Input:
Find x and y such that
1x + 10y = -4
4x + 4y = 64/5

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

Using elimination
4*(1x + 10y = -4)
1*(4x + 4y = 64/5)
4x + 40y = -16
4x + 4y = 64/5
Subtract equations
36y = -144/5
y = -144/5/36
y = -4/5

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


Input:
Find x and y such that
3x + 2y = -96/5
4x + 9y = -508/5

Output:
3x + 2y = -96/5
4x + 9y = -508/5

Using elimination
4*(3x + 2y = -96/5)
3*(4x + 9y = -508/5)
12x + 8y = -384/5
12x + 27y = -1524/5
Subtract equations
-19y = 228
y = 228/-19
y = -12

Substitute y
3x + 2(-12) = -96/5
3x = 24/5
x = 24/5/3
x = 8/5


Input:
Solve simultaneously:
4x + 4y = -12/7
1x + 9y = 29/7

Output:
4x + 4y = -12/7
1x + 9y = 29/7

Using elimination
1*(4x + 4y = -12/7)
4*(1x + 9y = 29/7)
4x + 4y = -12/7
4x + 36y = 116/7
Subtract equations
-32y = -128/7
y = -128/7/-32
y = 4/7

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


Input: Compute the solution of x^2 - 44/35x - 39/35 = 0

Output:
x^2 - 44/35x - 39/35 = 0
(x - 13/7)(x - -3/5) = 0
x - 13/7 = 0  or  x - -3/5 = 0
x = 13/7
x = -3/5


Input: Determine x in x^2 + 13/7x + 6/7 = 0

Output:
x^2 + 13/7x + 6/7 = 0
(x - -1)(x - -6/7) = 0
x - -1 = 0  or  x - -6/7 = 0
x = -1
x = -6/7


Input: Compute the solution of x^3 + 18/5x^2 - 8/5x  = 0

Output:
x^3 + 18/5x^2 - 8/5x  = 0
(x - 0)(x - 2/5)(x - -4) = 0
x - 0 = 0
x - 2/5 = 0
x - -4 = 0
x = 0
x = 2/5
x = -4


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

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


Input: Solve quickly: 4x - 56 = 0

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


Input:
Solve the equations:
2x + 1y = -44/9
10x + 10y = -310/9

Output:
2x + 1y = -44/9
10x + 10y = -310/9

Using elimination
10*(2x + 1y = -44/9)
2*(10x + 10y = -310/9)
20x + 10y = -440/9
20x + 20y = -620/9
Subtract equations
-10y = 20
y = 20/-10
y = -2

Substitute y
2x + 1(-2) = -44/9
2x = -26/9
x = -26/9/2
x = -13/9


Input: Find x for 5x + 25 = 0

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


Input: Compute the solution of x^2 - 19/2x - 30 = 0

Output:
x^2 - 19/2x - 30 = 0
(x - 12)(x - -5/2) = 0
x - 12 = 0  or  x - -5/2 = 0
x = 12
x = -5/2


Input:
Find x and y such that
5x + 6y = -75
9x + 4y = -135

Output:
5x + 6y = -75
9x + 4y = -135

Using elimination
9*(5x + 6y = -75)
5*(9x + 4y = -135)
45x + 54y = -675
45x + 20y = -675
Subtract equations
34y = 0
y = 0/34
y = 0

Substitute y
5x + 6(0) = -75
5x = -75
x = -75/5
x = -15


Input: Find x in x^2 + 19/4x  = 0

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


Input: Find x for x^2 - 23/12x + 5/12 = 0

Output:
x^2 - 23/12x + 5/12 = 0
(x - 1/4)(x - 5/3) = 0
x - 1/4 = 0  or  x - 5/3 = 0
x = 1/4
x = 5/3


Input: Solve quickly: x^2 - 83/7x + 180/7 = 0

Output:
x^2 - 83/7x + 180/7 = 0
(x - 9)(x - 20/7) = 0
x - 9 = 0  or  x - 20/7 = 0
x = 9
x = 20/7


Input: Solve 8x  = 0

Output:
8x  = 0
8x = 0
x = 0 / 8
x = 0


Input: Find the solution to x^3 - 23/6x^2 + 25/6x - 1 = 0

Output:
x^3 - 23/6x^2 + 25/6x - 1 = 0
(x - 1/3)(x - 2)(x - 3/2) = 0
x - 1/3 = 0
x - 2 = 0
x - 3/2 = 0
x = 1/3
x = 2
x = 3/2


