = -6
10x = 34
x = 34/10
x = 17/5


Input:
Solve simultaneously:
1x + 3y = -58/5
7x + 3y = -46/5

Output:
1x + 3y = -58/5
7x + 3y = -46/5

Using elimination
7*(1x + 3y = -58/5)
1*(7x + 3y = -46/5)
7x + 21y = -406/5
7x + 3y = -46/5
Subtract equations
18y = -72
y = -72/18
y = -4

Substitute y
1x + 3(-4) = -58/5
1x = 2/5
x = 2/5/1
x = 2/5


Input: Find x in 10x - 5/2 = 0

Output:
10x - 5/2 = 0
10x = 5/2
x = 5/2 / 10
x = 1/4


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

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


Input: Solve the equation x^2 + 27/10x + 7/5 = 0

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


Input: Determine x in x^3 + 15/2x^2 - 19x - 315/2 = 0

Output:
x^3 + 15/2x^2 - 19x - 315/2 = 0
(x - -5)(x - -7)(x - 9/2) = 0
x - -5 = 0
x - -7 = 0
x - 9/2 = 0
x = -5
x = -7
x = 9/2


Input: Solve x^2 - 13/9x - 10/9 = 0

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


Input: Find x in x^2 - 93/20x + 91/20 = 0

Output:
x^2 - 93/20x + 91/20 = 0
(x - 13/4)(x - 7/5) = 0
x - 13/4 = 0  or  x - 7/5 = 0
x = 13/4
x = 7/5


Input: Determine x in x^2 - 35/3x - 52/3 = 0

Output:
x^2 - 35/3x - 52/3 = 0
(x - 13)(x - -4/3) = 0
x - 13 = 0  or  x - -4/3 = 0
x = 13
x = -4/3


Input: What value of x satisfies 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: Determine x in x^3 - 167/280x^2 - 99/70x - 117/280 = 0

Output:
x^3 - 167/280x^2 - 99/70x - 117/280 = 0
(x - 13/8)(x - -3/5)(x - -3/7) = 0
x - 13/8 = 0
x - -3/5 = 0
x - -3/7 = 0
x = 13/8
x = -3/5
x = -3/7


Input: What value of x satisfies x^3 - 655/72x^2 - 93/8x + 935/36 = 0

Output:
x^3 - 655/72x^2 - 93/8x + 935/36 = 0
(x - 10)(x - -17/8)(x - 11/9) = 0
x - 10 = 0
x - -17/8 = 0
x - 11/9 = 0
x = 10
x = -17/8
x = 11/9


Input: Find the solution to x^3 - 16/9x^2 - 31/9x - 2/3 = 0

Output:
x^3 - 16/9x^2 - 31/9x - 2/3 = 0
(x - -2/9)(x - -1)(x - 3) = 0
x - -2/9 = 0
x - -1 = 0
x - 3 = 0
x = -2/9
x = -1
x = 3


Input:
Solve simultaneously:
3x + 7y = -25/2
5x + 3y = 19/2

Output:
3x + 7y = -25/2
5x + 3y = 19/2

Using elimination
5*(3x + 7y = -25/2)
3*(5x + 3y = 19/2)
15x + 35y = -125/2
15x + 9y = 57/2
Subtract equations
26y = -91
y = -91/26
y = -7/2

Substitute y
3x + 7(-7/2) = -25/2
3x = 12
x = 12/3
x = 4


Input: Find the solution to x^2 + 23/5x - 84/5 = 0

Output:
x^2 + 23/5x - 84/5 = 0
(x - 12/5)(x - -7) = 0
x - 12/5 = 0  or  x - -7 = 0
x = 12/5
x = -7


Input:
Solve simultaneously:
3x + 9y = -221/3
4x + 9y = -668/9

Output:
3x + 9y = -221/3
4x + 9y = -668/9

Using elimination
4*(3x + 9y = -221/3)
3*(4x + 9y = -668/9)
12x + 36y = -884/3
12x + 27y = -668/3
Subtract equations
9y = -72
y = -72/9
y = -8

