Input:
Solve the system:
5x + 4y = -619/20
2x + 6y = -203/10

Output:
5x + 4y = -619/20
2x + 6y = -203/10

Using elimination
2*(5x + 4y = -619/20)
5*(2x + 6y = -203/10)
10x + 8y = -619/10
10x + 30y = -203/2
Subtract equations
-22y = 198/5
y = 198/5/-22
y = -9/5

Substitute y
5x + 4(-9/5) = -619/20
5x = -95/4
x = -95/4/5
x = -19/4


Input: Find x in 6x + 34 = 0

Output:
6x + 34 = 0
6x = -34
x = -34 / 6
x = -17/3


Input:
Find x and y such that
2x + 9y = -79/2
3x + 6y = -137/4

Output:
2x + 9y = -79/2
3x + 6y = -137/4

Using elimination
3*(2x + 9y = -79/2)
2*(3x + 6y = -137/4)
6x + 27y = -237/2
6x + 12y = -137/2
Subtract equations
15y = -50
y = -50/15
y = -10/3

Substitute y
2x + 9(-10/3) = -79/2
2x = -19/2
x = -19/2/2
x = -19/4


Input:
Solve the equations:
1x + 6y = 348/35
7x + 2y = -12/5

Output:
1x + 6y = 348/35
7x + 2y = -12/5

Using elimination
7*(1x + 6y = 348/35)
1*(7x + 2y = -12/5)
7x + 42y = 348/5
7x + 2y = -12/5
Subtract equations
40y = 72
y = 72/40
y = 9/5

Substitute y
1x + 6(9/5) = 348/35
1x = -6/7
x = -6/7/1
x = -6/7


Input: Find x in x^3 + 209/84x^2 - 83/12x + 17/7 = 0

Output:
x^3 + 209/84x^2 - 83/12x + 17/7 = 0
(x - 4/3)(x - 3/7)(x - -17/4) = 0
x - 4/3 = 0
x - 3/7 = 0
x - -17/4 = 0
x = 4/3
x = 3/7
x = -17/4


Input: Solve 10x - 5 = 0

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


Input: Compute the solution of x^3 + 49/2x^2 + 107x + 95/2 = 0

Output:
x^3 + 49/2x^2 + 107x + 95/2 = 0
(x - -5)(x - -1/2)(x - -19) = 0
x - -5 = 0
x - -1/2 = 0
x - -19 = 0
x = -5
x = -1/2
x = -19


Input: Solve quickly: x^3 + 29/20x^2 - 199/20x + 663/80 = 0

Output:
x^3 + 29/20x^2 - 199/20x + 663/80 = 0
(x - -17/4)(x - 13/10)(x - 3/2) = 0
x - -17/4 = 0
x - 13/10 = 0
x - 3/2 = 0
x = -17/4
x = 13/10
x = 3/2


Input: Solve quickly: x^2 + 63/10x + 22/5 = 0

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


Input:
Solve the equations:
3x + 4y = -217/30
6x + 7y = -182/15

Output:
3x + 4y = -217/30
6x + 7y = -182/15

Using elimination
6*(3x + 4y = -217/30)
3*(6x + 7y = -182/15)
18x + 24y = -217/5
18x + 21y = -182/5
Subtract equations
3y = -7
y = -7/3
y = -7/3

Substitute y
3x + 4(-7/3) = -217/30
3x = 21/10
x = 21/10/3
x = 7/10


Input:
Find x and y such that
3x + 6y = -113
10x + 9y = -536/3

Output:
3x + 6y = -113
10x + 9y = -536/3

Using elimination
10*(3x + 6y = -113)
3*(10x + 9y = -536/3)
30x + 60y = -1130
30x + 27y = -536
Subtract equations
33y = -594
y = -594/33
y = -18

Substitute y
3x + 6(-18) = -113
3x = -5
x = -5/3
x = -5/3


Input: Determine x in 10x + 40/7 = 0

Output:
10x + 40/7 = 0
10x = -40/7
x = -40/7 / 10
x = -4/7


Input:
Find x and y such that
9x + 8y = -98/5
2x + 6y = -64/5

Output:
9x + 8y = -98/5
2x + 6y = -64/5

Using elimination
2*(9x + 8y = -98/5)
9*(2x + 6y = -64/5)
18x + 16y = -196/5
18x + 54y = -576/5
Subtract equations
-38y = 76
y = 76/-38
y = -2

Substitute y
9x + 8(-2) = -98/5
9x = -18/5
x = -18/5/9
x = -2/5


Input: Solve the equation x^2 - 8x - 17/4 = 0

Output:
x^2 - 8x - 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 x^3 - 41/20x^2 - 1/2x + 6/5 = 0

Output:
x^3 - 41/20x^2 - 1/2x + 6/5 = 0
(x - -3/4)(x - 4/5)(x - 2) = 0
x - -3/4 = 0
x - 4/5 = 0
x - 2 = 0
x = -3/4
x = 4/5
x = 2


Input:
Solve simultaneously:
5x + 7y = 217/8
4x + 6y = 89/4

Output:
5x + 7y = 217/8
4x + 6y = 89/4

Using elimination
4*(5x + 7y = 217/8)
5*(4x + 6y = 89/4)
20x + 28y = 217/2
20x + 30y = 445/4
Subtract equations
-2y = -11/4
y = -11/4/-2
y = 11/8

Substitute y
5x + 7(11/8) = 217/8
5x = 35/2
x = 35/2/5
x = 7/2


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

Output:
x^2 - 5/2x - 26 = 0
(x - -4)(x - 13/2) = 0
x - -4 = 0  or  x - 13/2 = 0
x = -4
x = 13/2


Input: Compute the solution of 2x - 1/2 = 0

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


Input:
Find x and y such that
3x + 3y = 27/2
5x + 2y = 30

Output:
3x + 3y = 27/2
5x + 2y = 30

Using elimination
5*(3x + 3y = 27/2)
3*(5x + 2y = 30)
15x + 15y = 135/2
15x + 6y = 90
Subtract equations
9y = -45/2
y = -45/2/9
y = -5/2

Substitute y
3x + 3(-5/2) = 27/2
3x = 21
x = 21/3
x = 7


Input: Find x in x^3 + 514/45x^2 + 349/15x + 66/5 = 0

Output:
x^3 + 514/45x^2 + 349/15x + 66/5 = 0
(x - -11/9)(x - -9)(x - -6/5) = 0
x - -11/9 = 0
x - -9 = 0
x - -6/5 = 0
x = -11/9
x = -9
x = -6/5


Input:
Solve the system:
6x + 4y = 100/7
4x + 5y = 83/7

Output:
6x + 4y = 100/7
4x + 5y = 83/7

Using elimination
4*(6x + 4y = 100/7)
6*(4x + 5y = 83/7)
24x + 16y = 400/7
24x + 30y = 498/7
Subtract equations
-14y = -14
y = -14/-14
y = 1

Substitute y
6x + 4(1) = 100/7
6x = 72/7
x = 72/7/6
x = 12/7


Input: Determine x in 10x - 35/2 = 0

Output:
10x - 35/2 = 0
10x = 35/2
x = 35/2 / 10
x = 7/4


Input:
Solve the equations:
6x + 2y = -8/9
2x + 6y = -8/3

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

Using elimination
2*(6x + 2y = -8/9)
6*(2x + 6y = -8/3)
12x + 4y = -16/9
12x + 36y = -16
Subtract equations
-32y = 128/9
y = 128/9/-32
y = -4/9

Substitute y
6x + 2(-4/9) = -8/9
6x = 0
x = 0/6
x = 0


Input: What value of x satisfies x^2 + 13/18x - 10/3 = 0

Output:
x^2 + 13/18x - 10/3 = 0
(x - 3/2)(x - -20/9) = 0
x - 3/2 = 0  or  x - -20/9 = 0
x = 3/2
x = -20/9


Input: Solve x^2 + 36/5x + 36/5 = 0

Output:
x^2 + 36/5x + 36/5 = 0
(x - -6/5)(x - -6) = 0
x - -6/5 = 0  or  x - -6 = 0
x = -6/5
x = -6


Input: Find x in x^3 - 59/3x^2 + 38/3x  = 0

Output:
x^3 - 59/3x^2 + 38/3x  = 0
(x - 0)(x - 19)(x - 2/3) = 0
x - 0 = 0
x - 19 = 0
x - 2/3 = 0
x = 0
x = 19
x = 2/3


Input: Find x in 1x - 17/3 = 0

Output:
1x - 17/3 = 0
1x = 17/3
x = 17/3 / 1
x = 17/3


Input: Compute the solution of 2x + 6 = 0

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


Input: Find the solution to x^2 + 7/6x - 1/2 = 0

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


Input: Find the solution to x^2 - 1x + 4/25 = 0

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


Input:
Solve simultaneously:
3x + 1y = -13/2
1x + 1y = -5/2

Output:
3x + 1y = -13/2
1x + 1y = -5/2

Using elimination
1*(3x + 1y = -13/2)
3*(1x + 1y = -5/2)
3x + 1y = -13/2
3x + 3y = -15/2
Subtract equations
-2y = 1
y = 1/-2
y = -1/2

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


Input: What value of x satisfies x^2 - 13/18x - 35/27 = 0

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


Input:
Solve simultaneously:
5x + 10y = -33
9x + 4y = 18/5

Output:
5x + 10y = -33
9x + 4y = 18/5

Using elimination
9*(5x + 10y = -33)
5*(9x + 4y = 18/5)
45x + 90y = -297
45x + 20y = 18
Subtract equations
70y = -315
y = -315/70
y = -9/2

Substitute y
5x + 10(-9/2) = -33
5x = 12
x = 12/5
x = 12/5


Input: Find x for 5x - 25 = 0

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


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

Output:
x^2 + 7/24x - 5/24 = 0
(x - 1/3)(x - -5/8) = 0
x - 1/3 = 0  or  x - -5/8 = 0
x = 1/3
x = -5/8


Input: What value of x satisfies 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:
Solve simultaneously:
4x + 8y = -169/6
10x + 7y = -481/12

Output:
4x + 8y = -169/6
10x + 7y = -481/12

Using elimination
10*(4x + 8y = -169/6)
4*(10x + 7y = -481/12)
40x + 80y = -845/3
40x + 28y = -481/3
Subtract equations
52y = -364/3
y = -364/3/52
y = -7/3

Substitute y
4x + 8(-7/3) = -169/6
4x = -19/2
x = -19/2/4
x = -19/8


Input: What value of x satisfies x^2 + 11/8x - 19/8 = 0

Output:
x^2 + 11/8x - 19/8 = 0
(x - -19/8)(x - 1) = 0
x - -19/8 = 0  or  x - 1 = 0
x = -19/8
x = 1


Input: Determine x in x^2 - 109/24x - 51/8 = 0

Output:
x^2 - 109/24x - 51/8 = 0
(x - 17/3)(x - -9/8) = 0
x - 17/3 = 0  or  x - -9/8 = 0
x = 17/3
x = -9/8


Input: Find x in 7x + 105/8 = 0

Output:
7x + 105/8 = 0
7x = -105/8
x = -105/8 / 7
x = -15/8


Input: Solve quickly: x^3 + 131/42x^2 - 11/7x - 5/6 = 0

Output:
x^3 + 131/42x^2 - 11/7x - 5/6 = 0
(x - -1/3)(x - -7/2)(x - 5/7) = 0
x - -1/3 = 0
x - -7/2 = 0
x - 5/7 = 0
x = -1/3
x = -7/2
x = 5/7


Input: What value of x satisfies x^2 + 1/20x - 3/40 = 0

Output:
x^2 + 1/20x - 3/40 = 0
(x - -3/10)(x - 1/4) = 0
x - -3/10 = 0  or  x - 1/4 = 0
x = -3/10
x = 1/4


Input: Solve quickly: x^3 + 625/36x^2 - 1025/18x - 250/3 = 0

Output:
x^3 + 625/36x^2 - 1025/18x - 250/3 = 0
(x - -10/9)(x - 15/4)(x - -20) = 0
x - -10/9 = 0
x - 15/4 = 0
x - -20 = 0
x = -10/9
x = 15/4
x = -20


Input: What value of x satisfies x^3 + 54/7x^2 + 2097/112x + 405/28 = 0

Output:
x^3 + 54/7x^2 + 2097/112x + 405/28 = 0
(x - -15/4)(x - -9/4)(x - -12/7) = 0
x - -15/4 = 0
x - -9/4 = 0
x - -12/7 = 0
x = -15/4
x = -9/4
x = -12/7


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

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


Input:
Find x and y such that
7x + 6y = -140
8x + 2y = -446/3

Output:
7x + 6y = -140
8x + 2y = -446/3

Using elimination
8*(7x + 6y = -140)
7*(8x + 2y = -446/3)
56x + 48y = -1120
56x + 14y = -3122/3
Subtract equations
34y = -238/3
y = -238/3/34
y = -7/3

Substitute y
7x + 6(-7/3) = -140
7x = -126
x = -126/7
x = -18


Input: Find x in x^2 + 23/2x + 15 = 0

Output:
x^2 + 23/2x + 15 = 0
(x - -10)(x - -3/2) = 0
x - -10 = 0  or  x - -3/2 = 0
x = -10
x = -3/2


Input: Find x for x^2 - 1/10x - 3/10 = 0

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


Input: Compute the solution of x^3 + 7/12x^2 - 203/12x - 17/3 = 0

Output:
x^3 + 7/12x^2 - 203/12x - 17/3 = 0
(x - -17/4)(x - -1/3)(x - 4) = 0
x - -17/4 = 0
x - -1/3 = 0
x - 4 = 0
x = -17/4
x = -1/3
x = 4


Input: What value of x satisfies x^3 - 493/28x^2 - 184/7x - 95/28 = 0

Output:
x^3 - 493/28x^2 - 184/7x - 95/28 = 0
(x - -5/4)(x - -1/7)(x - 19) = 0
x - -5/4 = 0
x - -1/7 = 0
x - 19 = 0
x = -5/4
x = -1/7
x = 19


Input: Determine x in x^2 + 172/9x + 323/9 = 0

Output:
x^2 + 172/9x + 323/9 = 0
(x - -19/9)(x - -17) = 0
x - -19/9 = 0  or  x - -17 = 0
x = -19/9
x = -17


Input: Solve quickly: x^2 + 32/3x + 256/9 = 0

Output:
x^2 + 32/3x + 256/9 = 0
(x - -16/3)(x - -16/3) = 0
x - -16/3 = 0  or  x - -16/3 = 0
x = -16/3
x = -16/3


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

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


Input:
Solve the equations:
5x + 10y = -10/3
10x + 5y = -85/6

Output:
5x + 10y = -10/3
10x + 5y = -85/6

Using elimination
10*(5x + 10y = -10/3)
5*(10x + 5y = -85/6)
50x + 100y = -100/3
50x + 25y = -425/6
Subtract equations
75y = 75/2
y = 75/2/75
y = 1/2

Substitute y
5x + 10(1/2) = -10/3
5x = -25/3
x = -25/3/5
x = -5/3


Input: Compute the solution of x^3 - 103/9x^2 + 941/36x - 85/9 = 0

Output:
x^3 - 103/9x^2 + 941/36x - 85/9 = 0
(x - 5/2)(x - 17/2)(x - 4/9) = 0
x - 5/2 = 0
x - 17/2 = 0
x - 4/9 = 0
x = 5/2
x = 17/2
x = 4/9


Input: What value of x satisfies x^3 + 6/5x^2 + 1/20x - 33/500 = 0

Output:
x^3 + 6/5x^2 + 1/20x - 33/500 = 0
(x - -11/10)(x - 1/5)(x - -3/10) = 0
x - -11/10 = 0
x - 1/5 = 0
x - -3/10 = 0
x = -11/10
x = 1/5
x = -3/10


Input: Determine x in 1x - 4/3 = 0

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


Input: Compute the solution of 2x - 14 = 0

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


Input:
Find x and y such that
2x + 5y = -163/9
8x + 3y = -193/9

Output:
2x + 5y = -163/9
8x + 3y = -193/9

Using elimination
8*(2x + 5y = -163/9)
2*(8x + 3y = -193/9)
16x + 40y = -1304/9
16x + 6y = -386/9
Subtract equations
34y = -102
y = -102/34
y = -3

Substitute y
2x + 5(-3) = -163/9
2x = -28/9
x = -28/9/2
x = -14/9


Input: Find the solution to x^2 - 37/20x - 63/10 = 0

Output:
x^2 - 37/20x - 63/10 = 0
(x - -7/4)(x - 18/5) = 0
x - -7/4 = 0  or  x - 18/5 = 0
x = -7/4
x = 18/5


Input: Solve x^2 + 26/3x - 95 = 0

Output:
x^2 + 26/3x - 95 = 0
(x - -15)(x - 19/3) = 0
x - -15 = 0  or  x - 19/3 = 0
x = -15
x = 19/3


Input: Compute the solution of x^3 + 143/18x^2 + 340/27x + 50/9 = 0

Output:
x^3 + 143/18x^2 + 340/27x + 50/9 = 0
(x - -6)(x - -10/9)(x - -5/6) = 0
x - -6 = 0
x - -10/9 = 0
x - -5/6 = 0
x = -6
x = -10/9
x = -5/6


Input: Find the solution to x^2 + 59/10x - 3/5 = 0

Output:
x^2 + 59/10x - 3/5 = 0
(x - 1/10)(x - -6) = 0
x - 1/10 = 0  or  x - -6 = 0
x = 1/10
x = -6


Input: Solve 9x - 54 = 0

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


Input: Solve quickly: 6x - 3 = 0

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


Input: Find x for x^3 - 22/35x^2 - 167/35x + 34/35 = 0

Output:
x^3 - 22/35x^2 - 167/35x + 34/35 = 0
(x - 17/7)(x - -2)(x - 1/5) = 0
x - 17/7 = 0
x - -2 = 0
x - 1/5 = 0
x = 17/7
x = -2
x = 1/5


Input: Compute the solution of x^3 + 13x^2 - 741/25x + 27/5 = 0

Output:
x^3 + 13x^2 - 741/25x + 27/5 = 0
(x - -15)(x - 1/5)(x - 9/5) = 0
x - -15 = 0
x - 1/5 = 0
x - 9/5 = 0
x = -15
x = 1/5
x = 9/5