Input: Compute the solution of 10x - 130/3 = 0

Output:
10x - 130/3 = 0
10x = 130/3
x = 130/3 / 10
x = 13/3


Input:
Solve the system:
7x + 10y = 198/5
3x + 9y = 132/5

Output:
7x + 10y = 198/5
3x + 9y = 132/5

Using elimination
3*(7x + 10y = 198/5)
7*(3x + 9y = 132/5)
21x + 30y = 594/5
21x + 63y = 924/5
Subtract equations
-33y = -66
y = -66/-33
y = 2

Substitute y
7x + 10(2) = 198/5
7x = 98/5
x = 98/5/7
x = 14/5


Input: Solve the equation x^3 - 267/40x^2 + 491/40x - 63/10 = 0

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


Input: Determine x in 1x + 3 = 0

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


Input: Find the solution to 7x + 91/6 = 0

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


Input: Compute the solution of 10x + 110/3 = 0

Output:
10x + 110/3 = 0
10x = -110/3
x = -110/3 / 10
x = -11/3


Input: Determine x in x^2 - 1/4x - 15/8 = 0

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


Input:
Solve the equations:
8x + 8y = -56
5x + 7y = -45

Output:
8x + 8y = -56
5x + 7y = -45

Using elimination
5*(8x + 8y = -56)
8*(5x + 7y = -45)
40x + 40y = -280
40x + 56y = -360
Subtract equations
-16y = 80
y = 80/-16
y = -5

Substitute y
8x + 8(-5) = -56
8x = -16
x = -16/8
x = -2


Input: Solve quickly: x^3 + 11/10x^2 - 51/5x - 63/10 = 0

Output:
x^3 + 11/10x^2 - 51/5x - 63/10 = 0
(x - 3)(x - -3/5)(x - -7/2) = 0
x - 3 = 0
x - -3/5 = 0
x - -7/2 = 0
x = 3
x = -3/5
x = -7/2


Input: Find x for x^3 - 142/15x^2 - 9x + 110/3 = 0

Output:
x^3 - 142/15x^2 - 9x + 110/3 = 0
(x - -11/5)(x - 5/3)(x - 10) = 0
x - -11/5 = 0
x - 5/3 = 0
x - 10 = 0
x = -11/5
x = 5/3
x = 10


Input:
Solve the equations:
1x + 8y = -7/2
10x + 1y = 9/2

Output:
1x + 8y = -7/2
10x + 1y = 9/2

Using elimination
10*(1x + 8y = -7/2)
1*(10x + 1y = 9/2)
10x + 80y = -35
10x + 1y = 9/2
Subtract equations
79y = -79/2
y = -79/2/79
y = -1/2

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


Input: Determine x in 5x + 4 = 0

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


Input: Solve quickly: 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: What value of x satisfies x^3 + 37/7x^2 + 52/7x + 12/7 = 0

Output:
x^3 + 37/7x^2 + 52/7x + 12/7 = 0
(x - -2)(x - -2/7)(x - -3) = 0
x - -2 = 0
x - -2/7 = 0
x - -3 = 0
x = -2
x = -2/7
x = -3


Input: Find x in x^3 - 221/72x^2 + 169/72x  = 0

Output:
x^3 - 221/72x^2 + 169/72x  = 0
(x - 0)(x - 13/8)(x - 13/9) = 0
x - 0 = 0
x - 13/8 = 0
x - 13/9 = 0
x = 0
x = 13/8
x = 13/9


Input: Determine x in 7x + 7 = 0

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


Input: Solve 8x - 10 = 0

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


Input: Solve 9x - 36 = 0

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


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

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


Input: Find x for x^3 - 245/72x^2 + 931/288x - 11/18 = 0

Output:
x^3 - 245/72x^2 + 931/288x - 11/18 = 0
(x - 16/9)(x - 1/4)(x - 11/8) = 0
x - 16/9 = 0
x - 1/4 = 0
x - 11/8 = 0
x = 16/9
x = 1/4
x = 11/8


Input: Find x for 8x - 8 = 0

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


Input:
Solve the system:
4x + 6y = -137/10
5x + 4y = -18

Output:
4x + 6y = -137/10
5x + 4y = -18

Using elimination
5*(4x + 6y = -137/10)
4*(5x + 4y = -18)
20x + 30y = -137/2
20x + 16y = -72
Subtract equations
14y = 7/2
y = 7/2/14
y = 1/4

Substitute y
4x + 6(1/4) = -137/10
4x = -76/5
x = -76/5/4
x = -19/5


Input: Determine x in x^2 - 1/6x - 5/6 = 0

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


Input: Solve quickly: 9x - 108/5 = 0

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


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

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


Input:
Solve the system:
8x + 2y = 96/7
8x + 6y = 32/7

Output:
8x + 2y = 96/7
8x + 6y = 32/7

Using elimination
8*(8x + 2y = 96/7)
8*(8x + 6y = 32/7)
64x + 16y = 768/7
64x + 48y = 256/7
Subtract equations
-32y = 512/7
y = 512/7/-32
y = -16/7