Substitute y
3x + 9(-8) = -221/3
3x = -5/3
x = -5/3/3
x = -5/9


Input:
Solve the system:
3x + 9y = 23/5
2x + 9y = 64/15

Output:
3x + 9y = 23/5
2x + 9y = 64/15

Using elimination
2*(3x + 9y = 23/5)
3*(2x + 9y = 64/15)
6x + 18y = 46/5
6x + 27y = 64/5
Subtract equations
-9y = -18/5
y = -18/5/-9
y = 2/5

Substitute y
3x + 9(2/5) = 23/5
3x = 1
x = 1/3
x = 1/3


Input:
Solve the system:
5x + 6y = -37
4x + 5y = -63/2

Output:
5x + 6y = -37
4x + 5y = -63/2

Using elimination
4*(5x + 6y = -37)
5*(4x + 5y = -63/2)
20x + 24y = -148
20x + 25y = -315/2
Subtract equations
-1y = 19/2
y = 19/2/-1
y = -19/2

Substitute y
5x + 6(-19/2) = -37
5x = 20
x = 20/5
x = 4


Input: Solve x^2 - 41/5x + 8/5 = 0

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


Input: Solve x^3 - 59/45x^2 + 2/9x  = 0

Output:
x^3 - 59/45x^2 + 2/9x  = 0
(x - 10/9)(x - 1/5)(x - 0) = 0
x - 10/9 = 0
x - 1/5 = 0
x - 0 = 0
x = 10/9
x = 1/5
x = 0


Input:
Solve the system:
5x + 5y = 9/2
7x + 2y = -37/10

Output:
5x + 5y = 9/2
7x + 2y = -37/10

Using elimination
7*(5x + 5y = 9/2)
5*(7x + 2y = -37/10)
35x + 35y = 63/2
35x + 10y = -37/2
Subtract equations
25y = 50
y = 50/25
y = 2

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


Input: Solve the equation x^2 - 16x + 28 = 0

Output:
x^2 - 16x + 28 = 0
(x - 2)(x - 14) = 0
x - 2 = 0  or  x - 14 = 0
x = 2
x = 14


Input: Determine x in x^3 - 4/3x^2 - 79/81x + 110/81 = 0

Output:
x^3 - 4/3x^2 - 79/81x + 110/81 = 0
(x - 11/9)(x - 10/9)(x - -1) = 0
x - 11/9 = 0
x - 10/9 = 0
x - -1 = 0
x = 11/9
x = 10/9
x = -1


Input: Find x in x^3 - 149/14x^2 - 425/7x - 975/14 = 0

Output:
x^3 - 149/14x^2 - 425/7x - 975/14 = 0
(x - -5/2)(x - -13/7)(x - 15) = 0
x - -5/2 = 0
x - -13/7 = 0
x - 15 = 0
x = -5/2
x = -13/7
x = 15


Input: Solve quickly: x^2 - 23/10x + 13/10 = 0

Output:
x^2 - 23/10x + 13/10 = 0
(x - 13/10)(x - 1) = 0
x - 13/10 = 0  or  x - 1 = 0
x = 13/10
x = 1


Input: Find x in x^2 + 31/3x + 10/3 = 0

Output:
x^2 + 31/3x + 10/3 = 0
(x - -10)(x - -1/3) = 0
x - -10 = 0  or  x - -1/3 = 0
x = -10
x = -1/3


Input:
Find x and y such that
6x + 7y = -80/3
1x + 10y = -28

Output:
6x + 7y = -80/3
1x + 10y = -28

Using elimination
1*(6x + 7y = -80/3)
6*(1x + 10y = -28)
6x + 7y = -80/3
6x + 60y = -168
Subtract equations
-53y = 424/3
y = 424/3/-53
y = -8/3

Substitute y
6x + 7(-8/3) = -80/3
6x = -8
x = -8/6
x = -4/3


Input: Find x in 10x - 55/2 = 0

Output:
10x - 55/2 = 0
10x = 55/2
x = 55/2 / 10
x = 11/4


Input:
Solve the system:
3x + 5y = 25/4
10x + 9y = 17

Output:
3x + 5y = 25/4
10x + 9y = 17

Using elimination
10*(3x + 5y = 25/4)
3*(10x + 9y = 17)
30x + 50y = 125/2
30x + 27y = 51
Subtract equations
23y = 23/2
y = 23/2/23
y = 1/2