Input:
Solve the system:
8x + 9y = -64/7
1x + 2y = -15/7

Output:
8x + 9y = -64/7
1x + 2y = -15/7

Using elimination
1*(8x + 9y = -64/7)
8*(1x + 2y = -15/7)
8x + 9y = -64/7
8x + 16y = -120/7
Subtract equations
-7y = 8
y = 8/-7
y = -8/7

Substitute y
8x + 9(-8/7) = -64/7
8x = 8/7
x = 8/7/8
x = 1/7


Input: Solve quickly: x^2 + 37/9x + 70/27 = 0

Output:
x^2 + 37/9x + 70/27 = 0
(x - -7/9)(x - -10/3) = 0
x - -7/9 = 0  or  x - -10/3 = 0
x = -7/9
x = -10/3


Input: Solve quickly: 9x - 63/5 = 0

Output:
9x - 63/5 = 0
9x = 63/5
x = 63/5 / 9
x = 7/5


Input: Solve x^2 + 4/3x + 1/3 = 0

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


Input: Find x in x^3 + 137/30x^2 - 28/3x - 22/5 = 0

Output:
x^3 + 137/30x^2 - 28/3x - 22/5 = 0
(x - -6)(x - -2/5)(x - 11/6) = 0
x - -6 = 0
x - -2/5 = 0
x - 11/6 = 0
x = -6
x = -2/5
x = 11/6


Input:
Solve the system:
4x + 8y = 62/3
8x + 8y = 92/3

Output:
4x + 8y = 62/3
8x + 8y = 92/3

Using elimination
8*(4x + 8y = 62/3)
4*(8x + 8y = 92/3)
32x + 64y = 496/3
32x + 32y = 368/3
Subtract equations
32y = 128/3
y = 128/3/32
y = 4/3

Substitute y
4x + 8(4/3) = 62/3
4x = 10
x = 10/4
x = 5/2


Input: Find the solution to 7x + 63/4 = 0

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


Input: Determine x in 8x - 112/9 = 0

Output:
8x - 112/9 = 0
8x = 112/9
x = 112/9 / 8
x = 14/9


Input: Find x in x^3 + 1x^2 - 35/4x  = 0

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


Input:
Solve the system:
3x + 5y = -333/20
8x + 6y = -279/10

Output:
3x + 5y = -333/20
8x + 6y = -279/10

Using elimination
8*(3x + 5y = -333/20)
3*(8x + 6y = -279/10)
24x + 40y = -666/5
24x + 18y = -837/10
Subtract equations
22y = -99/2
y = -99/2/22
y = -9/4

Substitute y
3x + 5(-9/4) = -333/20
3x = -27/5
x = -27/5/3
x = -9/5


Input: Solve x^2 + 31/6x + 7/3 = 0

Output:
x^2 + 31/6x + 7/3 = 0
(x - -1/2)(x - -14/3) = 0
x - -1/2 = 0  or  x - -14/3 = 0
x = -1/2
x = -14/3


Input: Find x for x^3 - 53/21x^2 - 974/147x + 816/49 = 0

Output:
x^3 - 53/21x^2 - 974/147x + 816/49 = 0
(x - 8/3)(x - 17/7)(x - -18/7) = 0
x - 8/3 = 0
x - 17/7 = 0
x - -18/7 = 0
x = 8/3
x = 17/7
x = -18/7


Input: Find x for 7x + 77/5 = 0

Output:
7x + 77/5 = 0
7x = -77/5
x = -77/5 / 7
x = -11/5


Input:
Solve the equations:
5x + 1y = -13/3
8x + 2y = -142/15

Output:
5x + 1y = -13/3
8x + 2y = -142/15

Using elimination
8*(5x + 1y = -13/3)
5*(8x + 2y = -142/15)
40x + 8y = -104/3
40x + 10y = -142/3
Subtract equations
-2y = 38/3
y = 38/3/-2
y = -19/3

Substitute y
5x + 1(-19/3) = -13/3
5x = 2
x = 2/5
x = 2/5


Input: What value of x satisfies 4x + 1/2 = 0

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


Input: Solve quickly: x^2 - 23/3x + 14/3 = 0

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


Input: Find the solution to x^3 + 53/9x^2 - 166/27x - 520/81 = 0

Output:
x^3 + 53/9x^2 - 166/27x - 520/81 = 0
(x - -2/3)(x - -20/3)(x - 13/9) = 0
x - -2/3 = 0
x - -20/3 = 0
x - 13/9 = 0
x = -2/3
x = -20/3
x = 13/9


Input: Solve quickly: x^3 + 81/20x^2 + 91/20x + 9/10 = 0

Output:
x^3 + 81/20x^2 + 91/20x + 9/10 = 0
(x - -2)(x - -1/4)(x - -9/5) = 0
x - -2 = 0
x - -1/4 = 0
x - -9/5 = 0
x = -2
x = -1/4
x = -9/5


Input:
Solve the system:
1x + 7y = 37
5x + 10y = 60

Output:
1x + 7y = 37
5x + 10y = 60

Using elimination
5*(1x + 7y = 37)
1*(5x + 10y = 60)
5x + 35y = 185
5x + 10y = 60
Subtract equations
25y = 125
y = 125/25
y = 5

Substitute y
1x + 7(5) = 37
1x = 2
x = 2/1
x = 2


Input: Find x in 8x - 96/5 = 0

Output:
8x - 96/5 = 0
8x = 96/5
x = 96/5 / 8
x = 12/5


Input: What value of x satisfies x^3 + 23/3x^2 - 556/81x - 2720/81 = 0

Output:
x^3 + 23/3x^2 - 556/81x - 2720/81 = 0
(x - 20/9)(x - -8)(x - -17/9) = 0
x - 20/9 = 0
x - -8 = 0
x - -17/9 = 0
x = 20/9
x = -8
x = -17/9


Input: Determine x in x^3 - 41/2x^2 + 1001/9x - 3211/18 = 0

Output:
x^3 - 41/2x^2 + 1001/9x - 3211/18 = 0
(x - 13/3)(x - 19/6)(x - 13) = 0
x - 13/3 = 0
x - 19/6 = 0
x - 13 = 0
x = 13/3
x = 19/6
x = 13


Input: Determine x in x^3 + 153/7x^2 + 258/7x - 40/7 = 0

Output:
x^3 + 153/7x^2 + 258/7x - 40/7 = 0
(x - -20)(x - -2)(x - 1/7) = 0
x - -20 = 0
x - -2 = 0
x - 1/7 = 0
x = -20
x = -2
x = 1/7


Input: Solve quickly: x^2 - 16x + 48 = 0

Output:
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x - 4 = 0  or  x - 12 = 0
x = 4
x = 12


Input: Solve quickly: x^2 + 29/15x - 52/5 = 0

Output:
x^2 + 29/15x - 52/5 = 0
(x - -13/3)(x - 12/5) = 0
x - -13/3 = 0  or  x - 12/5 = 0
x = -13/3
x = 12/5


Input:
Solve simultaneously:
3x + 1y = 559/10
10x + 1y = 1889/10

Output:
3x + 1y = 559/10
10x + 1y = 1889/10

Using elimination
10*(3x + 1y = 559/10)
3*(10x + 1y = 1889/10)
30x + 10y = 559
30x + 3y = 5667/10
Subtract equations
7y = -77/10
y = -77/10/7
y = -11/10

Substitute y
3x + 1(-11/10) = 559/10
3x = 57
x = 57/3
x = 19


Input: Determine x in x^2 + 41/8x + 165/32 = 0

Output:
x^2 + 41/8x + 165/32 = 0
(x - -11/8)(x - -15/4) = 0
x - -11/8 = 0  or  x - -15/4 = 0
x = -11/8
x = -15/4


Input: Find the solution to x^3 + 10/3x^2 - 8/3x  = 0

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


Input:
Solve simultaneously:
7x + 4y = -19/6
3x + 10y = 83/6

Output:
7x + 4y = -19/6
3x + 10y = 83/6

Using elimination
3*(7x + 4y = -19/6)
7*(3x + 10y = 83/6)
21x + 12y = -19/2
21x + 70y = 581/6
Subtract equations
-58y = -319/3
y = -319/3/-58
y = 11/6

Substitute y
7x + 4(11/6) = -19/6
7x = -21/2
x = -21/2/7
x = -3/2


Input: Find x for x^2 - 71/15x + 14/3 = 0

Output:
x^2 - 71/15x + 14/3 = 0
(x - 10/3)(x - 7/5) = 0
x - 10/3 = 0  or  x - 7/5 = 0
x = 10/3
x = 7/5


Input: What value of x satisfies x^3 - 8/3x^2 - 20/3x + 16/3 = 0

Output:
x^3 - 8/3x^2 - 20/3x + 16/3 = 0
(x - -2)(x - 4)(x - 2/3) = 0
x - -2 = 0
x - 4 = 0
x - 2/3 = 0
x = -2
x = 4
x = 2/3


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

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


Input: Find the solution to 3x + 9 = 0

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


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

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


Input:
Solve the system:
1x + 7y = 201/10
9x + 4y = 521/5

Output:
1x + 7y = 201/10
9x + 4y = 521/5

Using elimination
9*(1x + 7y = 201/10)
1*(9x + 4y = 521/5)
9x + 63y = 1809/10
9x + 4y = 521/5
Subtract equations
59y = 767/10
y = 767/10/59
y = 13/10

Substitute y
1x + 7(13/10) = 201/10
1x = 11
x = 11/1
x = 11


Input: Solve x^2 + 23/4x - 39/8 = 0

Output:
x^2 + 23/4x - 39/8 = 0
(x - 3/4)(x - -13/2) = 0
x - 3/4 = 0  or  x - -13/2 = 0
x = 3/4
x = -13/2


Input: Determine x in x^3 + 8/3x^2 - 11/4x - 21/4 = 0

Output:
x^3 + 8/3x^2 - 11/4x - 21/4 = 0
(x - -7/6)(x - -3)(x - 3/2) = 0
x - -7/6 = 0
x - -3 = 0
x - 3/2 = 0
x = -7/6
x = -3
x = 3/2


Input: What value of x satisfies x^3 + 85/42x^2 - 122/21x + 11/14 = 0

Output:
x^3 + 85/42x^2 - 122/21x + 11/14 = 0
(x - 3/2)(x - -11/3)(x - 1/7) = 0
x - 3/2 = 0
x - -11/3 = 0
x - 1/7 = 0
x = 3/2
x = -11/3
x = 1/7


Input: Find the solution to 7x - 7 = 0

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


Input: Solve quickly: 4x - 8/3 = 0

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


Input: Solve quickly: x^2 - 128/35x + 16/7 = 0

Output:
x^2 - 128/35x + 16/7 = 0
(x - 4/5)(x - 20/7) = 0
x - 4/5 = 0  or  x - 20/7 = 0
x = 4/5
x = 20/7


Input: What value of x satisfies x^3 - 5x^2 - 52/9x - 4/3 = 0

Output:
x^3 - 5x^2 - 52/9x - 4/3 = 0
(x - -1/3)(x - -2/3)(x - 6) = 0
x - -1/3 = 0
x - -2/3 = 0
x - 6 = 0
x = -1/3
x = -2/3
x = 6


Input: Solve the equation x^2 - 19x + 78 = 0

Output:
x^2 - 19x + 78 = 0
(x - 13)(x - 6) = 0
x - 13 = 0  or  x - 6 = 0
x = 13
x = 6


Input: Compute the solution of 6x + 90/7 = 0

Output:
6x + 90/7 = 0
6x = -90/7
x = -90/7 / 6
x = -15/7


Input:
Solve the system:
2x + 8y = -44/3
7x + 2y = -37/3

Output:
2x + 8y = -44/3
7x + 2y = -37/3

Using elimination
7*(2x + 8y = -44/3)
2*(7x + 2y = -37/3)
14x + 56y = -308/3
14x + 4y = -74/3
Subtract equations
52y = -78
y = -78/52
y = -3/2

Substitute y
2x + 8(-3/2) = -44/3
2x = -8/3
x = -8/3/2
x = -4/3


Input: Solve quickly: x^3 - 163/10x^2 + 647/10x + 68/5 = 0

Output:
x^3 - 163/10x^2 + 647/10x + 68/5 = 0
(x - 17/2)(x - 8)(x - -1/5) = 0
x - 17/2 = 0
x - 8 = 0
x - -1/5 = 0
x = 17/2
x = 8
x = -1/5


Input: Determine x in 10x - 70/9 = 0

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


Input:
Solve the system:
3x + 7y = 7/2
6x + 4y = 7

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

Using elimination
6*(3x + 7y = 7/2)
3*(6x + 4y = 7)
18x + 42y = 21
18x + 12y = 21
Subtract equations
30y = 0
y = 0/30
y = 0

Substitute y
3x + 7(0) = 7/2
3x = 7/2
x = 7/2/3
x = 7/6


Input: Solve quickly: x^3 - 43/4x^2 + 61/4x + 9/2 = 0

Output:
x^3 - 43/4x^2 + 61/4x + 9/2 = 0
(x - 9)(x - -1/4)(x - 2) = 0
x - 9 = 0
x - -1/4 = 0
x - 2 = 0
x = 9
x = -1/4
x = 2


Input:
Solve the system:
5x + 10y = 75/2
9x + 2y = -25/2

Output:
5x + 10y = 75/2
9x + 2y = -25/2

Using elimination
9*(5x + 10y = 75/2)
5*(9x + 2y = -25/2)
45x + 90y = 675/2
45x + 10y = -125/2
Subtract equations
80y = 400
y = 400/80
y = 5

Substitute y
5x + 10(5) = 75/2
5x = -25/2
x = -25/2/5
x = -5/2


Input:
Solve simultaneously:
9x + 7y = -125/7
4x + 1y = -26/7

Output:
9x + 7y = -125/7
4x + 1y = -26/7

Using elimination
4*(9x + 7y = -125/7)
9*(4x + 1y = -26/7)
36x + 28y = -500/7
36x + 9y = -234/7
Subtract equations
19y = -38
y = -38/19
y = -2

Substitute y
9x + 7(-2) = -125/7
9x = -27/7
x = -27/7/9
x = -3/7


Input: Solve the equation x^3 + 182/15x^2 + 3584/75x + 1536/25 = 0

Output:
x^3 + 182/15x^2 + 3584/75x + 1536/25 = 0
(x - -18/5)(x - -16/5)(x - -16/3) = 0
x - -18/5 = 0
x - -16/5 = 0
x - -16/3 = 0
x = -18/5
x = -16/5
x = -16/3


Input: Find the solution to x^2 - 39/10x + 7/2 = 0

Output:
x^2 - 39/10x + 7/2 = 0
(x - 7/5)(x - 5/2) = 0
x - 7/5 = 0  or  x - 5/2 = 0
x = 7/5
x = 5/2


Input:
Find x and y such that
4x + 3y = 79/6
7x + 5y = 133/6

Output:
4x + 3y = 79/6
7x + 5y = 133/6

Using elimination
7*(4x + 3y = 79/6)
4*(7x + 5y = 133/6)
28x + 21y = 553/6
28x + 20y = 266/3
Subtract equations
1y = 7/2
y = 7/2/1
y = 7/2

Substitute y
4x + 3(7/2) = 79/6
4x = 8/3
x = 8/3/4
x = 2/3


Input: Solve the equation 2x - 10 = 0

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


Input: Solve the equation 10x - 14 = 0

Output:
10x - 14 = 0
10x = 14
x = 14 / 10
x = 7/5


Input:
Solve the equations:
10x + 7y = -203/6
10x + 2y = -79/3

Output:
10x + 7y = -203/6
10x + 2y = -79/3

Using elimination
10*(10x + 7y = -203/6)
10*(10x + 2y = -79/3)
100x + 70y = -1015/3
100x + 20y = -790/3
Subtract equations
50y = -75
y = -75/50
y = -3/2

Substitute y
10x + 7(-3/2) = -203/6
10x = -70/3
x = -70/3/10
x = -7/3


Input: Find x in x^3 - 95/14x^2 + 1391/112x - 169/56 = 0

Output:
x^3 - 95/14x^2 + 1391/112x - 169/56 = 0
(x - 13/4)(x - 2/7)(x - 13/4) = 0
x - 13/4 = 0
x - 2/7 = 0
x - 13/4 = 0
x = 13/4
x = 2/7
x = 13/4


Input: Compute the solution of x^2 - 107/70x + 33/70 = 0

Output:
x^2 - 107/70x + 33/70 = 0
(x - 11/10)(x - 3/7) = 0
x - 11/10 = 0  or  x - 3/7 = 0
x = 11/10
x = 3/7


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

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


Input:
Find x and y such that
2x + 9y = -80/7
3x + 10y = -78/7

Output:
2x + 9y = -80/7
3x + 10y = -78/7

Using elimination
3*(2x + 9y = -80/7)
2*(3x + 10y = -78/7)
6x + 27y = -240/7
6x + 20y = -156/7
Subtract equations
7y = -12
y = -12/7
y = -12/7

Substitute y
2x + 9(-12/7) = -80/7
2x = 4
x = 4/2
x = 2


Input: Solve the equation x^2 - 5/6x - 25/18 = 0

Output:
x^2 - 5/6x - 25/18 = 0
(x - -5/6)(x - 5/3) = 0
x - -5/6 = 0  or  x - 5/3 = 0
x = -5/6
x = 5/3


Input:
Find x and y such that
6x + 10y = -38/7
8x + 9y = 10/7

Output:
6x + 10y = -38/7
8x + 9y = 10/7

Using elimination
8*(6x + 10y = -38/7)
6*(8x + 9y = 10/7)
48x + 80y = -304/7
48x + 54y = 60/7
Subtract equations
26y = -52
y = -52/26
y = -2

Substitute y
6x + 10(-2) = -38/7
6x = 102/7
x = 102/7/6
x = 17/7


Input: Determine x in x^2 - 33/10x - 19/10 = 0

Output:
x^2 - 33/10x - 19/10 = 0
(x - -1/2)(x - 19/5) = 0
x - -1/2 = 0  or  x - 19/5 = 0
x = -1/2
x = 19/5


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

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


Input: Compute the solution of x^3 - 41/36x^2 - 5/36x  = 0

Output:
x^3 - 41/36x^2 - 5/36x  = 0
(x - 5/4)(x - -1/9)(x - 0) = 0
x - 5/4 = 0
x - -1/9 = 0
x - 0 = 0
x = 5/4
x = -1/9
x = 0