Substitute y
8x + 2(-16/7) = 96/7
8x = 128/7
x = 128/7/8
x = 16/7


Input: Find the solution to x^2 - 13/3x + 14/3 = 0

Output:
x^2 - 13/3x + 14/3 = 0
(x - 2)(x - 7/3) = 0
x - 2 = 0  or  x - 7/3 = 0
x = 2
x = 7/3


Input: Find the solution to x^2 + 55/6x - 25/3 = 0

Output:
x^2 + 55/6x - 25/3 = 0
(x - -10)(x - 5/6) = 0
x - -10 = 0  or  x - 5/6 = 0
x = -10
x = 5/6


Input: Find x for x^3 - 32/9x^2 + 61/27x + 8/27 = 0

Output:
x^3 - 32/9x^2 + 61/27x + 8/27 = 0
(x - -1/9)(x - 8/3)(x - 1) = 0
x - -1/9 = 0
x - 8/3 = 0
x - 1 = 0
x = -1/9
x = 8/3
x = 1


Input:
Solve simultaneously:
6x + 7y = 943/14
4x + 2y = 137/7

Output:
6x + 7y = 943/14
4x + 2y = 137/7

Using elimination
4*(6x + 7y = 943/14)
6*(4x + 2y = 137/7)
24x + 28y = 1886/7
24x + 12y = 822/7
Subtract equations
16y = 152
y = 152/16
y = 19/2

Substitute y
6x + 7(19/2) = 943/14
6x = 6/7
x = 6/7/6
x = 1/7


Input: Solve quickly: x^2 - 32/7x + 16/7 = 0

Output:
x^2 - 32/7x + 16/7 = 0
(x - 4)(x - 4/7) = 0
x - 4 = 0  or  x - 4/7 = 0
x = 4
x = 4/7


Input: Compute the solution of x^2 - 19/5x - 6 = 0

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


Input: Determine x in 7x - 91/8 = 0

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


Input: Solve the equation x^3 + 41/24x^2 - 11/4x - 13/3 = 0

Output:
x^3 + 41/24x^2 - 11/4x - 13/3 = 0
(x - -4/3)(x - 13/8)(x - -2) = 0
x - -4/3 = 0
x - 13/8 = 0
x - -2 = 0
x = -4/3
x = 13/8
x = -2


Input: Solve quickly: 10x - 40/3 = 0

Output:
10x - 40/3 = 0
10x = 40/3
x = 40/3 / 10
x = 4/3


Input: Solve 7x + 7/3 = 0

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


Input: Find x for x^2 + 1/3x - 56/9 = 0

Output:
x^2 + 1/3x - 56/9 = 0
(x - 7/3)(x - -8/3) = 0
x - 7/3 = 0  or  x - -8/3 = 0
x = 7/3
x = -8/3


Input: Find x for x^2 + 116/45x + 7/5 = 0

Output:
x^2 + 116/45x + 7/5 = 0
(x - -7/9)(x - -9/5) = 0
x - -7/9 = 0  or  x - -9/5 = 0
x = -7/9
x = -9/5


Input: Find x in x^3 - 25/6x^2 + 1/2x + 2/3 = 0

Output:
x^3 - 25/6x^2 + 1/2x + 2/3 = 0
(x - 1/2)(x - -1/3)(x - 4) = 0
x - 1/2 = 0
x - -1/3 = 0
x - 4 = 0
x = 1/2
x = -1/3
x = 4


Input:
Solve the system:
5x + 9y = -109/4
3x + 9y = -87/4

Output:
5x + 9y = -109/4
3x + 9y = -87/4

Using elimination
3*(5x + 9y = -109/4)
5*(3x + 9y = -87/4)
15x + 27y = -327/4
15x + 45y = -435/4
Subtract equations
-18y = 27
y = 27/-18
y = -3/2

Substitute y
5x + 9(-3/2) = -109/4
5x = -55/4
x = -55/4/5
x = -11/4


Input:
Solve the equations:
6x + 10y = -1
2x + 2y = 1/5

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

Using elimination
2*(6x + 10y = -1)
6*(2x + 2y = 1/5)
12x + 20y = -2
12x + 12y = 6/5
Subtract equations
8y = -16/5
y = -16/5/8
y = -2/5

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


Input: Compute the solution of 3x - 12 = 0

Output:
3x - 12 = 0
3x = 12
x = 12 / 3
x = 4


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

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


Input: Find x in x^2 - 65/18x + 19/6 = 0

Output:
x^2 - 65/18x + 19/6 = 0
(x - 19/9)(x - 3/2) = 0
x - 19/9 = 0  or  x - 3/2 = 0
x = 19/9
x = 3/2