Substitute y
3x + 5(1/2) = 25/4
3x = 15/4
x = 15/4/3
x = 5/4


Input: Find x in 9x - 18/7 = 0

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


Input: Solve quickly: x^3 - 37/6x^2 - 85/6x - 4 = 0

Output:
x^3 - 37/6x^2 - 85/6x - 4 = 0
(x - 8)(x - -3/2)(x - -1/3) = 0
x - 8 = 0
x - -3/2 = 0
x - -1/3 = 0
x = 8
x = -3/2
x = -1/3


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 quickly: x^3 - 221/36x^2 - 703/24x - 1805/72 = 0

Output:
x^3 - 221/36x^2 - 703/24x - 1805/72 = 0
(x - -5/4)(x - 19/2)(x - -19/9) = 0
x - -5/4 = 0
x - 19/2 = 0
x - -19/9 = 0
x = -5/4
x = 19/2
x = -19/9


Input:
Solve simultaneously:
9x + 4y = 18
8x + 1y = 265/18

Output:
9x + 4y = 18
8x + 1y = 265/18

Using elimination
8*(9x + 4y = 18)
9*(8x + 1y = 265/18)
72x + 32y = 144
72x + 9y = 265/2
Subtract equations
23y = 23/2
y = 23/2/23
y = 1/2

Substitute y
9x + 4(1/2) = 18
9x = 16
x = 16/9
x = 16/9


Input: Determine x in 6x - 2 = 0

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


Input: Determine x in x^2 + 35/12x + 3/2 = 0

Output:
x^2 + 35/12x + 3/2 = 0
(x - -9/4)(x - -2/3) = 0
x - -9/4 = 0  or  x - -2/3 = 0
x = -9/4
x = -2/3


Input: What value of x satisfies x^2 + 116/45x - 209/45 = 0

Output:
x^2 + 116/45x - 209/45 = 0
(x - -19/5)(x - 11/9) = 0
x - -19/5 = 0  or  x - 11/9 = 0
x = -19/5
x = 11/9


Input: Solve x^2 + 34/15x - 13/15 = 0

Output:
x^2 + 34/15x - 13/15 = 0
(x - -13/5)(x - 1/3) = 0
x - -13/5 = 0  or  x - 1/3 = 0
x = -13/5
x = 1/3


Input:
Solve the equations:
10x + 8y = 163/9
3x + 2y = 421/90

Output:
10x + 8y = 163/9
3x + 2y = 421/90

Using elimination
3*(10x + 8y = 163/9)
10*(3x + 2y = 421/90)
30x + 24y = 163/3
30x + 20y = 421/9
Subtract equations
4y = 68/9
y = 68/9/4
y = 17/9

Substitute y
10x + 8(17/9) = 163/9
10x = 3
x = 3/10
x = 3/10


Input: Solve the equation 1x + 5/2 = 0

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


Input: Determine x in x^3 - 71/5x^2 - 238/5x  = 0

Output:
x^3 - 71/5x^2 - 238/5x  = 0
(x - -14/5)(x - 17)(x - 0) = 0
x - -14/5 = 0
x - 17 = 0
x - 0 = 0
x = -14/5
x = 17
x = 0


Input: Find x in x^2 + 8/7x - 80/7 = 0

Output:
x^2 + 8/7x - 80/7 = 0
(x - -4)(x - 20/7) = 0
x - -4 = 0  or  x - 20/7 = 0
x = -4
x = 20/7


Input: Find the solution to x^2 - 81/5x + 16/5 = 0

Output:
x^2 - 81/5x + 16/5 = 0
(x - 1/5)(x - 16) = 0
x - 1/5 = 0  or  x - 16 = 0
x = 1/5
x = 16