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

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


Input: Find x for x^3 + 13/5x^2 - 13/5x - 21/5 = 0

Output:
x^3 + 13/5x^2 - 13/5x - 21/5 = 0
(x - -1)(x - 7/5)(x - -3) = 0
x - -1 = 0
x - 7/5 = 0
x - -3 = 0
x = -1
x = 7/5
x = -3


Input: Find the solution to 4x  = 0

Output:
4x  = 0
4x = 0
x = 0 / 4
x = 0


Input: Compute the solution of 1x - 1/2 = 0

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


Input: Find x in x^2 - 26/7x + 24/7 = 0

Output:
x^2 - 26/7x + 24/7 = 0
(x - 12/7)(x - 2) = 0
x - 12/7 = 0  or  x - 2 = 0
x = 12/7
x = 2


Input: What value of x satisfies x^3 + 11/2x^2 + 15/2x  = 0

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


Input: Find x in x^3 - 14/5x^2 + 32/25x + 128/125 = 0

Output:
x^3 - 14/5x^2 + 32/25x + 128/125 = 0
(x - -2/5)(x - 8/5)(x - 8/5) = 0
x - -2/5 = 0
x - 8/5 = 0
x - 8/5 = 0
x = -2/5
x = 8/5
x = 8/5


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

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


Input:
Solve the equations:
4x + 7y = 31/5
4x + 4y = 34/5

Output:
4x + 7y = 31/5
4x + 4y = 34/5

Using elimination
4*(4x + 7y = 31/5)
4*(4x + 4y = 34/5)
16x + 28y = 124/5
16x + 16y = 136/5
Subtract equations
12y = -12/5
y = -12/5/12
y = -1/5

Substitute y
4x + 7(-1/5) = 31/5
4x = 38/5
x = 38/5/4
x = 19/10


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

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


Input: Compute the solution of 10x - 25/2 = 0

Output:
10x - 25/2 = 0
10x = 25/2
x = 25/2 / 10
x = 5/4


Input: Compute the solution of x^3 + 7/2x^2 + 17/9x - 35/18 = 0

Output:
x^3 + 7/2x^2 + 17/9x - 35/18 = 0
(x - -7/3)(x - -5/3)(x - 1/2) = 0
x - -7/3 = 0
x - -5/3 = 0
x - 1/2 = 0
x = -7/3
x = -5/3
x = 1/2


Input: Find x in 6x + 33/2 = 0

Output:
6x + 33/2 = 0
6x = -33/2
x = -33/2 / 6
x = -11/4


Input: Solve the equation 3x + 24 = 0

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


Input: What value of x satisfies x^2 - 115/36x + 91/36 = 0

Output:
x^2 - 115/36x + 91/36 = 0
(x - 7/4)(x - 13/9) = 0
x - 7/4 = 0  or  x - 13/9 = 0
x = 7/4
x = 13/9


Input: Find x for 6x - 40/3 = 0

Output:
6x - 40/3 = 0
6x = 40/3
x = 40/3 / 6
x = 20/9


Input: Solve x^2 + 19/5x + 14/5 = 0

Output:
x^2 + 19/5x + 14/5 = 0
(x - -14/5)(x - -1) = 0
x - -14/5 = 0  or  x - -1 = 0
x = -14/5
x = -1


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

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


Input:
Solve the system:
7x + 9y = 87/2
2x + 5y = 47/3

Output:
7x + 9y = 87/2
2x + 5y = 47/3

Using elimination
2*(7x + 9y = 87/2)
7*(2x + 5y = 47/3)
14x + 18y = 87
14x + 35y = 329/3
Subtract equations
-17y = -68/3
y = -68/3/-17
y = 4/3

Substitute y
7x + 9(4/3) = 87/2
7x = 63/2
x = 63/2/7
x = 9/2


Input: What value of x satisfies 6x + 33 = 0

Output:
6x + 33 = 0
6x = -33
x = -33 / 6
x = -11/2


Input:
Find x and y such that
8x + 2y = -127/10
10x + 6y = -37/2

Output:
8x + 2y = -127/10
10x + 6y = -37/2

Using elimination
10*(8x + 2y = -127/10)
8*(10x + 6y = -37/2)
80x + 20y = -127
80x + 48y = -148
Subtract equations
-28y = 21
y = 21/-28
y = -3/4

Substitute y
8x + 2(-3/4) = -127/10
8x = -56/5
x = -56/5/8
x = -7/5


Input:
Solve simultaneously:
7x + 10y = 391/10
9x + 2y = 177/10

Output:
7x + 10y = 391/10
9x + 2y = 177/10

Using elimination
9*(7x + 10y = 391/10)
7*(9x + 2y = 177/10)
63x + 90y = 3519/10
63x + 14y = 1239/10
Subtract equations
76y = 228
y = 228/76
y = 3

Substitute y
7x + 10(3) = 391/10
7x = 91/10
x = 91/10/7
x = 13/10


Input: What value of x satisfies 2x  = 0

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


Input:
Solve the equations:
5x + 1y = -59/8
9x + 1y = -119/8

Output:
5x + 1y = -59/8
9x + 1y = -119/8

Using elimination
9*(5x + 1y = -59/8)
5*(9x + 1y = -119/8)
45x + 9y = -531/8
45x + 5y = -595/8
Subtract equations
4y = 8
y = 8/4
y = 2

Substitute y
5x + 1(2) = -59/8
5x = -75/8
x = -75/8/5
x = -15/8


Input:
Solve the system:
2x + 8y = 48/5
3x + 3y = 9

Output:
2x + 8y = 48/5
3x + 3y = 9

Using elimination
3*(2x + 8y = 48/5)
2*(3x + 3y = 9)
6x + 24y = 144/5
6x + 6y = 18
Subtract equations
18y = 54/5
y = 54/5/18
y = 3/5

Substitute y
2x + 8(3/5) = 48/5
2x = 24/5
x = 24/5/2
x = 12/5


Input: Find the solution to x^3 + 9/10x^2 - 61/10x + 3/5 = 0

Output:
x^3 + 9/10x^2 - 61/10x + 3/5 = 0
(x - 1/10)(x - -3)(x - 2) = 0
x - 1/10 = 0
x - -3 = 0
x - 2 = 0
x = 1/10
x = -3
x = 2


Input: Compute the solution of x^3 + 83/42x^2 - 229/42x - 65/21 = 0

Output:
x^3 + 83/42x^2 - 229/42x - 65/21 = 0
(x - 13/7)(x - -1/2)(x - -10/3) = 0
x - 13/7 = 0
x - -1/2 = 0
x - -10/3 = 0
x = 13/7
x = -1/2
x = -10/3


Input: Determine x in 4x + 24 = 0

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


Input: Solve x^3 + 9/8x^2 - 4x - 9/2 = 0

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


Input: Solve 9x + 9 = 0

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


Input: Find x in x^3 + 35/3x^2 + 631/36x - 1235/12 = 0

Output:
x^3 + 35/3x^2 + 631/36x - 1235/12 = 0
(x - -19/3)(x - -15/2)(x - 13/6) = 0
x - -19/3 = 0
x - -15/2 = 0
x - 13/6 = 0
x = -19/3
x = -15/2
x = 13/6


Input: What value of x satisfies x^2 - 59/12x + 6 = 0

Output:
x^2 - 59/12x + 6 = 0
(x - 8/3)(x - 9/4) = 0
x - 8/3 = 0  or  x - 9/4 = 0
x = 8/3
x = 9/4


Input: Compute the solution of x^3 - 19/3x^2 - 302/3x - 280/3 = 0

Output:
x^3 - 19/3x^2 - 302/3x - 280/3 = 0
(x - 14)(x - -20/3)(x - -1) = 0
x - 14 = 0
x - -20/3 = 0
x - -1 = 0
x = 14
x = -20/3
x = -1


Input: What value of x satisfies 6x + 32 = 0

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


Input: Solve 7x - 91/6 = 0

Output:
7x - 91/6 = 0
7x = 91/6
x = 91/6 / 7
x = 13/6


Input: Find x in x^3 + 28/3x^2 + 19/9x - 616/9 = 0

Output:
x^3 + 28/3x^2 + 19/9x - 616/9 = 0
(x - -11/3)(x - 7/3)(x - -8) = 0
x - -11/3 = 0
x - 7/3 = 0
x - -8 = 0
x = -11/3
x = 7/3
x = -8


Input: Solve the equation x^3 + 15/4x^2 - 351/8x + 243/8 = 0

Output:
x^3 + 15/4x^2 - 351/8x + 243/8 = 0
(x - 3/4)(x - -9)(x - 9/2) = 0
x - 3/4 = 0
x - -9 = 0
x - 9/2 = 0
x = 3/4
x = -9
x = 9/2


Input:
Solve the system:
9x + 3y = -145/6
2x + 1y = -50/9

Output:
9x + 3y = -145/6
2x + 1y = -50/9

Using elimination
2*(9x + 3y = -145/6)
9*(2x + 1y = -50/9)
18x + 6y = -145/3
18x + 9y = -50
Subtract equations
-3y = 5/3
y = 5/3/-3
y = -5/9

Substitute y
9x + 3(-5/9) = -145/6
9x = -45/2
x = -45/2/9
x = -5/2


Input: Find the solution to x^3 - 61/12x^2 + 149/24x - 5/4 = 0

Output:
x^3 - 61/12x^2 + 149/24x - 5/4 = 0
(x - 10/3)(x - 1/4)(x - 3/2) = 0
x - 10/3 = 0
x - 1/4 = 0
x - 3/2 = 0
x = 10/3
x = 1/4
x = 3/2


Input: Determine x in 1x + 5/3 = 0

Output:
1x + 5/3 = 0
1x = -5/3
x = -5/3 / 1
x = -5/3


Input: Find x in x^3 + 6/7x^2 - 37/7x + 24/7 = 0

Output:
x^3 + 6/7x^2 - 37/7x + 24/7 = 0
(x - 1)(x - 8/7)(x - -3) = 0
x - 1 = 0
x - 8/7 = 0
x - -3 = 0
x = 1
x = 8/7
x = -3


Input: Solve quickly: x^3 - 1/8x^2 - 269/400x + 9/40 = 0

Output:
x^3 - 1/8x^2 - 269/400x + 9/40 = 0
(x - 5/8)(x - -9/10)(x - 2/5) = 0
x - 5/8 = 0
x - -9/10 = 0
x - 2/5 = 0
x = 5/8
x = -9/10
x = 2/5


Input: What value of x satisfies x^2 + 25x + 136 = 0

Output:
x^2 + 25x + 136 = 0
(x - -17)(x - -8) = 0
x - -17 = 0  or  x - -8 = 0
x = -17
x = -8


Input: Solve x^3 - 45/28x^2 - 375/56x + 125/14 = 0

Output:
x^3 - 45/28x^2 - 375/56x + 125/14 = 0
(x - -5/2)(x - 20/7)(x - 5/4) = 0
x - -5/2 = 0
x - 20/7 = 0
x - 5/4 = 0
x = -5/2
x = 20/7
x = 5/4


Input: Solve quickly: x^3 + 203/12x^2 + 287/24x - 130/3 = 0

Output:
x^3 + 203/12x^2 + 287/24x - 130/3 = 0
(x - -13/6)(x - 5/4)(x - -16) = 0
x - -13/6 = 0
x - 5/4 = 0
x - -16 = 0
x = -13/6
x = 5/4
x = -16


Input: Solve x^3 + 121/45x^2 + 31/36x - 221/180 = 0

Output:
x^3 + 121/45x^2 + 31/36x - 221/180 = 0
(x - -17/9)(x - 1/2)(x - -13/10) = 0
x - -17/9 = 0
x - 1/2 = 0
x - -13/10 = 0
x = -17/9
x = 1/2
x = -13/10


Input: Find the solution to x^2 - 11/7x - 6/7 = 0

Output:
x^2 - 11/7x - 6/7 = 0
(x - -3/7)(x - 2) = 0
x - -3/7 = 0  or  x - 2 = 0
x = -3/7
x = 2


Input: Find x for 3x + 7 = 0

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


Input: Determine x in x^3 - 31/10x^2 - 651/10x + 108 = 0

Output:
x^3 - 31/10x^2 - 651/10x + 108 = 0
(x - 9)(x - 8/5)(x - -15/2) = 0
x - 9 = 0
x - 8/5 = 0
x - -15/2 = 0
x = 9
x = 8/5
x = -15/2


Input: Determine x in x^3 + 23/6x^2 - 35/9x - 4 = 0

Output:
x^3 + 23/6x^2 - 35/9x - 4 = 0
(x - -2/3)(x - 4/3)(x - -9/2) = 0
x - -2/3 = 0
x - 4/3 = 0
x - -9/2 = 0
x = -2/3
x = 4/3
x = -9/2


Input: Find x for x^2 + 29/5x - 88/5 = 0

Output:
x^2 + 29/5x - 88/5 = 0
(x - 11/5)(x - -8) = 0
x - 11/5 = 0  or  x - -8 = 0
x = 11/5
x = -8


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

Output:
2x - 11/3 = 0
2x = 11/3
x = 11/3 / 2
x = 11/6


Input: Find x for x^3 - 103/20x^2 + 17/4x + 7/5 = 0

Output:
x^3 - 103/20x^2 + 17/4x + 7/5 = 0
(x - -1/4)(x - 7/5)(x - 4) = 0
x - -1/4 = 0
x - 7/5 = 0
x - 4 = 0
x = -1/4
x = 7/5
x = 4


Input: Solve 9x + 1 = 0

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


Input: Solve the equation 9x - 63/8 = 0

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


Input: Solve 6x + 48/5 = 0

Output:
6x + 48/5 = 0
6x = -48/5
x = -48/5 / 6
x = -8/5


Input: Find the solution to x^3 - 23/5x^2 + 146/25x - 56/25 = 0

Output:
x^3 - 23/5x^2 + 146/25x - 56/25 = 0
(x - 1)(x - 4/5)(x - 14/5) = 0
x - 1 = 0
x - 4/5 = 0
x - 14/5 = 0
x = 1
x = 4/5
x = 14/5


Input: Find x for 9x + 15 = 0

Output:
9x + 15 = 0
9x = -15
x = -15 / 9
x = -5/3


Input: Solve the equation 6x + 108/7 = 0

Output:
6x + 108/7 = 0
6x = -108/7
x = -108/7 / 6
x = -18/7


Input:
Find x and y such that
3x + 6y = -73/7
5x + 9y = -332/21

Output:
3x + 6y = -73/7
5x + 9y = -332/21

Using elimination
5*(3x + 6y = -73/7)
3*(5x + 9y = -332/21)
15x + 30y = -365/7
15x + 27y = -332/7
Subtract equations
3y = -33/7
y = -33/7/3
y = -11/7

Substitute y
3x + 6(-11/7) = -73/7
3x = -1
x = -1/3
x = -1/3


Input: Find the solution to x^2 + 80/7x + 153/7 = 0

Output:
x^2 + 80/7x + 153/7 = 0
(x - -17/7)(x - -9) = 0
x - -17/7 = 0  or  x - -9 = 0
x = -17/7
x = -9


Input: Determine x in x^2 - 10x + 24 = 0

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


Input:
Solve the system:
9x + 10y = -321/4
3x + 4y = -27

Output:
9x + 10y = -321/4
3x + 4y = -27

Using elimination
3*(9x + 10y = -321/4)
9*(3x + 4y = -27)
27x + 30y = -963/4
27x + 36y = -243
Subtract equations
-6y = 9/4
y = 9/4/-6
y = -3/8

Substitute y
9x + 10(-3/8) = -321/4
9x = -153/2
x = -153/2/9
x = -17/2


Input: Find x for 3x + 33/5 = 0

Output:
3x + 33/5 = 0
3x = -33/5
x = -33/5 / 3
x = -11/5


Input: Find the solution to 6x + 18/5 = 0

Output:
6x + 18/5 = 0
6x = -18/5
x = -18/5 / 6
x = -3/5


Input: Compute the solution of 7x + 91/8 = 0

Output:
7x + 91/8 = 0
7x = -91/8
x = -91/8 / 7
x = -13/8


Input:
Solve the system:
8x + 8y = 276/5
10x + 3y = 34

Output:
8x + 8y = 276/5
10x + 3y = 34

Using elimination
10*(8x + 8y = 276/5)
8*(10x + 3y = 34)
80x + 80y = 552
80x + 24y = 272
Subtract equations
56y = 280
y = 280/56
y = 5

Substitute y
8x + 8(5) = 276/5
8x = 76/5
x = 76/5/8
x = 19/10


Input: Determine x in 8x - 12 = 0

Output:
8x - 12 = 0
8x = 12
x = 12 / 8
x = 3/2


Input: Determine x in x^3 - 381/35x^2 + 198/35x + 32 = 0

Output:
x^3 - 381/35x^2 + 198/35x + 32 = 0
(x - -7/5)(x - 10)(x - 16/7) = 0
x - -7/5 = 0
x - 10 = 0
x - 16/7 = 0
x = -7/5
x = 10
x = 16/7


Input: Solve the equation x^3 - 7/2x^2 - 153/4x + 495/8 = 0

Output:
x^3 - 7/2x^2 - 153/4x + 495/8 = 0
(x - 3/2)(x - 15/2)(x - -11/2) = 0
x - 3/2 = 0
x - 15/2 = 0
x - -11/2 = 0
x = 3/2
x = 15/2
x = -11/2


Input: Compute the solution of x^2 + 17/8x + 9/8 = 0

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


Input: What value of x satisfies 9x - 117/5 = 0

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


Input:
Find x and y such that
2x + 5y = 67/10
1x + 7y = 83/10

Output:
2x + 5y = 67/10
1x + 7y = 83/10

Using elimination
1*(2x + 5y = 67/10)
2*(1x + 7y = 83/10)
2x + 5y = 67/10
2x + 14y = 83/5
Subtract equations
-9y = -99/10
y = -99/10/-9
y = 11/10

Substitute y
2x + 5(11/10) = 67/10
2x = 6/5
x = 6/5/2
x = 3/5


Input:
Solve the equations:
6x + 3y = 20
1x + 10y = 67/3

Output:
6x + 3y = 20
1x + 10y = 67/3

Using elimination
1*(6x + 3y = 20)
6*(1x + 10y = 67/3)
6x + 3y = 20
6x + 60y = 134
Subtract equations
-57y = -114
y = -114/-57
y = 2