Input: Solve the equation x^3 - 17/12x^2 - 155/12x - 21/2 = 0

Output:
x^3 - 17/12x^2 - 155/12x - 21/2 = 0
(x - -9/4)(x - 14/3)(x - -1) = 0
x - -9/4 = 0
x - 14/3 = 0
x - -1 = 0
x = -9/4
x = 14/3
x = -1


Input:
Find x and y such that
7x + 9y = 1084/9
4x + 2y = 280/9

Output:
7x + 9y = 1084/9
4x + 2y = 280/9

Using elimination
4*(7x + 9y = 1084/9)
7*(4x + 2y = 280/9)
28x + 36y = 4336/9
28x + 14y = 1960/9
Subtract equations
22y = 264
y = 264/22
y = 12

Substitute y
7x + 9(12) = 1084/9
7x = 112/9
x = 112/9/7
x = 16/9


Input: Determine x in x^2 + 19/3x + 16/3 = 0

Output:
x^2 + 19/3x + 16/3 = 0
(x - -16/3)(x - -1) = 0
x - -16/3 = 0  or  x - -1 = 0
x = -16/3
x = -1


Input:
Find x and y such that
9x + 4y = -191/5
6x + 10y = -13

Output:
9x + 4y = -191/5
6x + 10y = -13

Using elimination
6*(9x + 4y = -191/5)
9*(6x + 10y = -13)
54x + 24y = -1146/5
54x + 90y = -117
Subtract equations
-66y = -561/5
y = -561/5/-66
y = 17/10

Substitute y
9x + 4(17/10) = -191/5
9x = -45
x = -45/9
x = -5


Input: Find x for x^2 + 91/72x + 1/3 = 0

Output:
x^2 + 91/72x + 1/3 = 0
(x - -8/9)(x - -3/8) = 0
x - -8/9 = 0  or  x - -3/8 = 0
x = -8/9
x = -3/8


Input: Solve the equation x^3 + 307/40x^2 + 2279/160x + 133/80 = 0

Output:
x^3 + 307/40x^2 + 2279/160x + 133/80 = 0
(x - -19/4)(x - -1/8)(x - -14/5) = 0
x - -19/4 = 0
x - -1/8 = 0
x - -14/5 = 0
x = -19/4
x = -1/8
x = -14/5


Input:
Solve the equations:
5x + 9y = -40/7
4x + 7y = -32/7

Output:
5x + 9y = -40/7
4x + 7y = -32/7

Using elimination
4*(5x + 9y = -40/7)
5*(4x + 7y = -32/7)
20x + 36y = -160/7
20x + 35y = -160/7
Subtract equations
1y = 0
y = 0/1
y = 0

Substitute y
5x + 9(0) = -40/7
5x = -40/7
x = -40/7/5
x = -8/7


Input: Find the solution to x^3 + 415/42x^2 + 1558/63x + 1805/126 = 0

Output:
x^3 + 415/42x^2 + 1558/63x + 1805/126 = 0
(x - -19/3)(x - -19/7)(x - -5/6) = 0
x - -19/3 = 0
x - -19/7 = 0
x - -5/6 = 0
x = -19/3
x = -19/7
x = -5/6


Input:
Solve simultaneously:
6x + 2y = -230/7
9x + 4y = -415/7

Output:
6x + 2y = -230/7
9x + 4y = -415/7

Using elimination
9*(6x + 2y = -230/7)
6*(9x + 4y = -415/7)
54x + 18y = -2070/7
54x + 24y = -2490/7
Subtract equations
-6y = 60
y = 60/-6
y = -10

Substitute y
6x + 2(-10) = -230/7
6x = -90/7
x = -90/7/6
x = -15/7


Input: Compute the solution of 8x - 56/3 = 0

Output:
8x - 56/3 = 0
8x = 56/3
x = 56/3 / 8
x = 7/3


Input: Compute the solution of x^2 + 13x + 22 = 0

Output:
x^2 + 13x + 22 = 0
(x - -2)(x - -11) = 0
x - -2 = 0  or  x - -11 = 0
x = -2
x = -11


Input: What value of x satisfies x^2 - 117/70x - 81/35 = 0

Output:
x^2 - 117/70x - 81/35 = 0
(x - 18/7)(x - -9/10) = 0
x - 18/7 = 0  or  x - -9/10 = 0
x = 18/7
x = -9/10


Input: Find x in x^2 - 1/24x - 1/8 = 0

Output:
x^2 - 1/24x - 1/8 = 0
(x - -1/3)(x - 3/8) = 0
x - -1/3 = 0  or  x - 3/8 = 0
x = -1/3
x = 3/8


Input:
Solve the equations:
3x + 6y = -450/7
2x + 5y = -377/7

Output:
3x + 6y = -450/7
2x + 5y = -377/7

Using elimination
2*(3x + 6y = -450/7)
3*(2x + 5y = -377/7)
6x + 12y = -900/7
6x + 15y = -1131/7
Subtract equations
-3y = 33
y = 33/-3
y = -11

Substitute y
3x + 6(-11) = -450/7
3x = 12/7
x = 12/7/3
x = 4/7


Input: Solve the equation 4x + 36/5 = 0

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


Input: Find x for x^3 - 25/24x^2 - 313/48x + 35/6 = 0

Output:
x^3 - 25/24x^2 - 313/48x + 35/6 = 0
(x - -5/2)(x - 8/3)(x - 7/8) = 0
x - -5/2 = 0
x - 8/3 = 0
x - 7/8 = 0
x = -5/2
x = 8/3
x = 7/8


Input: Compute the solution of x^3 - 117/35x^2 + 26/7x - 48/35 = 0

Output:
x^3 - 117/35x^2 + 26/7x - 48/35 = 0
(x - 6/5)(x - 1)(x - 8/7) = 0
x - 6/5 = 0
x - 1 = 0
x - 8/7 = 0
x = 6/5
x = 1
x = 8/7


Input: Find x for x^3 + 52/5x^2 + 25x + 42/5 = 0

Output:
x^3 + 52/5x^2 + 25x + 42/5 = 0
(x - -7)(x - -2/5)(x - -3) = 0
x - -7 = 0
x - -2/5 = 0
x - -3 = 0
x = -7
x = -2/5
x = -3


Input:
Solve simultaneously:
8x + 3y = 67/8
10x + 4y = 43/4

Output:
8x + 3y = 67/8
10x + 4y = 43/4

Using elimination
10*(8x + 3y = 67/8)
8*(10x + 4y = 43/4)
80x + 30y = 335/4
80x + 32y = 86
Subtract equations
-2y = -9/4
y = -9/4/-2
y = 9/8

Substitute y
8x + 3(9/8) = 67/8
8x = 5
x = 5/8
x = 5/8


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

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


Input: Solve quickly: 7x + 10 = 0

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


Input:
Solve the equations:
9x + 7y = -2
9x + 5y = 0

Output:
9x + 7y = -2
9x + 5y = 0

Using elimination
9*(9x + 7y = -2)
9*(9x + 5y = 0)
81x + 63y = -18
81x + 45y = 0
Subtract equations
18y = -18
y = -18/18
y = -1

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


Input: Find the solution to x^2 - 29/40x - 9/20 = 0

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


Input: Determine x in x^2 + 71/30x + 17/15 = 0

Output:
x^2 + 71/30x + 17/15 = 0
(x - -2/3)(x - -17/10) = 0
x - -2/3 = 0  or  x - -17/10 = 0
x = -2/3
x = -17/10


Input: Solve the equation x^3 + 33/40x^2 - 2907/400x + 2023/400 = 0

Output:
x^3 + 33/40x^2 - 2907/400x + 2023/400 = 0
(x - 7/8)(x - 17/10)(x - -17/5) = 0
x - 7/8 = 0
x - 17/10 = 0
x - -17/5 = 0
x = 7/8
x = 17/10
x = -17/5