Substitute y
6x + 3(2) = 20
6x = 14
x = 14/6
x = 7/3


Input: Determine x in x^2 - 15/2x + 14 = 0

Output:
x^2 - 15/2x + 14 = 0
(x - 7/2)(x - 4) = 0
x - 7/2 = 0  or  x - 4 = 0
x = 7/2
x = 4


Input: Find x in x^3 + 395/126x^2 - 43/63x - 715/126 = 0

Output:
x^3 + 395/126x^2 - 43/63x - 715/126 = 0
(x - -13/7)(x - 11/9)(x - -5/2) = 0
x - -13/7 = 0
x - 11/9 = 0
x - -5/2 = 0
x = -13/7
x = 11/9
x = -5/2


Input: Find the solution to x^2 + 13/4x + 5/2 = 0

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


Input:
Find x and y such that
5x + 1y = -47/8
5x + 2y = -11/2

Output:
5x + 1y = -47/8
5x + 2y = -11/2

Using elimination
5*(5x + 1y = -47/8)
5*(5x + 2y = -11/2)
25x + 5y = -235/8
25x + 10y = -55/2
Subtract equations
-5y = -15/8
y = -15/8/-5
y = 3/8

Substitute y
5x + 1(3/8) = -47/8
5x = -25/4
x = -25/4/5
x = -5/4


Input: Find x in 8x - 112/3 = 0

Output:
8x - 112/3 = 0
8x = 112/3
x = 112/3 / 8
x = 14/3


Input: Find x in x^2 + 137/24x + 95/12 = 0

Output:
x^2 + 137/24x + 95/12 = 0
(x - -19/8)(x - -10/3) = 0
x - -19/8 = 0  or  x - -10/3 = 0
x = -19/8
x = -10/3


Input: Find the solution to x^2 - 27/2x + 81/2 = 0

Output:
x^2 - 27/2x + 81/2 = 0
(x - 9)(x - 9/2) = 0
x - 9 = 0  or  x - 9/2 = 0
x = 9
x = 9/2


Input: Find the solution to x^3 + 121/60x^2 - 161/30x + 6/5 = 0

Output:
x^3 + 121/60x^2 - 161/30x + 6/5 = 0
(x - 1/4)(x - 4/3)(x - -18/5) = 0
x - 1/4 = 0
x - 4/3 = 0
x - -18/5 = 0
x = 1/4
x = 4/3
x = -18/5


Input: Determine x in x^3 - 110/9x^2 + 233/9x + 28 = 0

Output:
x^3 - 110/9x^2 + 233/9x + 28 = 0
(x - -7/9)(x - 4)(x - 9) = 0
x - -7/9 = 0
x - 4 = 0
x - 9 = 0
x = -7/9
x = 4
x = 9


Input: What value of x satisfies 10x - 80/3 = 0

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


Input:
Solve the equations:
7x + 9y = -279/2
6x + 1y = 8

Output:
7x + 9y = -279/2
6x + 1y = 8

Using elimination
6*(7x + 9y = -279/2)
7*(6x + 1y = 8)
42x + 54y = -837
42x + 7y = 56
Subtract equations
47y = -893
y = -893/47
y = -19

Substitute y
7x + 9(-19) = -279/2
7x = 63/2
x = 63/2/7
x = 9/2


Input: Solve 9x + 21/2 = 0

Output:
9x + 21/2 = 0
9x = -21/2
x = -21/2 / 9
x = -7/6


Input: Find x for x^2 - 121/63x - 10/21 = 0

Output:
x^2 - 121/63x - 10/21 = 0
(x - -2/9)(x - 15/7) = 0
x - -2/9 = 0  or  x - 15/7 = 0
x = -2/9
x = 15/7


Input: Find x for x^2 + 110/9x + 200/9 = 0

Output:
x^2 + 110/9x + 200/9 = 0
(x - -10)(x - -20/9) = 0
x - -10 = 0  or  x - -20/9 = 0
x = -10
x = -20/9


Input: Solve quickly: 8x + 16/9 = 0

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


Input:
Solve simultaneously:
8x + 5y = 50
1x + 7y = 191/2

Output:
8x + 5y = 50
1x + 7y = 191/2

Using elimination
1*(8x + 5y = 50)
8*(1x + 7y = 191/2)
8x + 5y = 50
8x + 56y = 764
Subtract equations
-51y = -714
y = -714/-51
y = 14

Substitute y
8x + 5(14) = 50
8x = -20
x = -20/8
x = -5/2


Input: Compute the solution of x^3 - 50/3x^2 - 79/3x + 42 = 0

Output:
x^3 - 50/3x^2 - 79/3x + 42 = 0
(x - 1)(x - 18)(x - -7/3) = 0
x - 1 = 0
x - 18 = 0
x - -7/3 = 0
x = 1
x = 18
x = -7/3


Input: Solve quickly: 5x + 50 = 0

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


Input: What value of x satisfies 4x - 44 = 0

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


Input: Compute the solution of x^3 - 41/9x^2 - 1297/36x + 85/4 = 0

Output:
x^3 - 41/9x^2 - 1297/36x + 85/4 = 0
(x - 17/2)(x - 5/9)(x - -9/2) = 0
x - 17/2 = 0
x - 5/9 = 0
x - -9/2 = 0
x = 17/2
x = 5/9
x = -9/2


Input: Solve x^3 + 1/3x^2 - 34/3x + 40/3 = 0

Output:
x^3 + 1/3x^2 - 34/3x + 40/3 = 0
(x - 2)(x - -4)(x - 5/3) = 0
x - 2 = 0
x - -4 = 0
x - 5/3 = 0
x = 2
x = -4
x = 5/3


Input: Compute the solution of 9x + 81/5 = 0

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


Input: Find x for 2x - 16/5 = 0

Output:
2x - 16/5 = 0
2x = 16/5
x = 16/5 / 2
x = 8/5


Input: Solve the equation x^3 + 59/24x^2 - 23/2x - 117/8 = 0

Output:
x^3 + 59/24x^2 - 23/2x - 117/8 = 0
(x - -13/3)(x - 3)(x - -9/8) = 0
x - -13/3 = 0
x - 3 = 0
x - -9/8 = 0
x = -13/3
x = 3
x = -9/8


Input:
Solve the equations:
4x + 7y = 197/7
9x + 7y = 277/7

Output:
4x + 7y = 197/7
9x + 7y = 277/7

Using elimination
9*(4x + 7y = 197/7)
4*(9x + 7y = 277/7)
36x + 63y = 1773/7
36x + 28y = 1108/7
Subtract equations
35y = 95
y = 95/35
y = 19/7

Substitute y
4x + 7(19/7) = 197/7
4x = 64/7
x = 64/7/4
x = 16/7


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

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


Input: Find x in x^3 + 23/2x^2 + 10x - 225/2 = 0

Output:
x^3 + 23/2x^2 + 10x - 225/2 = 0
(x - -9)(x - 5/2)(x - -5) = 0
x - -9 = 0
x - 5/2 = 0
x - -5 = 0
x = -9
x = 5/2
x = -5


Input: Find x in x^3 - 419/120x^2 + 145/48x - 13/40 = 0

Output:
x^3 - 419/120x^2 + 145/48x - 13/40 = 0
(x - 13/6)(x - 6/5)(x - 1/8) = 0
x - 13/6 = 0
x - 6/5 = 0
x - 1/8 = 0
x = 13/6
x = 6/5
x = 1/8


Input: Solve the equation 10x - 1 = 0

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


Input: Solve 4x - 68/5 = 0

Output:
4x - 68/5 = 0
4x = 68/5
x = 68/5 / 4
x = 17/5


Input: Compute the solution of 3x + 27/5 = 0

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


Input: Solve the equation x^2  - 25/4 = 0

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


Input: Solve the equation x^3 - 43/70x^2 - 264/35x - 459/70 = 0

Output:
x^3 - 43/70x^2 - 264/35x - 459/70 = 0
(x - -9/7)(x - 17/5)(x - -3/2) = 0
x - -9/7 = 0
x - 17/5 = 0
x - -3/2 = 0
x = -9/7
x = 17/5
x = -3/2


Input: Compute the solution of x^3 - 449/42x^2 + 632/21x - 130/7 = 0

Output:
x^3 - 449/42x^2 + 632/21x - 130/7 = 0
(x - 6/7)(x - 13/2)(x - 10/3) = 0
x - 6/7 = 0
x - 13/2 = 0
x - 10/3 = 0
x = 6/7
x = 13/2
x = 10/3


Input: Find the solution to x^3 + 109/60x^2 - 123/40x - 133/24 = 0

Output:
x^3 + 109/60x^2 - 123/40x - 133/24 = 0
(x - 7/4)(x - -5/3)(x - -19/10) = 0
x - 7/4 = 0
x - -5/3 = 0
x - -19/10 = 0
x = 7/4
x = -5/3
x = -19/10


Input:
Solve the system:
5x + 10y = 45/2
9x + 5y = 71/4

Output:
5x + 10y = 45/2
9x + 5y = 71/4

Using elimination
9*(5x + 10y = 45/2)
5*(9x + 5y = 71/4)
45x + 90y = 405/2
45x + 25y = 355/4
Subtract equations
65y = 455/4
y = 455/4/65
y = 7/4

Substitute y
5x + 10(7/4) = 45/2
5x = 5
x = 5/5
x = 1


Input: Compute the solution of x^2 - 13x - 14 = 0

Output:
x^2 - 13x - 14 = 0
(x - 14)(x - -1) = 0
x - 14 = 0  or  x - -1 = 0
x = 14
x = -1


Input: Find the solution to 4x + 20 = 0

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


Input:
Solve the system:
7x + 6y = 9/8
7x + 7y = 7/8

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

Using elimination
7*(7x + 6y = 9/8)
7*(7x + 7y = 7/8)
49x + 42y = 63/8
49x + 49y = 49/8
Subtract equations
-7y = 7/4
y = 7/4/-7
y = -1/4

Substitute y
7x + 6(-1/4) = 9/8
7x = 21/8
x = 21/8/7
x = 3/8


Input: Find the solution to x^2 - 3/7x - 88/49 = 0

Output:
x^2 - 3/7x - 88/49 = 0
(x - -8/7)(x - 11/7) = 0
x - -8/7 = 0  or  x - 11/7 = 0
x = -8/7
x = 11/7


Input:
Solve the system:
2x + 4y = 0
5x + 4y = -6

Output:
2x + 4y = 0
5x + 4y = -6

Using elimination
5*(2x + 4y = 0)
2*(5x + 4y = -6)
10x + 20y = 0
10x + 8y = -12
Subtract equations
12y = 12
y = 12/12
y = 1

Substitute y
2x + 4(1) = 0
2x = -4
x = -4/2
x = -2


Input:
Solve the system:
8x + 5y = 28
10x + 9y = 46

Output:
8x + 5y = 28
10x + 9y = 46

Using elimination
10*(8x + 5y = 28)
8*(10x + 9y = 46)
80x + 50y = 280
80x + 72y = 368
Subtract equations
-22y = -88
y = -88/-22
y = 4

Substitute y
8x + 5(4) = 28
8x = 8
x = 8/8
x = 1


Input: Solve x^3 + 21/4x^2 + 1/2x - 15/4 = 0

Output:
x^3 + 21/4x^2 + 1/2x - 15/4 = 0
(x - -1)(x - 3/4)(x - -5) = 0
x - -1 = 0
x - 3/4 = 0
x - -5 = 0
x = -1
x = 3/4
x = -5


Input:
Solve simultaneously:
7x + 4y = -209/2
10x + 6y = -595/4

Output:
7x + 4y = -209/2
10x + 6y = -595/4

Using elimination
10*(7x + 4y = -209/2)
7*(10x + 6y = -595/4)
70x + 40y = -1045
70x + 42y = -4165/4
Subtract equations
-2y = -15/4
y = -15/4/-2
y = 15/8

Substitute y
7x + 4(15/8) = -209/2
7x = -112
x = -112/7
x = -16


Input: Find x for x^2 - 11/12x - 5/12 = 0

Output:
x^2 - 11/12x - 5/12 = 0
(x - -1/3)(x - 5/4) = 0
x - -1/3 = 0  or  x - 5/4 = 0
x = -1/3
x = 5/4


Input: Compute the solution of 6x + 114/5 = 0

Output:
6x + 114/5 = 0
6x = -114/5
x = -114/5 / 6
x = -19/5


Input: Solve the equation x^3 - 97/30x^2 + 59/30x - 1/3 = 0

Output:
x^3 - 97/30x^2 + 59/30x - 1/3 = 0
(x - 5/2)(x - 2/5)(x - 1/3) = 0
x - 5/2 = 0
x - 2/5 = 0
x - 1/3 = 0
x = 5/2
x = 2/5
x = 1/3


Input:
Solve the system:
7x + 8y = 64/3
10x + 8y = 67/3

Output:
7x + 8y = 64/3
10x + 8y = 67/3

Using elimination
10*(7x + 8y = 64/3)
7*(10x + 8y = 67/3)
70x + 80y = 640/3
70x + 56y = 469/3
Subtract equations
24y = 57
y = 57/24
y = 19/8

Substitute y
7x + 8(19/8) = 64/3
7x = 7/3
x = 7/3/7
x = 1/3


Input: Find the solution to 10x - 24 = 0

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


Input: Find the solution to x^3 - 118/21x^2 + 104/21x + 128/21 = 0

Output:
x^3 - 118/21x^2 + 104/21x + 128/21 = 0
(x - 16/7)(x - 4)(x - -2/3) = 0
x - 16/7 = 0
x - 4 = 0
x - -2/3 = 0
x = 16/7
x = 4
x = -2/3


Input:
Find x and y such that
4x + 9y = 11/6
1x + 6y = 7/3

Output:
4x + 9y = 11/6
1x + 6y = 7/3

Using elimination
1*(4x + 9y = 11/6)
4*(1x + 6y = 7/3)
4x + 9y = 11/6
4x + 24y = 28/3
Subtract equations
-15y = -15/2
y = -15/2/-15
y = 1/2

Substitute y
4x + 9(1/2) = 11/6
4x = -8/3
x = -8/3/4
x = -2/3


Input:
Find x and y such that
7x + 3y = 25
2x + 3y = 95/7

Output:
7x + 3y = 25
2x + 3y = 95/7

Using elimination
2*(7x + 3y = 25)
7*(2x + 3y = 95/7)
14x + 6y = 50
14x + 21y = 95
Subtract equations
-15y = -45
y = -45/-15
y = 3

Substitute y
7x + 3(3) = 25
7x = 16
x = 16/7
x = 16/7


Input: Find x for 2x + 5 = 0

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


Input: Solve the equation x^2 - 29/6x - 5/6 = 0

Output:
x^2 - 29/6x - 5/6 = 0
(x - 5)(x - -1/6) = 0
x - 5 = 0  or  x - -1/6 = 0
x = 5
x = -1/6


Input: Find x for x^2 - 16/15x - 7/15 = 0

Output:
x^2 - 16/15x - 7/15 = 0
(x - -1/3)(x - 7/5) = 0
x - -1/3 = 0  or  x - 7/5 = 0
x = -1/3
x = 7/5


Input:
Solve the system:
9x + 9y = 378/5
2x + 5y = 12

Output:
9x + 9y = 378/5
2x + 5y = 12

Using elimination
2*(9x + 9y = 378/5)
9*(2x + 5y = 12)
18x + 18y = 756/5
18x + 45y = 108
Subtract equations
-27y = 216/5
y = 216/5/-27
y = -8/5

Substitute y
9x + 9(-8/5) = 378/5
9x = 90
x = 90/9
x = 10


Input: Find x for x^2 + 13/5x + 6/5 = 0

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


Input: Solve the equation x^2 - 7/10x + 1/10 = 0

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


Input: What value of x satisfies 6x + 6 = 0

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


Input: What value of x satisfies x^3 + 239/35x^2 - 352/35x - 192/35 = 0

Output:
x^3 + 239/35x^2 - 352/35x - 192/35 = 0
(x - 8/5)(x - -8)(x - -3/7) = 0
x - 8/5 = 0
x - -8 = 0
x - -3/7 = 0
x = 8/5
x = -8
x = -3/7


Input: Solve x^3 + 1/2x^2 - 71/16x - 63/16 = 0

Output:
x^3 + 1/2x^2 - 71/16x - 63/16 = 0
(x - 9/4)(x - -7/4)(x - -1) = 0
x - 9/4 = 0
x - -7/4 = 0
x - -1 = 0
x = 9/4
x = -7/4
x = -1


Input: Find x for 2x + 10 = 0

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


Input: Find x for 1x  = 0

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


Input: Solve the equation x^3 + 11/4x^2 + 29/64x - 133/128 = 0

Output:
x^3 + 11/4x^2 + 29/64x - 133/128 = 0
(x - 1/2)(x - -19/8)(x - -7/8) = 0
x - 1/2 = 0
x - -19/8 = 0
x - -7/8 = 0
x = 1/2
x = -19/8
x = -7/8


Input: What value of x satisfies x^2 + 41/4x + 45/4 = 0

Output:
x^2 + 41/4x + 45/4 = 0
(x - -9)(x - -5/4) = 0
x - -9 = 0  or  x - -5/4 = 0
x = -9
x = -5/4


Input: Find the solution to 9x - 18 = 0

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


Input: Solve x^3 + 415/84x^2 + 91/12x + 7/2 = 0

Output:
x^3 + 415/84x^2 + 91/12x + 7/2 = 0
(x - -6/7)(x - -7/4)(x - -7/3) = 0
x - -6/7 = 0
x - -7/4 = 0
x - -7/3 = 0
x = -6/7
x = -7/4
x = -7/3


Input: Find the solution to 6x - 42/5 = 0

Output:
6x - 42/5 = 0
6x = 42/5
x = 42/5 / 6
x = 7/5


Input: Solve the equation 8x - 48/7 = 0

Output:
8x - 48/7 = 0
8x = 48/7
x = 48/7 / 8
x = 6/7


Input: Solve x^3 + 379/90x^2 + 89/18x + 5/3 = 0

Output:
x^3 + 379/90x^2 + 89/18x + 5/3 = 0
(x - -10/9)(x - -5/2)(x - -3/5) = 0
x - -10/9 = 0
x - -5/2 = 0
x - -3/5 = 0
x = -10/9
x = -5/2
x = -3/5