Input: What value of x satisfies 9x - 27/2 = 0

Output:
9x - 27/2 = 0
9x = 27/2
x = 27/2 / 9
x = 3/2


Input: Solve 1x + 11/5 = 0

Output:
1x + 11/5 = 0
1x = -11/5
x = -11/5 / 1
x = -11/5


Input: Compute the solution of x^2 - 8x + 7 = 0

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


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

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


Input: What value of x satisfies 5x - 95 = 0

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


Input: Compute the solution of x^3 + 97/40x^2 - 89/50x - 1001/200 = 0

Output:
x^3 + 97/40x^2 - 89/50x - 1001/200 = 0
(x - -11/5)(x - 7/5)(x - -13/8) = 0
x - -11/5 = 0
x - 7/5 = 0
x - -13/8 = 0
x = -11/5
x = 7/5
x = -13/8


Input: Find x in x^3 - 101/42x^2 - 3/7x  = 0

Output:
x^3 - 101/42x^2 - 3/7x  = 0
(x - -1/6)(x - 18/7)(x - 0) = 0
x - -1/6 = 0
x - 18/7 = 0
x - 0 = 0
x = -1/6
x = 18/7
x = 0


Input: Solve quickly: 7x - 6 = 0

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


Input:
Solve simultaneously:
2x + 4y = 22/5
8x + 8y = 164/5

Output:
2x + 4y = 22/5
8x + 8y = 164/5

Using elimination
8*(2x + 4y = 22/5)
2*(8x + 8y = 164/5)
16x + 32y = 176/5
16x + 16y = 328/5
Subtract equations
16y = -152/5
y = -152/5/16
y = -19/10

Substitute y
2x + 4(-19/10) = 22/5
2x = 12
x = 12/2
x = 6


Input: Find x for 5x - 25/7 = 0

Output:
5x - 25/7 = 0
5x = 25/7
x = 25/7 / 5
x = 5/7


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

Output:
2x + 16/3 = 0
2x = -16/3
x = -16/3 / 2
x = -8/3


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 x in 3x - 1 = 0

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


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

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


Input: Find the solution to 7x - 133/4 = 0

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


Input: Find x in 3x + 6 = 0

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


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

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


Input: Solve x^2 - 43/7x + 6/7 = 0

Output:
x^2 - 43/7x + 6/7 = 0
(x - 6)(x - 1/7) = 0
x - 6 = 0  or  x - 1/7 = 0
x = 6
x = 1/7


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

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

Using elimination
1*(3x + 6y = -30)
3*(1x + 4y = -15)
3x + 6y = -30
3x + 12y = -45
Subtract equations
-6y = 15
y = 15/-6
y = -5/2

Substitute y
3x + 6(-5/2) = -30
3x = -15
x = -15/3
x = -5


Input: Determine x in x^3 - 89/35x^2 - 391/35x - 39/7 = 0

Output:
x^3 - 89/35x^2 - 391/35x - 39/7 = 0
(x - 5)(x - -13/7)(x - -3/5) = 0
x - 5 = 0
x - -13/7 = 0
x - -3/5 = 0
x = 5
x = -13/7
x = -3/5


Input: Compute the solution of x^2 + 77/5x + 156/5 = 0

Output:
x^2 + 77/5x + 156/5 = 0
(x - -12/5)(x - -13) = 0
x - -12/5 = 0  or  x - -13 = 0
x = -12/5
x = -13


Input: Solve the equation x^3 - 25/2x^2 - 92x - 126 = 0

Output:
x^3 - 25/2x^2 - 92x - 126 = 0
(x - 18)(x - -2)(x - -7/2) = 0
x - 18 = 0
x - -2 = 0
x - -7/2 = 0
x = 18
x = -2
x = -7/2


Input: Find x in x^3 - 1/3x^2 - 158/9x + 104/9 = 0

Output:
x^3 - 1/3x^2 - 158/9x + 104/9 = 0
(x - 2/3)(x - 4)(x - -13/3) = 0
x - 2/3 = 0
x - 4 = 0
x - -13/3 = 0
x = 2/3
x = 4
x = -13/3


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

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


Input: Solve quickly: x^2 + 23/8x + 15/8 = 0

Output:
x^2 + 23/8x + 15/8 = 0
(x - -15/8)(x - -1) = 0
x - -15/8 = 0  or  x - -1 = 0
x = -15/8
x = -1


Input: Determine x in 4x + 4/7 = 0

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


Input: Find x for x^2 + 19/4x - 26 = 0

Output:
x^2 + 19/4x - 26 = 0
(x - -8)(x - 13/4) = 0
x - -8 = 0  or  x - 13/4 = 0
x = -8
x = 13/4


Input:
Solve the system:
2x + 6y = -8
7x + 3y = -4

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

Using elimination
7*(2x + 6y = -8)
2*(7x + 3y = -4)
14x + 42y = -56
14x + 6y = -8
Subtract equations
36y = -48
y = -48/36
y = -4/3

Substitute y
2x + 6(-4/3) = -8
2x = 0
x = 0/2
x = 0


Input:
Solve the system:
4x + 6y = 12
5x + 8y = 15

Output:
4x + 6y = 12
5x + 8y = 15

Using elimination
5*(4x + 6y = 12)
4*(5x + 8y = 15)
20x + 30y = 60
20x + 32y = 60
Subtract equations
-2y = 0
y = 0/-2
y = 0

Substitute y
4x + 6(0) = 12
4x = 12
x = 12/4
x = 3


Input: Find x in x^3 - 16/3x^2 - 125/3x - 50 = 0

Output:
x^3 - 16/3x^2 - 125/3x - 50 = 0
(x - -5/3)(x - 10)(x - -3) = 0
x - -5/3 = 0
x - 10 = 0
x - -3 = 0
x = -5/3
x = 10
x = -3


Input: Find x in 4x + 28/3 = 0

Output:
4x + 28/3 = 0
4x = -28/3
x = -28/3 / 4
x = -7/3


Input: Find x for x^3 - 23/15x^2 - 4/15x + 4/5 = 0

Output:
x^3 - 23/15x^2 - 4/15x + 4/5 = 0
(x - 6/5)(x - -2/3)(x - 1) = 0
x - 6/5 = 0
x - -2/3 = 0
x - 1 = 0
x = 6/5
x = -2/3
x = 1


Input: Solve quickly: 5x - 5 = 0

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


Input: Find x for x^3 - 29/42x^2 - 8/3x + 13/14 = 0

Output:
x^3 - 29/42x^2 - 8/3x + 13/14 = 0
(x - -3/2)(x - 1/3)(x - 13/7) = 0
x - -3/2 = 0
x - 1/3 = 0
x - 13/7 = 0
x = -3/2
x = 1/3
x = 13/7


Input: Find the solution to x^3 + 664/105x^2 + 4559/420x + 19/7 = 0

Output:
x^3 + 664/105x^2 + 4559/420x + 19/7 = 0
(x - -20/7)(x - -3/10)(x - -19/6) = 0
x - -20/7 = 0
x - -3/10 = 0
x - -19/6 = 0
x = -20/7
x = -3/10
x = -19/6


Input: Solve the equation x^3 + 23/3x^2 + 52/3x + 32/3 = 0

Output:
x^3 + 23/3x^2 + 52/3x + 32/3 = 0
(x - -8/3)(x - -4)(x - -1) = 0
x - -8/3 = 0
x - -4 = 0
x - -1 = 0
x = -8/3
x = -4
x = -1


Input: Find x for x^2 - 1/15x - 28/5 = 0

Output:
x^2 - 1/15x - 28/5 = 0
(x - -7/3)(x - 12/5) = 0
x - -7/3 = 0  or  x - 12/5 = 0
x = -7/3
x = 12/5


Input: Solve the equation x^3 + 23/4x^2 - 5/4x - 231/16 = 0

Output:
x^3 + 23/4x^2 - 5/4x - 231/16 = 0
(x - -7/4)(x - 3/2)(x - -11/2) = 0
x - -7/4 = 0
x - 3/2 = 0
x - -11/2 = 0
x = -7/4
x = 3/2
x = -11/2