Input: Find x for x^2 - 32/5x + 12/5 = 0

Output:
x^2 - 32/5x + 12/5 = 0
(x - 2/5)(x - 6) = 0
x - 2/5 = 0  or  x - 6 = 0
x = 2/5
x = 6


Input: Find x in 1x - 17 = 0

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


Input:
Find x and y such that
9x + 6y = 165/4
8x + 4y = 71/2

Output:
9x + 6y = 165/4
8x + 4y = 71/2

Using elimination
8*(9x + 6y = 165/4)
9*(8x + 4y = 71/2)
72x + 48y = 330
72x + 36y = 639/2
Subtract equations
12y = 21/2
y = 21/2/12
y = 7/8

Substitute y
9x + 6(7/8) = 165/4
9x = 36
x = 36/9
x = 4


Input: Determine x in x^3 - 7/10x^2 - 61/2x - 234/5 = 0

Output:
x^3 - 7/10x^2 - 61/2x - 234/5 = 0
(x - -9/5)(x - 13/2)(x - -4) = 0
x - -9/5 = 0
x - 13/2 = 0
x - -4 = 0
x = -9/5
x = 13/2
x = -4


Input:
Find x and y such that
5x + 4y = 75/4
7x + 7y = 105/4

Output:
5x + 4y = 75/4
7x + 7y = 105/4

Using elimination
7*(5x + 4y = 75/4)
5*(7x + 7y = 105/4)
35x + 28y = 525/4
35x + 35y = 525/4
Subtract equations
-7y = 0
y = 0/-7
y = 0

Substitute y
5x + 4(0) = 75/4
5x = 75/4
x = 75/4/5
x = 15/4


Input: What value of x satisfies 9x + 45 = 0

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


Input: Solve the equation x^2 - 6/5x - 13/4 = 0

Output:
x^2 - 6/5x - 13/4 = 0
(x - -13/10)(x - 5/2) = 0
x - -13/10 = 0  or  x - 5/2 = 0
x = -13/10
x = 5/2


Input:
Solve the equations:
7x + 8y = 215/9
10x + 8y = 230/9

Output:
7x + 8y = 215/9
10x + 8y = 230/9

Using elimination
10*(7x + 8y = 215/9)
7*(10x + 8y = 230/9)
70x + 80y = 2150/9
70x + 56y = 1610/9
Subtract equations
24y = 60
y = 60/24
y = 5/2

Substitute y
7x + 8(5/2) = 215/9
7x = 35/9
x = 35/9/7
x = 5/9


Input:
Solve simultaneously:
10x + 7y = -58/3
4x + 9y = 14/3

Output:
10x + 7y = -58/3
4x + 9y = 14/3

Using elimination
4*(10x + 7y = -58/3)
10*(4x + 9y = 14/3)
40x + 28y = -232/3
40x + 90y = 140/3
Subtract equations
-62y = -124
y = -124/-62
y = 2

Substitute y
10x + 7(2) = -58/3
10x = -100/3
x = -100/3/10
x = -10/3


Input: Solve quickly: 7x + 98/3 = 0

Output:
7x + 98/3 = 0
7x = -98/3
x = -98/3 / 7
x = -14/3


Input: Solve quickly: 8x - 88/9 = 0

Output:
8x - 88/9 = 0
8x = 88/9
x = 88/9 / 8
x = 11/9


Input:
Solve the equations:
8x + 9y = 909/14
2x + 3y = 327/14

Output:
8x + 9y = 909/14
2x + 3y = 327/14

Using elimination
2*(8x + 9y = 909/14)
8*(2x + 3y = 327/14)
16x + 18y = 909/7
16x + 24y = 1308/7
Subtract equations
-6y = -57
y = -57/-6
y = 19/2

Substitute y
8x + 9(19/2) = 909/14
8x = -144/7
x = -144/7/8
x = -18/7


Input: What value of x satisfies x^3 + 3/10x^2 - 41/80x - 21/160 = 0

Output:
x^3 + 3/10x^2 - 41/80x - 21/160 = 0
(x - -1/4)(x - -3/4)(x - 7/10) = 0
x - -1/4 = 0
x - -3/4 = 0
x - 7/10 = 0
x = -1/4
x = -3/4
x = 7/10


Input: Determine x in x^3 + 1/8x^2 - 505/144x + 143/72 = 0

Output:
x^3 + 1/8x^2 - 505/144x + 143/72 = 0
(x - -13/6)(x - 2/3)(x - 11/8) = 0
x - -13/6 = 0
x - 2/3 = 0
x - 11/8 = 0
x = -13/6
x = 2/3
x = 11/8


Input: Compute the solution of x^2 + 33/10x + 13/5 = 0

Output:
x^2 + 33/10x + 13/5 = 0
(x - -2)(x - -13/10) = 0
x - -2 = 0  or  x - -13/10 = 0
x = -2
x = -13/10


Input: Solve x^2 - 43/35x - 102/35 = 0

Output:
x^2 - 43/35x - 102/35 = 0
(x - 17/7)(x - -6/5) = 0
x - 17/7 = 0  or  x - -6/5 = 0
x = 17/7
x = -6/5


Input: Solve quickly: x^3 + 171/40x^2 + 491/160x + 51/160 = 0

Output:
x^3 + 171/40x^2 + 491/160x + 51/160 = 0
(x - -1/8)(x - -3/4)(x - -17/5) = 0
x - -1/8 = 0
x - -3/4 = 0
x - -17/5 = 0
x = -1/8
x = -3/4
x = -17/5


Input:
Solve the system:
8x + 3y = 41/5
10x + 8y = 23

Output:
8x + 3y = 41/5
10x + 8y = 23

Using elimination
10*(8x + 3y = 41/5)
8*(10x + 8y = 23)
80x + 30y = 82
80x + 64y = 184
Subtract equations
-34y = -102
y = -102/-34
y = 3

Substitute y
8x + 3(3) = 41/5
8x = -4/5
x = -4/5/8
x = -1/10


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

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


Input: Find x in x^3 - 29/42x^2 - 1111/126x - 484/63 = 0

Output:
x^3 - 29/42x^2 - 1111/126x - 484/63 = 0
(x - -8/7)(x - 11/3)(x - -11/6) = 0
x - -8/7 = 0
x - 11/3 = 0
x - -11/6 = 0
x = -8/7
x = 11/3
x = -11/6


Input: Solve the equation x^2 - 3x - 70 = 0

Output:
x^2 - 3x - 70 = 0
(x - -7)(x - 10) = 0
x - -7 = 0  or  x - 10 = 0
x = -7
x = 10


Input: Find x in x^2 - 61/70x - 39/70 = 0

Output:
x^2 - 61/70x - 39/70 = 0
(x - -3/7)(x - 13/10) = 0
x - -3/7 = 0  or  x - 13/10 = 0
x = -3/7
x = 13/10


Input: Find x for x^3 + 2x^2 - 5/4x  = 0

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


Input: Solve quickly: x^2 - 25/12x + 11/24 = 0

Output:
x^2 - 25/12x + 11/24 = 0
(x - 1/4)(x - 11/6) = 0
x - 1/4 = 0  or  x - 11/6 = 0
x = 1/4
x = 11/6


Input: Solve x^3 + 11/2x^2 - 65/2x - 154 = 0

Output:
x^3 + 11/2x^2 - 65/2x - 154 = 0
(x - -4)(x - -7)(x - 11/2) = 0
x - -4 = 0
x - -7 = 0
x - 11/2 = 0
x = -4
x = -7
x = 11/2


Input: Solve quickly: x^3 - 1/14x^2 - 541/350x + 18/25 = 0

Output:
x^3 - 1/14x^2 - 541/350x + 18/25 = 0
(x - -7/5)(x - 4/7)(x - 9/10) = 0
x - -7/5 = 0
x - 4/7 = 0
x - 9/10 = 0
x = -7/5
x = 4/7
x = 9/10


Input: Compute the solution of x^3 + 359/35x^2 + 781/35x - 17/5 = 0

Output:
x^3 + 359/35x^2 + 781/35x - 17/5 = 0
(x - -17/5)(x - 1/7)(x - -7) = 0
x - -17/5 = 0
x - 1/7 = 0
x - -7 = 0
x = -17/5
x = 1/7
x = -7


Input: Solve quickly: x^3 + 4/3x^2 - 15x + 50/3 = 0

Output:
x^3 + 4/3x^2 - 15x + 50/3 = 0
(x - -5)(x - 2)(x - 5/3) = 0
x - -5 = 0
x - 2 = 0
x - 5/3 = 0
x = -5
x = 2
x = 5/3


Input: Find x for 7x + 42/5 = 0

Output:
7x + 42/5 = 0
7x = -42/5
x = -42/5 / 7
x = -6/5


Input: Solve the equation x^2 - 160/9x + 256/9 = 0

Output:
x^2 - 160/9x + 256/9 = 0
(x - 16)(x - 16/9) = 0
x - 16 = 0  or  x - 16/9 = 0
x = 16
x = 16/9


Input: Find the solution to x^3 + 121/72x^2 - 45/16x - 275/144 = 0

Output:
x^3 + 121/72x^2 - 45/16x - 275/144 = 0
(x - -5/9)(x - 11/8)(x - -5/2) = 0
x - -5/9 = 0
x - 11/8 = 0
x - -5/2 = 0
x = -5/9
x = 11/8
x = -5/2


Input: Find x for x^3 + 23/10x^2 + 1/2x - 1/5 = 0

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


Input:
Solve the system:
9x + 6y = -69/7
8x + 10y = -192/7

Output:
9x + 6y = -69/7
8x + 10y = -192/7

Using elimination
8*(9x + 6y = -69/7)
9*(8x + 10y = -192/7)
72x + 48y = -552/7
72x + 90y = -1728/7
Subtract equations
-42y = 168
y = 168/-42
y = -4

Substitute y
9x + 6(-4) = -69/7
9x = 99/7
x = 99/7/9
x = 11/7


Input: Find the solution to x^2 + 47/12x + 5/8 = 0

Output:
x^2 + 47/12x + 5/8 = 0
(x - -15/4)(x - -1/6) = 0
x - -15/4 = 0  or  x - -1/6 = 0
x = -15/4
x = -1/6


Input: Solve 8x + 12 = 0

Output:
8x + 12 = 0
8x = -12
x = -12 / 8
x = -3/2


Input: Find x in x^3 - 47/4x^2 - 37/2x + 117/4 = 0

Output:
x^3 - 47/4x^2 - 37/2x + 117/4 = 0
(x - 13)(x - 1)(x - -9/4) = 0
x - 13 = 0
x - 1 = 0
x - -9/4 = 0
x = 13
x = 1
x = -9/4


Input: Find x in x^3 - 27/7x^2 - 120/7x + 400/7 = 0

Output:
x^3 - 27/7x^2 - 120/7x + 400/7 = 0
(x - -4)(x - 5)(x - 20/7) = 0
x - -4 = 0
x - 5 = 0
x - 20/7 = 0
x = -4
x = 5
x = 20/7


Input: What value of x satisfies x^3 + 277/84x^2 - 131/84x - 39/7 = 0

Output:
x^3 + 277/84x^2 - 131/84x - 39/7 = 0
(x - 9/7)(x - -4/3)(x - -13/4) = 0
x - 9/7 = 0
x - -4/3 = 0
x - -13/4 = 0
x = 9/7
x = -4/3
x = -13/4


Input: What value of x satisfies x^3 - 37/4x^2 + 17/8x + 63 = 0

Output:
x^3 - 37/4x^2 + 17/8x + 63 = 0
(x - 8)(x - 7/2)(x - -9/4) = 0
x - 8 = 0
x - 7/2 = 0
x - -9/4 = 0
x = 8
x = 7/2
x = -9/4


Input: Solve quickly: x^3 - 29/40x^2 - 131/40x + 3 = 0

Output:
x^3 - 29/40x^2 - 131/40x + 3 = 0
(x - 8/5)(x - 1)(x - -15/8) = 0
x - 8/5 = 0
x - 1 = 0
x - -15/8 = 0
x = 8/5
x = 1
x = -15/8


Input:
Solve simultaneously:
2x + 1y = -23/6
7x + 2y = -101/12

Output:
2x + 1y = -23/6
7x + 2y = -101/12

Using elimination
7*(2x + 1y = -23/6)
2*(7x + 2y = -101/12)
14x + 7y = -161/6
14x + 4y = -101/6
Subtract equations
3y = -10
y = -10/3
y = -10/3

Substitute y
2x + 1(-10/3) = -23/6
2x = -1/2
x = -1/2/2
x = -1/4


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

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


Input: Find x for x^2 + 16/3x - 19/3 = 0

Output:
x^2 + 16/3x - 19/3 = 0
(x - 1)(x - -19/3) = 0
x - 1 = 0  or  x - -19/3 = 0
x = 1
x = -19/3


Input: Find x in 9x + 108 = 0

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


Input: Determine x in 7x + 21/5 = 0

Output:
7x + 21/5 = 0
7x = -21/5
x = -21/5 / 7
x = -3/5


Input:
Solve the system:
3x + 5y = -31/2
10x + 2y = 43/3

Output:
3x + 5y = -31/2
10x + 2y = 43/3

Using elimination
10*(3x + 5y = -31/2)
3*(10x + 2y = 43/3)
30x + 50y = -155
30x + 6y = 43
Subtract equations
44y = -198
y = -198/44
y = -9/2

Substitute y
3x + 5(-9/2) = -31/2
3x = 7
x = 7/3
x = 7/3


Input: Find the solution to 4x - 8 = 0

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


Input: Find x in x^3 - 27/4x^2 + 853/72x - 187/36 = 0

Output:
x^3 - 27/4x^2 + 853/72x - 187/36 = 0
(x - 2/3)(x - 17/4)(x - 11/6) = 0
x - 2/3 = 0
x - 17/4 = 0
x - 11/6 = 0
x = 2/3
x = 17/4
x = 11/6


Input: Solve the equation x^3 + 52/3x^2 + 299/3x + 190 = 0

Output:
x^3 + 52/3x^2 + 299/3x + 190 = 0
(x - -6)(x - -19/3)(x - -5) = 0
x - -6 = 0
x - -19/3 = 0
x - -5 = 0
x = -6
x = -19/3
x = -5


Input: Compute the solution of x^3 - 116/21x^2 - 247/21x + 10 = 0

Output:
x^3 - 116/21x^2 - 247/21x + 10 = 0
(x - -15/7)(x - 7)(x - 2/3) = 0
x - -15/7 = 0
x - 7 = 0
x - 2/3 = 0
x = -15/7
x = 7
x = 2/3


Input:
Solve the system:
7x + 6y = -1/8
9x + 3y = -39/8

Output:
7x + 6y = -1/8
9x + 3y = -39/8

Using elimination
9*(7x + 6y = -1/8)
7*(9x + 3y = -39/8)
63x + 54y = -9/8
63x + 21y = -273/8
Subtract equations
33y = 33
y = 33/33
y = 1

Substitute y
7x + 6(1) = -1/8
7x = -49/8
x = -49/8/7
x = -7/8


Input:
Find x and y such that
9x + 3y = -119/2
1x + 1y = -47/6

Output:
9x + 3y = -119/2
1x + 1y = -47/6

Using elimination
1*(9x + 3y = -119/2)
9*(1x + 1y = -47/6)
9x + 3y = -119/2
9x + 9y = -141/2
Subtract equations
-6y = 11
y = 11/-6
y = -11/6

Substitute y
9x + 3(-11/6) = -119/2
9x = -54
x = -54/9
x = -6


Input:
Solve the equations:
4x + 9y = 48
10x + 4y = 83

Output:
4x + 9y = 48
10x + 4y = 83

Using elimination
10*(4x + 9y = 48)
4*(10x + 4y = 83)
40x + 90y = 480
40x + 16y = 332
Subtract equations
74y = 148
y = 148/74
y = 2

Substitute y
4x + 9(2) = 48
4x = 30
x = 30/4
x = 15/2


Input: Determine x in x^2 - 81/56x - 81/28 = 0

Output:
x^2 - 81/56x - 81/28 = 0
(x - -9/8)(x - 18/7) = 0
x - -9/8 = 0  or  x - 18/7 = 0
x = -9/8
x = 18/7


Input:
Solve the system:
5x + 2y = 19/14
5x + 9y = -37/14

Output:
5x + 2y = 19/14
5x + 9y = -37/14

Using elimination
5*(5x + 2y = 19/14)
5*(5x + 9y = -37/14)
25x + 10y = 95/14
25x + 45y = -185/14
Subtract equations
-35y = 20
y = 20/-35
y = -4/7

Substitute y
5x + 2(-4/7) = 19/14
5x = 5/2
x = 5/2/5
x = 1/2


Input:
Solve the system:
5x + 7y = 51
9x + 2y = -18/5

Output:
5x + 7y = 51
9x + 2y = -18/5

Using elimination
9*(5x + 7y = 51)
5*(9x + 2y = -18/5)
45x + 63y = 459
45x + 10y = -18
Subtract equations
53y = 477
y = 477/53
y = 9

Substitute y
5x + 7(9) = 51
5x = -12
x = -12/5
x = -12/5


Input:
Find x and y such that
3x + 7y = -75/8
6x + 3y = -51/8

Output:
3x + 7y = -75/8
6x + 3y = -51/8

Using elimination
6*(3x + 7y = -75/8)
3*(6x + 3y = -51/8)
18x + 42y = -225/4
18x + 9y = -153/8
Subtract equations
33y = -297/8
y = -297/8/33
y = -9/8

Substitute y
3x + 7(-9/8) = -75/8
3x = -3/2
x = -3/2/3
x = -1/2


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

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


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 x^3 + 814/105x^2 + 112/15x + 32/21 = 0

Output:
x^3 + 814/105x^2 + 112/15x + 32/21 = 0
(x - -4/5)(x - -20/3)(x - -2/7) = 0
x - -4/5 = 0
x - -20/3 = 0
x - -2/7 = 0
x = -4/5
x = -20/3
x = -2/7


Input:
Solve the system:
10x + 7y = 467/9
9x + 10y = 80

Output:
10x + 7y = 467/9
9x + 10y = 80

Using elimination
9*(10x + 7y = 467/9)
10*(9x + 10y = 80)
90x + 63y = 467
90x + 100y = 800
Subtract equations
-37y = -333
y = -333/-37
y = 9

Substitute y
10x + 7(9) = 467/9
10x = -100/9
x = -100/9/10
x = -10/9


Input: Compute the solution of x^2 - 128/9x - 35/3 = 0

Output:
x^2 - 128/9x - 35/3 = 0
(x - 15)(x - -7/9) = 0
x - 15 = 0  or  x - -7/9 = 0
x = 15
x = -7/9


Input: Determine x in x^2  - 81/4 = 0

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


Input: Solve x^2 + 19/5x - 66/5 = 0

Output:
x^2 + 19/5x - 66/5 = 0
(x - 11/5)(x - -6) = 0
x - 11/5 = 0  or  x - -6 = 0
x = 11/5
x = -6


Input: Find the solution to x^2 + 2/5x - 39/5 = 0

Output:
x^2 + 2/5x - 39/5 = 0
(x - -3)(x - 13/5) = 0
x - -3 = 0  or  x - 13/5 = 0
x = -3
x = 13/5


Input: Find the solution to x^3 + 145/18x^2 + 473/27x + 605/54 = 0

Output:
x^3 + 145/18x^2 + 473/27x + 605/54 = 0
(x - -5)(x - -11/6)(x - -11/9) = 0
x - -5 = 0
x - -11/6 = 0
x - -11/9 = 0
x = -5
x = -11/6
x = -11/9


Input:
Find x and y such that
2x + 4y = 6
3x + 3y = 15/2

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

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

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


Input:
Solve the equations:
9x + 6y = 75/2
1x + 2y = 21/2

Output:
9x + 6y = 75/2
1x + 2y = 21/2

Using elimination
1*(9x + 6y = 75/2)
9*(1x + 2y = 21/2)
9x + 6y = 75/2
9x + 18y = 189/2
Subtract equations
-12y = -57
y = -57/-12
y = 19/4

Substitute y
9x + 6(19/4) = 75/2
9x = 9
x = 9/9
x = 1


Input:
Find x and y such that
8x + 5y = -259/18
7x + 5y = -221/18

Output:
8x + 5y = -259/18
7x + 5y = -221/18

Using elimination
7*(8x + 5y = -259/18)
8*(7x + 5y = -221/18)
56x + 35y = -1813/18
56x + 40y = -884/9
Subtract equations
-5y = -5/2
y = -5/2/-5
y = 1/2

Substitute y
8x + 5(1/2) = -259/18
8x = -152/9
x = -152/9/8
x = -19/9


Input: What value of x satisfies x^3 - 22/21x^2 + 13/84x + 5/84 = 0

Output:
x^3 - 22/21x^2 + 13/84x + 5/84 = 0
(x - 5/7)(x - 1/2)(x - -1/6) = 0
x - 5/7 = 0
x - 1/2 = 0
x - -1/6 = 0
x = 5/7
x = 1/2
x = -1/6


Input: Compute the solution of x^3 + 4/35x^2 - 143/35x - 16/5 = 0

Output:
x^3 + 4/35x^2 - 143/35x - 16/5 = 0
(x - -7/5)(x - -1)(x - 16/7) = 0
x - -7/5 = 0
x - -1 = 0
x - 16/7 = 0
x = -7/5
x = -1
x = 16/7


Input: Find the solution to x^2 + 23/7x - 20/7 = 0

Output:
x^2 + 23/7x - 20/7 = 0
(x - -4)(x - 5/7) = 0
x - -4 = 0  or  x - 5/7 = 0
x = -4
x = 5/7


Input: Compute the solution of x^2 + 37/10x + 21/10 = 0

Output:
x^2 + 37/10x + 21/10 = 0
(x - -7/10)(x - -3) = 0
x - -7/10 = 0  or  x - -3 = 0
x = -7/10
x = -3


Input: Solve quickly: x^2 - 43/6x - 5/2 = 0

Output:
x^2 - 43/6x - 5/2 = 0
(x - 15/2)(x - -1/3) = 0
x - 15/2 = 0  or  x - -1/3 = 0
x = 15/2
x = -1/3


Input: Find the solution to x^2 + 17/3x - 56/3 = 0

Output:
x^2 + 17/3x - 56/3 = 0
(x - -8)(x - 7/3) = 0
x - -8 = 0  or  x - 7/3 = 0
x = -8
x = 7/3


Input: Find x for x^3 - 377/30x^2 + 98/3x - 51/10 = 0

Output:
x^3 - 377/30x^2 + 98/3x - 51/10 = 0
(x - 17/5)(x - 1/6)(x - 9) = 0
x - 17/5 = 0
x - 1/6 = 0
x - 9 = 0
x = 17/5
x = 1/6
x = 9


Input: What value of x satisfies x^3 + 37/30x^2 - 137/15x - 76/5 = 0

Output:
x^3 + 37/30x^2 - 137/15x - 76/5 = 0
(x - 19/6)(x - -2)(x - -12/5) = 0
x - 19/6 = 0
x - -2 = 0
x - -12/5 = 0
x = 19/6
x = -2
x = -12/5


Input:
Solve the equations:
6x + 4y = -65
3x + 7y = -235/2

Output:
6x + 4y = -65
3x + 7y = -235/2

Using elimination
3*(6x + 4y = -65)
6*(3x + 7y = -235/2)
18x + 12y = -195
18x + 42y = -705
Subtract equations
-30y = 510
y = 510/-30
y = -17

Substitute y
6x + 4(-17) = -65
6x = 3
x = 3/6
x = 1/2


Input: Solve x^3 - 9/10x^2 - 21/10x - 1/5 = 0

Output:
x^3 - 9/10x^2 - 21/10x - 1/5 = 0
(x - -1/10)(x - -1)(x - 2) = 0
x - -1/10 = 0
x - -1 = 0
x - 2 = 0
x = -1/10
x = -1
x = 2


Input: Find x for x^3 + 61/40x^2 - 247/160x - 77/32 = 0

Output:
x^3 + 61/40x^2 - 247/160x - 77/32 = 0
(x - -7/5)(x - 5/4)(x - -11/8) = 0
x - -7/5 = 0
x - 5/4 = 0
x - -11/8 = 0
x = -7/5
x = 5/4
x = -11/8


Input: Find x in 7x - 15 = 0

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


Input: Determine x in x^3 - 169/280x^2 - 17/40x + 3/14 = 0

Output:
x^3 - 169/280x^2 - 17/40x + 3/14 = 0
(x - -5/8)(x - 3/7)(x - 4/5) = 0
x - -5/8 = 0
x - 3/7 = 0
x - 4/5 = 0
x = -5/8
x = 3/7
x = 4/5


Input: Determine x in x^3 - 1/45x^2 - 158/135x + 16/45 = 0

Output:
x^3 - 1/45x^2 - 158/135x + 16/45 = 0
(x - 8/9)(x - 1/3)(x - -6/5) = 0
x - 8/9 = 0
x - 1/3 = 0
x - -6/5 = 0
x = 8/9
x = 1/3
x = -6/5


Input: Find x in x^2 + 18/7x + 11/7 = 0

Output:
x^2 + 18/7x + 11/7 = 0
(x - -1)(x - -11/7) = 0
x - -1 = 0  or  x - -11/7 = 0
x = -1
x = -11/7


Input: Solve x^2 + 53/4x + 323/8 = 0

Output:
x^2 + 53/4x + 323/8 = 0
(x - -17/2)(x - -19/4) = 0
x - -17/2 = 0  or  x - -19/4 = 0
x = -17/2
x = -19/4


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 quickly: x^2 + 1/21x - 152/21 = 0

Output:
x^2 + 1/21x - 152/21 = 0
(x - 8/3)(x - -19/7) = 0
x - 8/3 = 0  or  x - -19/7 = 0
x = 8/3
x = -19/7


Input: Find x for x^2 - 5/56x - 38/7 = 0

Output:
x^2 - 5/56x - 38/7 = 0
(x - 19/8)(x - -16/7) = 0
x - 19/8 = 0  or  x - -16/7 = 0
x = 19/8
x = -16/7


Input: Compute the solution of 4x - 10/3 = 0

Output:
4x - 10/3 = 0
4x = 10/3
x = 10/3 / 4
x = 5/6


Input:
Find x and y such that
9x + 10y = 940/7
6x + 4y = 328/7

Output:
9x + 10y = 940/7
6x + 4y = 328/7

Using elimination
6*(9x + 10y = 940/7)
9*(6x + 4y = 328/7)
54x + 60y = 5640/7
54x + 36y = 2952/7
Subtract equations
24y = 384
y = 384/24
y = 16

Substitute y
9x + 10(16) = 940/7
9x = -180/7
x = -180/7/9
x = -20/7


Input:
Find x and y such that
10x + 8y = -179/6
3x + 5y = -97/12

Output:
10x + 8y = -179/6
3x + 5y = -97/12

Using elimination
3*(10x + 8y = -179/6)
10*(3x + 5y = -97/12)
30x + 24y = -179/2
30x + 50y = -485/6
Subtract equations
-26y = -26/3
y = -26/3/-26
y = 1/3

Substitute y
10x + 8(1/3) = -179/6
10x = -65/2
x = -65/2/10
x = -13/4


Input:
Solve simultaneously:
8x + 7y = 46
1x + 1y = 51/8

Output:
8x + 7y = 46
1x + 1y = 51/8

Using elimination
1*(8x + 7y = 46)
8*(1x + 1y = 51/8)
8x + 7y = 46
8x + 8y = 51
Subtract equations
-1y = -5
y = -5/-1
y = 5

Substitute y
8x + 7(5) = 46
8x = 11
x = 11/8
x = 11/8


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

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


Input: Find the solution to x^3 + 37/6x^2 - 92/3x + 19/2 = 0

Output:
x^3 + 37/6x^2 - 92/3x + 19/2 = 0
(x - 3)(x - -19/2)(x - 1/3) = 0
x - 3 = 0
x - -19/2 = 0
x - 1/3 = 0
x = 3
x = -19/2
x = 1/3


Input: Find x in x^2 - 94/21x + 80/21 = 0

Output:
x^2 - 94/21x + 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 5x - 85/6 = 0

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


Input: Solve 6x - 3/5 = 0

Output:
6x - 3/5 = 0
6x = 3/5
x = 3/5 / 6
x = 1/10


Input: Find the solution to x^3 - 321/40x^2 - 383/20x - 6 = 0

Output:
x^3 - 321/40x^2 - 383/20x - 6 = 0
(x - 10)(x - -3/8)(x - -8/5) = 0
x - 10 = 0
x - -3/8 = 0
x - -8/5 = 0
x = 10
x = -3/8
x = -8/5


Input: Solve 9x + 153/4 = 0

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


Input:
Solve simultaneously:
5x + 1y = -477/56
8x + 2y = -93/7

Output:
5x + 1y = -477/56
8x + 2y = -93/7

Using elimination
8*(5x + 1y = -477/56)
5*(8x + 2y = -93/7)
40x + 8y = -477/7
40x + 10y = -465/7
Subtract equations
-2y = -12/7
y = -12/7/-2
y = 6/7

Substitute y
5x + 1(6/7) = -477/56
5x = -75/8
x = -75/8/5
x = -15/8


Input: Solve the equation x^2 - 81/7x - 34 = 0

Output:
x^2 - 81/7x - 34 = 0
(x - 14)(x - -17/7) = 0
x - 14 = 0  or  x - -17/7 = 0
x = 14
x = -17/7


Input:
Solve the system:
10x + 5y = 25/4
4x + 1y = 3/2

Output:
10x + 5y = 25/4
4x + 1y = 3/2

Using elimination
4*(10x + 5y = 25/4)
10*(4x + 1y = 3/2)
40x + 20y = 25
40x + 10y = 15
Subtract equations
10y = 10
y = 10/10
y = 1

Substitute y
10x + 5(1) = 25/4
10x = 5/4
x = 5/4/10
x = 1/8


Input:
Find x and y such that
10x + 2y = 16
2x + 6y = -26/5

Output:
10x + 2y = 16
2x + 6y = -26/5

Using elimination
2*(10x + 2y = 16)
10*(2x + 6y = -26/5)
20x + 4y = 32
20x + 60y = -52
Subtract equations
-56y = 84
y = 84/-56
y = -3/2

Substitute y
10x + 2(-3/2) = 16
10x = 19
x = 19/10
x = 19/10


Input: Find the solution to x^3 - 7/3x^2 - 6x - 8/3 = 0

Output:
x^3 - 7/3x^2 - 6x - 8/3 = 0
(x - -1)(x - -2/3)(x - 4) = 0
x - -1 = 0
x - -2/3 = 0
x - 4 = 0
x = -1
x = -2/3
x = 4


Input: Solve quickly: x^3 + 53/24x^2 - 77/12x + 3 = 0

Output:
x^3 + 53/24x^2 - 77/12x + 3 = 0
(x - -4)(x - 2/3)(x - 9/8) = 0
x - -4 = 0
x - 2/3 = 0
x - 9/8 = 0
x = -4
x = 2/3
x = 9/8


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

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


Input: Find x for 9x + 45/4 = 0

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


Input:
Solve simultaneously:
7x + 8y = -141/5
5x + 9y = -866/35

Output:
7x + 8y = -141/5
5x + 9y = -866/35

Using elimination
5*(7x + 8y = -141/5)
7*(5x + 9y = -866/35)
35x + 40y = -141
35x + 63y = -866/5
Subtract equations
-23y = 161/5
y = 161/5/-23
y = -7/5

Substitute y
7x + 8(-7/5) = -141/5
7x = -17
x = -17/7
x = -17/7


Input: Solve the equation x^3 - 209/30x^2 + 47/3x - 56/5 = 0

Output:
x^3 - 209/30x^2 + 47/3x - 56/5 = 0
(x - 14/5)(x - 3/2)(x - 8/3) = 0
x - 14/5 = 0
x - 3/2 = 0
x - 8/3 = 0
x = 14/5
x = 3/2
x = 8/3


Input: Solve the equation x^3 - 247/56x^2 + 335/56x - 18/7 = 0

Output:
x^3 - 247/56x^2 + 335/56x - 18/7 = 0
(x - 1)(x - 16/7)(x - 9/8) = 0
x - 1 = 0
x - 16/7 = 0
x - 9/8 = 0
x = 1
x = 16/7
x = 9/8


Input: Find the solution to x^2 - 49/8x - 323/16 = 0

Output:
x^2 - 49/8x - 323/16 = 0
(x - 17/2)(x - -19/8) = 0
x - 17/2 = 0  or  x - -19/8 = 0
x = 17/2
x = -19/8


Input: Find x for x^3 + 80/21x^2 - 281/21x - 340/21 = 0

Output:
x^3 + 80/21x^2 - 281/21x - 340/21 = 0
(x - -17/3)(x - -1)(x - 20/7) = 0
x - -17/3 = 0
x - -1 = 0
x - 20/7 = 0
x = -17/3
x = -1
x = 20/7


Input: Solve quickly: x^3 + 17/3x^2 + 10/3x  = 0

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


Input:
Solve the system:
9x + 7y = 117/4
5x + 2y = 55/6

Output:
9x + 7y = 117/4
5x + 2y = 55/6

Using elimination
5*(9x + 7y = 117/4)
9*(5x + 2y = 55/6)
45x + 35y = 585/4
45x + 18y = 165/2
Subtract equations
17y = 255/4
y = 255/4/17
y = 15/4

Substitute y
9x + 7(15/4) = 117/4
9x = 3
x = 3/9
x = 1/3


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

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


Input: Find the solution to 8x + 36 = 0

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


Input: Find the solution to x^2 + 13/5x + 153/100 = 0

Output:
x^2 + 13/5x + 153/100 = 0
(x - -17/10)(x - -9/10) = 0
x - -17/10 = 0  or  x - -9/10 = 0
x = -17/10
x = -9/10


Input: Find x in x^2 + 19/3x + 10 = 0

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


Input: Solve quickly: x^2 + 16/9x - 80/9 = 0

Output:
x^2 + 16/9x - 80/9 = 0
(x - -4)(x - 20/9) = 0
x - -4 = 0  or  x - 20/9 = 0
x = -4
x = 20/9


Input:
Solve simultaneously:
10x + 3y = 94/7
1x + 2y = 57/7

Output:
10x + 3y = 94/7
1x + 2y = 57/7

Using elimination
1*(10x + 3y = 94/7)
10*(1x + 2y = 57/7)
10x + 3y = 94/7
10x + 20y = 570/7
Subtract equations
-17y = -68
y = -68/-17
y = 4

Substitute y
10x + 3(4) = 94/7
10x = 10/7
x = 10/7/10
x = 1/7


Input: Find x for x^3 + 21/2x^2 - 57/50x - 2527/25 = 0

Output:
x^3 + 21/2x^2 - 57/50x - 2527/25 = 0
(x - -19/2)(x - 14/5)(x - -19/5) = 0
x - -19/2 = 0
x - 14/5 = 0
x - -19/5 = 0
x = -19/2
x = 14/5
x = -19/5


Input: Determine x in 3x - 3/8 = 0

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


Input: Determine x in x^2 - 29/18x + 5/9 = 0

Output:
x^2 - 29/18x + 5/9 = 0
(x - 1/2)(x - 10/9) = 0
x - 1/2 = 0  or  x - 10/9 = 0
x = 1/2
x = 10/9


Input:
Solve the equations:
4x + 4y = -72/35
6x + 4y = -52/35

Output:
4x + 4y = -72/35
6x + 4y = -52/35

Using elimination
6*(4x + 4y = -72/35)
4*(6x + 4y = -52/35)
24x + 24y = -432/35
24x + 16y = -208/35
Subtract equations
8y = -32/5
y = -32/5/8
y = -4/5

Substitute y
4x + 4(-4/5) = -72/35
4x = 8/7
x = 8/7/4
x = 2/7


Input: Solve x^3 - 33/5x^2 - 327/20x + 17/10 = 0

Output:
x^3 - 33/5x^2 - 327/20x + 17/10 = 0
(x - 17/2)(x - -2)(x - 1/10) = 0
x - 17/2 = 0
x - -2 = 0
x - 1/10 = 0
x = 17/2
x = -2
x = 1/10


Input: Compute the solution of x^3 - 29/24x^2 + 7/24x  = 0

Output:
x^3 - 29/24x^2 + 7/24x  = 0
(x - 7/8)(x - 0)(x - 1/3) = 0
x - 7/8 = 0
x - 0 = 0
x - 1/3 = 0
x = 7/8
x = 0
x = 1/3