Input:
Solve the equations:
5x + 6y = -97/2
9x + 8y = -493/6

Output:
5x + 6y = -97/2
9x + 8y = -493/6

Using elimination
9*(5x + 6y = -97/2)
5*(9x + 8y = -493/6)
45x + 54y = -873/2
45x + 40y = -2465/6
Subtract equations
14y = -77/3
y = -77/3/14
y = -11/6

Substitute y
5x + 6(-11/6) = -97/2
5x = -75/2
x = -75/2/5
x = -15/2


Input: Determine x in 5x - 9/2 = 0

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


Input: Solve 7x + 28 = 0

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


Input:
Find x and y such that
10x + 8y = -1246/9
2x + 10y = -140/9

Output:
10x + 8y = -1246/9
2x + 10y = -140/9

Using elimination
2*(10x + 8y = -1246/9)
10*(2x + 10y = -140/9)
20x + 16y = -2492/9
20x + 100y = -1400/9
Subtract equations
-84y = -364/3
y = -364/3/-84
y = 13/9

Substitute y
10x + 8(13/9) = -1246/9
10x = -150
x = -150/10
x = -15


Input:
Solve the system:
2x + 5y = -4
8x + 3y = -46/5

Output:
2x + 5y = -4
8x + 3y = -46/5

Using elimination
8*(2x + 5y = -4)
2*(8x + 3y = -46/5)
16x + 40y = -32
16x + 6y = -92/5
Subtract equations
34y = -68/5
y = -68/5/34
y = -2/5

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


Input: Find x for x^3 - 73/4x^2 + 173/8x - 51/8 = 0

Output:
x^3 - 73/4x^2 + 173/8x - 51/8 = 0
(x - 1/2)(x - 3/4)(x - 17) = 0
x - 1/2 = 0
x - 3/4 = 0
x - 17 = 0
x = 1/2
x = 3/4
x = 17


Input: Determine x in x^2 - 138/7x - 40/7 = 0

Output:
x^2 - 138/7x - 40/7 = 0
(x - -2/7)(x - 20) = 0
x - -2/7 = 0  or  x - 20 = 0
x = -2/7
x = 20


Input: Solve the equation x^3 - 67/12x^2 + 67/9x - 55/36 = 0

Output:
x^3 - 67/12x^2 + 67/9x - 55/36 = 0
(x - 5/3)(x - 11/3)(x - 1/4) = 0
x - 5/3 = 0
x - 11/3 = 0
x - 1/4 = 0
x = 5/3
x = 11/3
x = 1/4


Input: Solve the equation 6x - 15/2 = 0

Output:
6x - 15/2 = 0
6x = 15/2
x = 15/2 / 6
x = 5/4


Input: Determine x in x^3 - 21/10x^2 - 21/5x + 8 = 0

Output:
x^3 - 21/10x^2 - 21/5x + 8 = 0
(x - 8/5)(x - 5/2)(x - -2) = 0
x - 8/5 = 0
x - 5/2 = 0
x - -2 = 0
x = 8/5
x = 5/2
x = -2


Input: Determine x in x^2 + 63/10x - 187/10 = 0

Output:
x^2 + 63/10x - 187/10 = 0
(x - -17/2)(x - 11/5) = 0
x - -17/2 = 0  or  x - 11/5 = 0
x = -17/2
x = 11/5


Input: What value of x satisfies 5x  = 0

Output:
5x  = 0
5x = 0
x = 0 / 5
x = 0


Input: Solve quickly: x^3 - 443/63x^2 + 704/63x - 320/63 = 0

Output:
x^3 - 443/63x^2 + 704/63x - 320/63 = 0
(x - 8/9)(x - 8/7)(x - 5) = 0
x - 8/9 = 0
x - 8/7 = 0
x - 5 = 0
x = 8/9
x = 8/7
x = 5


Input: Compute the solution of x^3 + 2x^2 + 99/100x  = 0

Output:
x^3 + 2x^2 + 99/100x  = 0
(x - -9/10)(x - -11/10)(x - 0) = 0
x - -9/10 = 0
x - -11/10 = 0
x - 0 = 0
x = -9/10
x = -11/10
x = 0


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

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