Input:
Solve simultaneously:
6x + 10y = -65
3x + 8y = -34

Output:
6x + 10y = -65
3x + 8y = -34

Using elimination
3*(6x + 10y = -65)
6*(3x + 8y = -34)
18x + 30y = -195
18x + 48y = -204
Subtract equations
-18y = 9
y = 9/-18
y = -1/2

Substitute y
6x + 10(-1/2) = -65
6x = -60
x = -60/6
x = -10


Input: Find x in x^2 - 1/6x - 35/3 = 0

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


Input:
Find x and y such that
5x + 1y = 167/10
10x + 9y = 453/10

Output:
5x + 1y = 167/10
10x + 9y = 453/10

Using elimination
10*(5x + 1y = 167/10)
5*(10x + 9y = 453/10)
50x + 10y = 167
50x + 45y = 453/2
Subtract equations
-35y = -119/2
y = -119/2/-35
y = 17/10

Substitute y
5x + 1(17/10) = 167/10
5x = 15
x = 15/5
x = 3


Input: Find x for x^3 + 152/7x^2 + 1712/49x + 640/49 = 0

Output:
x^3 + 152/7x^2 + 1712/49x + 640/49 = 0
(x - -20)(x - -4/7)(x - -8/7) = 0
x - -20 = 0
x - -4/7 = 0
x - -8/7 = 0
x = -20
x = -4/7
x = -8/7


Input: What value of x satisfies x^3 + 66/7x^2 + 521/49x - 312/49 = 0

Output:
x^3 + 66/7x^2 + 521/49x - 312/49 = 0
(x - -8)(x - -13/7)(x - 3/7) = 0
x - -8 = 0
x - -13/7 = 0
x - 3/7 = 0
x = -8
x = -13/7
x = 3/7


Input:
Solve simultaneously:
4x + 10y = -63/2
2x + 8y = -543/20

Output:
4x + 10y = -63/2
2x + 8y = -543/20

Using elimination
2*(4x + 10y = -63/2)
4*(2x + 8y = -543/20)
8x + 20y = -63
8x + 32y = -543/5
Subtract equations
-12y = 228/5
y = 228/5/-12
y = -19/5

Substitute y
4x + 10(-19/5) = -63/2
4x = 13/2
x = 13/2/4
x = 13/8


Input: Find x in 10x + 170/3 = 0

Output:
10x + 170/3 = 0
10x = -170/3
x = -170/3 / 10
x = -17/3


Input: Solve quickly: 4x - 32/3 = 0

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


Input: Solve the equation x^2 + 1/3x - 10 = 0

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


Input: Solve 7x - 7/3 = 0

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


Input: Determine x in x^3 - 7/9x^2 - 14/3x + 40/9 = 0

Output:
x^3 - 7/9x^2 - 14/3x + 40/9 = 0
(x - -20/9)(x - 1)(x - 2) = 0
x - -20/9 = 0
x - 1 = 0
x - 2 = 0
x = -20/9
x = 1
x = 2


Input: Find x for x^3 - 10x^2 + 509/81x + 220/9 = 0

Output:
x^3 - 10x^2 + 509/81x + 220/9 = 0
(x - -11/9)(x - 9)(x - 20/9) = 0
x - -11/9 = 0
x - 9 = 0
x - 20/9 = 0
x = -11/9
x = 9
x = 20/9


Input: Determine x in x^3 - 17/6x^2 - 7/3x  = 0

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


Input: Find x for 6x - 2 = 0

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


Input: Determine x in 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^2 + 67/40x - 133/80 = 0

Output:
x^2 + 67/40x - 133/80 = 0
(x - -19/8)(x - 7/10) = 0
x - -19/8 = 0  or  x - 7/10 = 0
x = -19/8
x = 7/10


Input: Solve quickly: x^2 - 9x - 10 = 0

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


Input: Find the solution to x^2 - 7/3x - 10/3 = 0

Output:
x^2 - 7/3x - 10/3 = 0
(x - -1)(x - 10/3) = 0
x - -1 = 0  or  x - 10/3 = 0
x = -1
x = 10/3


Input: Find x for x^2 - 146/21x + 51/7 = 0

Output:
x^2 - 146/21x + 51/7 = 0
(x - 9/7)(x - 17/3) = 0
x - 9/7 = 0  or  x - 17/3 = 0
x = 9/7
x = 17/3


Input: Solve the equation 2x - 16 = 0

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


Input: Solve quickly: x^2 + 4x  = 0

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


Input: Solve quickly: x^2 + 117/10x + 17 = 0

Output:
x^2 + 117/10x + 17 = 0
(x - -10)(x - -17/10) = 0
x - -10 = 0  or  x - -17/10 = 0
x = -10
x = -17/10


Input: Find x for x^2 - 1/10x - 1/5 = 0

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


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

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


Input:
Find x and y such that
9x + 4y = 77
6x + 2y = 58

Output:
9x + 4y = 77
6x + 2y = 58

Using elimination
6*(9x + 4y = 77)
9*(6x + 2y = 58)
54x + 24y = 462
54x + 18y = 522
Subtract equations
6y = -60
y = -60/6
y = -10

Substitute y
9x + 4(-10) = 77
9x = 117
x = 117/9
x = 13


Input: What value of x satisfies x^2 - 8x - 20 = 0

Output:
x^2 - 8x - 20 = 0
(x - 10)(x - -2) = 0
x - 10 = 0  or  x - -2 = 0
x = 10
x = -2


Input:
Solve the system:
10x + 10y = 860/7
10x + 1y = 41/7

Output:
10x + 10y = 860/7
10x + 1y = 41/7

Using elimination
10*(10x + 10y = 860/7)
10*(10x + 1y = 41/7)
100x + 100y = 8600/7
100x + 10y = 410/7
Subtract equations
90y = 1170
y = 1170/90
y = 13

Substitute y
10x + 10(13) = 860/7
10x = -50/7
x = -50/7/10
x = -5/7


Input: Find x in x^2 - 29/35x - 4/5 = 0

Output:
x^2 - 29/35x - 4/5 = 0
(x - -4/7)(x - 7/5) = 0
x - -4/7 = 0  or  x - 7/5 = 0
x = -4/7
x = 7/5


Input: Compute the solution of x^3 + 111/4x^2 + 615/4x - 475/2 = 0

Output:
x^3 + 111/4x^2 + 615/4x - 475/2 = 0
(x - -10)(x - 5/4)(x - -19) = 0
x - -10 = 0
x - 5/4 = 0
x - -19 = 0
x = -10
x = 5/4
x = -19


Input: Find the solution to 3x + 24/5 = 0

Output:
3x + 24/5 = 0
3x = -24/5
x = -24/5 / 3
x = -8/5


Input: Find the solution to x^3 + 54/5x^2 + 79/5x - 18/5 = 0

Output:
x^3 + 54/5x^2 + 79/5x - 18/5 = 0
(x - 1/5)(x - -2)(x - -9) = 0
x - 1/5 = 0
x - -2 = 0
x - -9 = 0
x = 1/5
x = -2
x = -9


Input: Determine x in 1x  = 0

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


Input: Compute the solution of 5x + 35/4 = 0

Output:
5x + 35/4 = 0
5x = -35/4
x = -35/4 / 5
x = -7/4


Input: What value of x satisfies x^3 + 43/2x^2 + 114x + 126 = 0

Output:
x^3 + 43/2x^2 + 114x + 126 = 0
(x - -6)(x - -14)(x - -3/2) = 0
x - -6 = 0
x - -14 = 0
x - -3/2 = 0
x = -6
x = -14
x = -3/2


Input:
Find x and y such that
1x + 3y = 146/9
7x + 2y = 167/9

Output:
1x + 3y = 146/9
7x + 2y = 167/9

Using elimination
7*(1x + 3y = 146/9)
1*(7x + 2y = 167/9)
7x + 21y = 1022/9
7x + 2y = 167/9
Subtract equations
19y = 95
y = 95/19
y = 5

Substitute y
1x + 3(5) = 146/9
1x = 11/9
x = 11/9/1
x = 11/9


Input: Determine x in x^2 - 17/6x + 5/3 = 0

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


Input: Solve quickly: x^3 + 9/4x^2 - 5/8x - 21/8 = 0

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


Input:
Find x and y such that
9x + 4y = -109/12
10x + 5y = -55/6

Output:
9x + 4y = -109/12
10x + 5y = -55/6

Using elimination
10*(9x + 4y = -109/12)
9*(10x + 5y = -55/6)
90x + 40y = -545/6
90x + 45y = -165/2
Subtract equations
-5y = -25/3
y = -25/3/-5
y = 5/3

Substitute y
9x + 4(5/3) = -109/12
9x = -63/4
x = -63/4/9
x = -7/4


Input:
Find x and y such that
9x + 4y = -46/3
2x + 3y = -2

Output:
9x + 4y = -46/3
2x + 3y = -2

Using elimination
2*(9x + 4y = -46/3)
9*(2x + 3y = -2)
18x + 8y = -92/3
18x + 27y = -18
Subtract equations
-19y = -38/3
y = -38/3/-19
y = 2/3

Substitute y
9x + 4(2/3) = -46/3
9x = -18
x = -18/9
x = -2


Input: Solve x^2 + 63/40x - 26/5 = 0

Output:
x^2 + 63/40x - 26/5 = 0
(x - 13/8)(x - -16/5) = 0
x - 13/8 = 0  or  x - -16/5 = 0
x = 13/8
x = -16/5


Input:
Find x and y such that
6x + 7y = 12
4x + 1y = 13/3

Output:
6x + 7y = 12
4x + 1y = 13/3

Using elimination
4*(6x + 7y = 12)
6*(4x + 1y = 13/3)
24x + 28y = 48
24x + 6y = 26
Subtract equations
22y = 22
y = 22/22
y = 1

Substitute y
6x + 7(1) = 12
6x = 5
x = 5/6
x = 5/6


Input: Determine x in 6x - 114 = 0

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


Input: Find the solution to x^2 - 121/7x + 144/7 = 0

Output:
x^2 - 121/7x + 144/7 = 0
(x - 16)(x - 9/7) = 0
x - 16 = 0  or  x - 9/7 = 0
x = 16
x = 9/7


Input: Find x for x^3 + 115/28x^2 + 107/28x + 5/7 = 0

Output:
x^3 + 115/28x^2 + 107/28x + 5/7 = 0
(x - -20/7)(x - -1)(x - -1/4) = 0
x - -20/7 = 0
x - -1 = 0
x - -1/4 = 0
x = -20/7
x = -1
x = -1/4


Input:
Solve simultaneously:
8x + 5y = 4
10x + 9y = 16

Output:
8x + 5y = 4
10x + 9y = 16

Using elimination
10*(8x + 5y = 4)
8*(10x + 9y = 16)
80x + 50y = 40
80x + 72y = 128
Subtract equations
-22y = -88
y = -88/-22
y = 4

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


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

Output:
5x - 19/2 = 0
5x = 19/2
x = 19/2 / 5
x = 19/10


Input:
Find x and y such that
8x + 2y = -25
4x + 10y = 28

Output:
8x + 2y = -25
4x + 10y = 28

Using elimination
4*(8x + 2y = -25)
8*(4x + 10y = 28)
32x + 8y = -100
32x + 80y = 224
Subtract equations
-72y = -324
y = -324/-72
y = 9/2

Substitute y
8x + 2(9/2) = -25
8x = -34
x = -34/8
x = -17/4


Input: Solve 9x - 63/5 = 0

Output:
9x - 63/5 = 0
9x = 63/5
x = 63/5 / 9
x = 7/5


Input: Solve x^3 - 71/9x^2 + 127/9x + 5/3 = 0

Output:
x^3 - 71/9x^2 + 127/9x + 5/3 = 0
(x - 5)(x - -1/9)(x - 3) = 0
x - 5 = 0
x - -1/9 = 0
x - 3 = 0
x = 5
x = -1/9
x = 3


Input:
Solve the equations:
6x + 9y = 354/5
8x + 2y = 612/5

Output:
6x + 9y = 354/5
8x + 2y = 612/5

Using elimination
8*(6x + 9y = 354/5)
6*(8x + 2y = 612/5)
48x + 72y = 2832/5
48x + 12y = 3672/5
Subtract equations
60y = -168
y = -168/60
y = -14/5

Substitute y
6x + 9(-14/5) = 354/5
6x = 96
x = 96/6
x = 16


Input: Solve 10x - 32 = 0

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


Input:
Solve the equations:
9x + 9y = -444/7
4x + 3y = -167/7

Output:
9x + 9y = -444/7
4x + 3y = -167/7

Using elimination
4*(9x + 9y = -444/7)
9*(4x + 3y = -167/7)
36x + 36y = -1776/7
36x + 27y = -1503/7
Subtract equations
9y = -39
y = -39/9
y = -13/3

Substitute y
9x + 9(-13/3) = -444/7
9x = -171/7
x = -171/7/9
x = -19/7


Input: Find the solution to x^3 - 36/7x^2 - 1056/49x - 512/49 = 0

Output:
x^3 - 36/7x^2 - 1056/49x - 512/49 = 0
(x - 8)(x - -16/7)(x - -4/7) = 0
x - 8 = 0
x - -16/7 = 0
x - -4/7 = 0
x = 8
x = -16/7
x = -4/7


Input: Compute the solution of x^3 - 23/36x^2 - 83/18x + 17/4 = 0

Output:
x^3 - 23/36x^2 - 83/18x + 17/4 = 0
(x - -9/4)(x - 17/9)(x - 1) = 0
x - -9/4 = 0
x - 17/9 = 0
x - 1 = 0
x = -9/4
x = 17/9
x = 1


Input: Solve 6x + 12 = 0

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


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

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


Input: Determine x in x^2 - 14/9x - 40/27 = 0

Output:
x^2 - 14/9x - 40/27 = 0
(x - -2/3)(x - 20/9) = 0
x - -2/3 = 0  or  x - 20/9 = 0
x = -2/3
x = 20/9


Input: Solve quickly: x^2 - 17/4x - 9/8 = 0

Output:
x^2 - 17/4x - 9/8 = 0
(x - -1/4)(x - 9/2) = 0
x - -1/4 = 0  or  x - 9/2 = 0
x = -1/4
x = 9/2


Input: Find the solution to x^2 - 1x - 3/4 = 0

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


Input: Determine x in 3x + 15/2 = 0

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


Input: Solve 1x - 7/6 = 0

Output:
1x - 7/6 = 0
1x = 7/6
x = 7/6 / 1
x = 7/6


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

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


Input: Find x in x^2 - 25/2x + 36 = 0

Output:
x^2 - 25/2x + 36 = 0
(x - 8)(x - 9/2) = 0
x - 8 = 0  or  x - 9/2 = 0
x = 8
x = 9/2


Input: Find the solution to x^2 + 3/2x - 136/25 = 0

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


Input:
Find x and y such that
9x + 7y = 761/10
10x + 3y = 107/2

Output:
9x + 7y = 761/10
10x + 3y = 107/2

Using elimination
10*(9x + 7y = 761/10)
9*(10x + 3y = 107/2)
90x + 70y = 761
90x + 27y = 963/2
Subtract equations
43y = 559/2
y = 559/2/43
y = 13/2

Substitute y
9x + 7(13/2) = 761/10
9x = 153/5
x = 153/5/9
x = 17/5


Input: What value of x satisfies x^2 + 12/5x + 7/5 = 0

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


Input: Find x for x^3 + 32/9x^2 - 1088/27x - 1024/27 = 0

Output:
x^3 + 32/9x^2 - 1088/27x - 1024/27 = 0
(x - 16/3)(x - -8)(x - -8/9) = 0
x - 16/3 = 0
x - -8 = 0
x - -8/9 = 0
x = 16/3
x = -8
x = -8/9


Input: Solve quickly: 6x + 48 = 0

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


Input: Solve quickly: x^2 + 25/2x + 33/2 = 0

Output:
x^2 + 25/2x + 33/2 = 0
(x - -11)(x - -3/2) = 0
x - -11 = 0  or  x - -3/2 = 0
x = -11
x = -3/2


Input: Solve quickly: x^3 - 127/24x^2 + 33/4x - 10/3 = 0

Output:
x^3 - 127/24x^2 + 33/4x - 10/3 = 0
(x - 2)(x - 8/3)(x - 5/8) = 0
x - 2 = 0
x - 8/3 = 0
x - 5/8 = 0
x = 2
x = 8/3
x = 5/8


Input: Determine x in x^2 + 52/15x + 28/15 = 0

Output:
x^2 + 52/15x + 28/15 = 0
(x - -2/3)(x - -14/5) = 0
x - -2/3 = 0  or  x - -14/5 = 0
x = -2/3
x = -14/5


Input: Compute the solution of x^3 + 17/2x^2 + 341/16x + 221/16 = 0

Output:
x^3 + 17/2x^2 + 341/16x + 221/16 = 0
(x - -17/4)(x - -1)(x - -13/4) = 0
x - -17/4 = 0
x - -1 = 0
x - -13/4 = 0
x = -17/4
x = -1
x = -13/4


Input: Solve 1x - 10/3 = 0

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


Input:
Find x and y such that
6x + 3y = 46/3
5x + 2y = 106/9

Output:
6x + 3y = 46/3
5x + 2y = 106/9

Using elimination
5*(6x + 3y = 46/3)
6*(5x + 2y = 106/9)
30x + 15y = 230/3
30x + 12y = 212/3
Subtract equations
3y = 6
y = 6/3
y = 2

Substitute y
6x + 3(2) = 46/3
6x = 28/3
x = 28/3/6
x = 14/9


Input:
Solve the system:
8x + 3y = 9/10
7x + 6y = 36/5

Output:
8x + 3y = 9/10
7x + 6y = 36/5

Using elimination
7*(8x + 3y = 9/10)
8*(7x + 6y = 36/5)
56x + 21y = 63/10
56x + 48y = 288/5
Subtract equations
-27y = -513/10
y = -513/10/-27
y = 19/10

Substitute y
8x + 3(19/10) = 9/10
8x = -24/5
x = -24/5/8
x = -3/5


Input:
Solve the equations:
6x + 4y = 16
7x + 6y = 20

Output:
6x + 4y = 16
7x + 6y = 20

Using elimination
7*(6x + 4y = 16)
6*(7x + 6y = 20)
42x + 28y = 112
42x + 36y = 120
Subtract equations
-8y = -8
y = -8/-8
y = 1

Substitute y
6x + 4(1) = 16
6x = 12
x = 12/6
x = 2


Input: Compute the solution of x^3 + 16/35x^2 - 208/175x - 128/175 = 0

Output:
x^3 + 16/35x^2 - 208/175x - 128/175 = 0
(x - 8/7)(x - -4/5)(x - -4/5) = 0
x - 8/7 = 0
x - -4/5 = 0
x - -4/5 = 0
x = 8/7
x = -4/5
x = -4/5


Input: Find x for x^3 + 14/15x^2 - 27x - 884/15 = 0

Output:
x^3 + 14/15x^2 - 27x - 884/15 = 0
(x - -4)(x - -13/5)(x - 17/3) = 0
x - -4 = 0
x - -13/5 = 0
x - 17/3 = 0
x = -4
x = -13/5
x = 17/3


Input: Solve x^3 - 14x^2 - 81x + 1134 = 0

Output:
x^3 - 14x^2 - 81x + 1134 = 0
(x - 14)(x - -9)(x - 9) = 0
x - 14 = 0
x - -9 = 0
x - 9 = 0
x = 14
x = -9
x = 9


Input: What value of x satisfies x^2 - 8/7x - 15/7 = 0

Output:
x^2 - 8/7x - 15/7 = 0
(x - 15/7)(x - -1) = 0
x - 15/7 = 0  or  x - -1 = 0
x = 15/7
x = -1


Input: Find x in 6x - 18 = 0

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


Input: Find x for x^2 - 5x + 21/4 = 0

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


Input: Find x in 6x + 21 = 0

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


Input:
Find x and y such that
3x + 6y = -156/7
10x + 2y = -16/7

Output:
3x + 6y = -156/7
10x + 2y = -16/7

Using elimination
10*(3x + 6y = -156/7)
3*(10x + 2y = -16/7)
30x + 60y = -1560/7
30x + 6y = -48/7
Subtract equations
54y = -216
y = -216/54
y = -4

Substitute y
3x + 6(-4) = -156/7
3x = 12/7
x = 12/7/3
x = 4/7


Input:
Find x and y such that
3x + 5y = 19/70
2x + 7y = 14/5

Output:
3x + 5y = 19/70
2x + 7y = 14/5

Using elimination
2*(3x + 5y = 19/70)
3*(2x + 7y = 14/5)
6x + 10y = 19/35
6x + 21y = 42/5
Subtract equations
-11y = -55/7
y = -55/7/-11
y = 5/7

Substitute y
3x + 5(5/7) = 19/70
3x = -33/10
x = -33/10/3
x = -11/10


Input: What value of x satisfies x^3 + 12/5x^2 + 173/100x + 33/100 = 0

Output:
x^3 + 12/5x^2 + 173/100x + 33/100 = 0
(x - -1)(x - -3/10)(x - -11/10) = 0
x - -1 = 0
x - -3/10 = 0
x - -11/10 = 0
x = -1
x = -3/10
x = -11/10


Input: Find x for x^2 - 16/9x - 11/3 = 0

Output:
x^2 - 16/9x - 11/3 = 0
(x - -11/9)(x - 3) = 0
x - -11/9 = 0  or  x - 3 = 0
x = -11/9
x = 3


Input:
Solve the system:
9x + 6y = 131/7
5x + 10y = 1615/63

Output:
9x + 6y = 131/7
5x + 10y = 1615/63

Using elimination
5*(9x + 6y = 131/7)
9*(5x + 10y = 1615/63)
45x + 30y = 655/7
45x + 90y = 1615/7
Subtract equations
-60y = -960/7
y = -960/7/-60
y = 16/7

Substitute y
9x + 6(16/7) = 131/7
9x = 5
x = 5/9
x = 5/9


Input: Solve the equation 5x - 5/6 = 0

Output:
5x - 5/6 = 0
5x = 5/6
x = 5/6 / 5
x = 1/6


Input: Solve quickly: x^3 - 59/24x^2 - 83/24x + 35/4 = 0

Output:
x^3 - 59/24x^2 - 83/24x + 35/4 = 0
(x - -15/8)(x - 7/3)(x - 2) = 0
x - -15/8 = 0
x - 7/3 = 0
x - 2 = 0
x = -15/8
x = 7/3
x = 2


Input: Determine x in x^3 - 1583/504x^2 - 116/63x + 17/2 = 0

Output:
x^3 - 1583/504x^2 - 116/63x + 17/2 = 0
(x - 18/7)(x - -14/9)(x - 17/8) = 0
x - 18/7 = 0
x - -14/9 = 0
x - 17/8 = 0
x = 18/7
x = -14/9
x = 17/8


Input: Solve quickly: x^2 + 11/72x - 26/9 = 0

Output:
x^2 + 11/72x - 26/9 = 0
(x - -16/9)(x - 13/8) = 0
x - -16/9 = 0  or  x - 13/8 = 0
x = -16/9
x = 13/8


Input: Compute the solution of x^2 - 41/2x + 195/2 = 0

Output:
x^2 - 41/2x + 195/2 = 0
(x - 13)(x - 15/2) = 0
x - 13 = 0  or  x - 15/2 = 0
x = 13
x = 15/2


Input: Compute the solution of x^3 - 118/45x^2 - 44/75x + 56/225 = 0

Output:
x^3 - 118/45x^2 - 44/75x + 56/225 = 0
(x - -2/5)(x - 2/9)(x - 14/5) = 0
x - -2/5 = 0
x - 2/9 = 0
x - 14/5 = 0
x = -2/5
x = 2/9
x = 14/5


Input: What value of x satisfies x^3 - 25/9x^2 - 88/27x  = 0

Output:
x^3 - 25/9x^2 - 88/27x  = 0
(x - -8/9)(x - 11/3)(x - 0) = 0
x - -8/9 = 0
x - 11/3 = 0
x - 0 = 0
x = -8/9
x = 11/3
x = 0


Input: Compute the solution of 9x + 45/4 = 0

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


Input: Solve quickly: x^3 + 347/70x^2 - 19/35x - 117/10 = 0

Output:
x^3 + 347/70x^2 - 19/35x - 117/10 = 0
(x - -9/2)(x - -13/7)(x - 7/5) = 0
x - -9/2 = 0
x - -13/7 = 0
x - 7/5 = 0
x = -9/2
x = -13/7
x = 7/5


Input: Solve x^2 - 65/21x - 22/3 = 0

Output:
x^2 - 65/21x - 22/3 = 0
(x - 14/3)(x - -11/7) = 0
x - 14/3 = 0  or  x - -11/7 = 0
x = 14/3
x = -11/7


Input:
Solve the equations:
1x + 6y = 49/4
9x + 3y = 627/8

Output:
1x + 6y = 49/4
9x + 3y = 627/8

Using elimination
9*(1x + 6y = 49/4)
1*(9x + 3y = 627/8)
9x + 54y = 441/4
9x + 3y = 627/8
Subtract equations
51y = 255/8
y = 255/8/51
y = 5/8

Substitute y
1x + 6(5/8) = 49/4
1x = 17/2
x = 17/2/1
x = 17/2


Input: Solve 10x + 75/4 = 0

Output:
10x + 75/4 = 0
10x = -75/4
x = -75/4 / 10
x = -15/8


Input: Compute the solution of 4x - 26/5 = 0

Output:
4x - 26/5 = 0
4x = 26/5
x = 26/5 / 4
x = 13/10


Input:
Find x and y such that
4x + 8y = -34
7x + 7y = -217/4

Output:
4x + 8y = -34
7x + 7y = -217/4

Using elimination
7*(4x + 8y = -34)
4*(7x + 7y = -217/4)
28x + 56y = -238
28x + 28y = -217
Subtract equations
28y = -21
y = -21/28
y = -3/4

Substitute y
4x + 8(-3/4) = -34
4x = -28
x = -28/4
x = -7


Input: Solve x^3 + 23/70x^2 - 423/70x - 18/7 = 0

Output:
x^3 + 23/70x^2 - 423/70x - 18/7 = 0
(x - -12/5)(x - 5/2)(x - -3/7) = 0
x - -12/5 = 0
x - 5/2 = 0
x - -3/7 = 0
x = -12/5
x = 5/2
x = -3/7


Input: Solve quickly: x^2 - 3x - 27/4 = 0

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


Input: What value of x satisfies x^2 + 64/15x + 13/3 = 0

Output:
x^2 + 64/15x + 13/3 = 0
(x - -13/5)(x - -5/3) = 0
x - -13/5 = 0  or  x - -5/3 = 0
x = -13/5
x = -5/3


Input:
Solve the equations:
4x + 10y = -94/3
4x + 7y = -67/3

Output:
4x + 10y = -94/3
4x + 7y = -67/3

Using elimination
4*(4x + 10y = -94/3)
4*(4x + 7y = -67/3)
16x + 40y = -376/3
16x + 28y = -268/3
Subtract equations
12y = -36
y = -36/12
y = -3

Substitute y
4x + 10(-3) = -94/3
4x = -4/3
x = -4/3/4
x = -1/3


Input: Solve the equation x^2 - 13/18x + 1/9 = 0

Output:
x^2 - 13/18x + 1/9 = 0
(x - 1/2)(x - 2/9) = 0
x - 1/2 = 0  or  x - 2/9 = 0
x = 1/2
x = 2/9


Input: Solve the equation x^3 - 8x^2 + 12x  = 0

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


Input: Solve quickly: x^3 + 1349/56x^2 + 722/7x + 6859/56 = 0

Output:
x^3 + 1349/56x^2 + 722/7x + 6859/56 = 0
(x - -19/8)(x - -19)(x - -19/7) = 0
x - -19/8 = 0
x - -19 = 0
x - -19/7 = 0
x = -19/8
x = -19
x = -19/7


Input:
Solve the system:
6x + 10y = -87
5x + 6y = -337/6

Output:
6x + 10y = -87
5x + 6y = -337/6

Using elimination
5*(6x + 10y = -87)
6*(5x + 6y = -337/6)
30x + 50y = -435
30x + 36y = -337
Subtract equations
14y = -98
y = -98/14
y = -7

Substitute y
6x + 10(-7) = -87
6x = -17
x = -17/6
x = -17/6


Input: Determine x in x^2 + 121/72x - 17/18 = 0

Output:
x^2 + 121/72x - 17/18 = 0
(x - -17/8)(x - 4/9) = 0
x - -17/8 = 0  or  x - 4/9 = 0
x = -17/8
x = 4/9


Input: Solve x^3 + 13/10x^2 - 931/10x + 748/5 = 0

Output:
x^3 + 13/10x^2 - 931/10x + 748/5 = 0
(x - 17/10)(x - 8)(x - -11) = 0
x - 17/10 = 0
x - 8 = 0
x - -11 = 0
x = 17/10
x = 8
x = -11


Input:
Solve the equations:
5x + 1y = 197/10
3x + 6y = 21

Output:
5x + 1y = 197/10
3x + 6y = 21

Using elimination
3*(5x + 1y = 197/10)
5*(3x + 6y = 21)
15x + 3y = 591/10
15x + 30y = 105
Subtract equations
-27y = -459/10
y = -459/10/-27
y = 17/10

Substitute y
5x + 1(17/10) = 197/10
5x = 18
x = 18/5
x = 18/5


Input: Compute the solution of x^2 + 47/6x + 26/3 = 0

Output:
x^2 + 47/6x + 26/3 = 0
(x - -4/3)(x - -13/2) = 0
x - -4/3 = 0  or  x - -13/2 = 0
x = -4/3
x = -13/2


Input:
Solve the system:
6x + 3y = 18
10x + 7y = 30

Output:
6x + 3y = 18
10x + 7y = 30

Using elimination
10*(6x + 3y = 18)
6*(10x + 7y = 30)
60x + 30y = 180
60x + 42y = 180
Subtract equations
-12y = 0
y = 0/-12
y = 0

Substitute y
6x + 3(0) = 18
6x = 18
x = 18/6
x = 3


Input: Solve 8x + 80/3 = 0

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


Input: Solve 2x + 12 = 0

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


Input: Determine x in 7x + 49/10 = 0

Output:
7x + 49/10 = 0
7x = -49/10
x = -49/10 / 7
x = -7/10


Input: Solve the equation 9x + 57 = 0

Output:
9x + 57 = 0
9x = -57
x = -57 / 9
x = -19/3


Input: Compute the solution of x^3 - 29/6x^2 + 1409/192x - 57/16 = 0

Output:
x^3 - 29/6x^2 + 1409/192x - 57/16 = 0
(x - 4/3)(x - 19/8)(x - 9/8) = 0
x - 4/3 = 0
x - 19/8 = 0
x - 9/8 = 0
x = 4/3
x = 19/8
x = 9/8


Input:
Solve the equations:
5x + 4y = 44
9x + 10y = 75

Output:
5x + 4y = 44
9x + 10y = 75

Using elimination
9*(5x + 4y = 44)
5*(9x + 10y = 75)
45x + 36y = 396
45x + 50y = 375
Subtract equations
-14y = 21
y = 21/-14
y = -3/2

Substitute y
5x + 4(-3/2) = 44
5x = 50
x = 50/5
x = 10


Input:
Solve the equations:
7x + 9y = 34
4x + 1y = 7

Output:
7x + 9y = 34
4x + 1y = 7

Using elimination
4*(7x + 9y = 34)
7*(4x + 1y = 7)
28x + 36y = 136
28x + 7y = 49
Subtract equations
29y = 87
y = 87/29
y = 3

Substitute y
7x + 9(3) = 34
7x = 7
x = 7/7
x = 1


Input:
Solve simultaneously:
2x + 2y = 26/3
4x + 1y = 58/3

Output:
2x + 2y = 26/3
4x + 1y = 58/3

Using elimination
4*(2x + 2y = 26/3)
2*(4x + 1y = 58/3)
8x + 8y = 104/3
8x + 2y = 116/3
Subtract equations
6y = -4
y = -4/6
y = -2/3

Substitute y
2x + 2(-2/3) = 26/3
2x = 10
x = 10/2
x = 5


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

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


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

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


Input: Find x in x^2 - 27/10x + 17/10 = 0

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


Input: Solve the equation 10x - 20 = 0

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


Input: Solve quickly: 10x + 35/4 = 0

Output:
10x + 35/4 = 0
10x = -35/4
x = -35/4 / 10
x = -7/8


Input: Find x for 10x - 10 = 0

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


Input: Solve the equation x^3 + 257/28x^2 + 81/4x + 99/14 = 0

Output:
x^3 + 257/28x^2 + 81/4x + 99/14 = 0
(x - -6)(x - -3/7)(x - -11/4) = 0
x - -6 = 0
x - -3/7 = 0
x - -11/4 = 0
x = -6
x = -3/7
x = -11/4


Input: Compute the solution of x^3 + 17/8x^2 - 29/16x - 33/8 = 0

Output:
x^3 + 17/8x^2 - 29/16x - 33/8 = 0
(x - -3/2)(x - 11/8)(x - -2) = 0
x - -3/2 = 0
x - 11/8 = 0
x - -2 = 0
x = -3/2
x = 11/8
x = -2


Input: Determine x in x^3 + 389/36x^2 + 3553/108x + 578/27 = 0

Output:
x^3 + 389/36x^2 + 3553/108x + 578/27 = 0
(x - -17/4)(x - -17/3)(x - -8/9) = 0
x - -17/4 = 0
x - -17/3 = 0
x - -8/9 = 0
x = -17/4
x = -17/3
x = -8/9


Input:
Solve the system:
4x + 7y = -27/4
10x + 7y = -183/4

Output:
4x + 7y = -27/4
10x + 7y = -183/4

Using elimination
10*(4x + 7y = -27/4)
4*(10x + 7y = -183/4)
40x + 70y = -135/2
40x + 28y = -183
Subtract equations
42y = 231/2
y = 231/2/42
y = 11/4

Substitute y
4x + 7(11/4) = -27/4
4x = -26
x = -26/4
x = -13/2


Input: What value of x satisfies x^2 + 8/7x - 12/7 = 0

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


Input: What value of x satisfies x^3 + 387/28x^2 + 209/28x - 585/14 = 0

Output:
x^3 + 387/28x^2 + 209/28x - 585/14 = 0
(x - 10/7)(x - -13)(x - -9/4) = 0
x - 10/7 = 0
x - -13 = 0
x - -9/4 = 0
x = 10/7
x = -13
x = -9/4


Input: Find x in x^3 - 205/63x^2 + 919/441x - 85/441 = 0

Output:
x^3 - 205/63x^2 + 919/441x - 85/441 = 0
(x - 17/7)(x - 5/7)(x - 1/9) = 0
x - 17/7 = 0
x - 5/7 = 0
x - 1/9 = 0
x = 17/7
x = 5/7
x = 1/9


Input: Determine x in 5x + 11 = 0

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


Input: Find x in x^2 - 17/7x + 30/49 = 0

Output:
x^2 - 17/7x + 30/49 = 0
(x - 2/7)(x - 15/7) = 0
x - 2/7 = 0  or  x - 15/7 = 0
x = 2/7
x = 15/7


Input: What value of x satisfies x^2 + 21/5x + 22/5 = 0

Output:
x^2 + 21/5x + 22/5 = 0
(x - -11/5)(x - -2) = 0
x - -11/5 = 0  or  x - -2 = 0
x = -11/5
x = -2


Input: What value of x satisfies x^2 + 25/9x + 52/27 = 0

Output:
x^2 + 25/9x + 52/27 = 0
(x - -4/3)(x - -13/9) = 0
x - -4/3 = 0  or  x - -13/9 = 0
x = -4/3
x = -13/9


Input: Solve the equation x^2 + 37/9x + 4/9 = 0

Output:
x^2 + 37/9x + 4/9 = 0
(x - -1/9)(x - -4) = 0
x - -1/9 = 0  or  x - -4 = 0
x = -1/9
x = -4


Input:
Find x and y such that
8x + 2y = -32
10x + 4y = -43

Output:
8x + 2y = -32
10x + 4y = -43

Using elimination
10*(8x + 2y = -32)
8*(10x + 4y = -43)
80x + 20y = -320
80x + 32y = -344
Subtract equations
-12y = 24
y = 24/-12
y = -2

Substitute y
8x + 2(-2) = -32
8x = -28
x = -28/8
x = -7/2