Input: Solve quickly: x^3 - 349/60x^2 + 417/40x - 27/5 = 0

Output:
x^3 - 349/60x^2 + 417/40x - 27/5 = 0
(x - 8/3)(x - 9/10)(x - 9/4) = 0
x - 8/3 = 0
x - 9/10 = 0
x - 9/4 = 0
x = 8/3
x = 9/10
x = 9/4


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

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


Input: Solve x^3 - 61/20x^2 - 249/40x + 513/40 = 0

Output:
x^3 - 61/20x^2 - 249/40x + 513/40 = 0
(x - -9/4)(x - 3/2)(x - 19/5) = 0
x - -9/4 = 0
x - 3/2 = 0
x - 19/5 = 0
x = -9/4
x = 3/2
x = 19/5


Input:
Solve the equations:
3x + 7y = -42
1x + 1y = -114/7

Output:
3x + 7y = -42
1x + 1y = -114/7

Using elimination
1*(3x + 7y = -42)
3*(1x + 1y = -114/7)
3x + 7y = -42
3x + 3y = -342/7
Subtract equations
4y = 48/7
y = 48/7/4
y = 12/7

Substitute y
3x + 7(12/7) = -42
3x = -54
x = -54/3
x = -18


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

Output:
x^2 + 22/3x - 15 = 0
(x - 5/3)(x - -9) = 0
x - 5/3 = 0  or  x - -9 = 0
x = 5/3
x = -9


Input:
Solve the system:
10x + 4y = -4/3
2x + 7y = 55/3

Output:
10x + 4y = -4/3
2x + 7y = 55/3

Using elimination
2*(10x + 4y = -4/3)
10*(2x + 7y = 55/3)
20x + 8y = -8/3
20x + 70y = 550/3
Subtract equations
-62y = -186
y = -186/-62
y = 3

Substitute y
10x + 4(3) = -4/3
10x = -40/3
x = -40/3/10
x = -4/3


Input: Determine x in x^3 - 148/35x^2 - 127/7x - 44/5 = 0

Output:
x^3 - 148/35x^2 - 127/7x - 44/5 = 0
(x - -4/7)(x - 7)(x - -11/5) = 0
x - -4/7 = 0
x - 7 = 0
x - -11/5 = 0
x = -4/7
x = 7
x = -11/5


Input: Find x in x^3 + 27/4x^2 + 59/4x + 21/2 = 0

Output:
x^3 + 27/4x^2 + 59/4x + 21/2 = 0
(x - -2)(x - -3)(x - -7/4) = 0
x - -2 = 0
x - -3 = 0
x - -7/4 = 0
x = -2
x = -3
x = -7/4


Input: Compute the solution of x^3 - 23/20x^2 - 89/40x + 21/8 = 0

Output:
x^3 - 23/20x^2 - 89/40x + 21/8 = 0
(x - 7/5)(x - 5/4)(x - -3/2) = 0
x - 7/5 = 0
x - 5/4 = 0
x - -3/2 = 0
x = 7/5
x = 5/4
x = -3/2


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

Output:
x^2 - 3/2x + 7/18 = 0
(x - 7/6)(x - 1/3) = 0
x - 7/6 = 0  or  x - 1/3 = 0
x = 7/6
x = 1/3


Input: Solve quickly: x^2 - 127/30x + 3 = 0

Output:
x^2 - 127/30x + 3 = 0
(x - 10/3)(x - 9/10) = 0
x - 10/3 = 0  or  x - 9/10 = 0
x = 10/3
x = 9/10


Input: Find the solution to 4x + 32 = 0

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


Input:
Solve simultaneously:
10x + 4y = 118/3
2x + 2y = 29/3

Output:
10x + 4y = 118/3
2x + 2y = 29/3

Using elimination
2*(10x + 4y = 118/3)
10*(2x + 2y = 29/3)
20x + 8y = 236/3
20x + 20y = 290/3
Subtract equations
-12y = -18
y = -18/-12
y = 3/2

Substitute y
10x + 4(3/2) = 118/3
10x = 100/3
x = 100/3/10
x = 10/3


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

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


Input: Find the solution to 3x - 21/10 = 0

Output:
3x - 21/10 = 0
3x = 21/10
x = 21/10 / 3
x = 7/10


Input: Find x in x^2 + 61/6x + 133/6 = 0

Output:
x^2 + 61/6x + 133/6 = 0
(x - -7)(x - -19/6) = 0
x - -7 = 0  or  x - -19/6 = 0
x = -7
x = -19/6


Input: Compute the solution of x^3 - 9/28x^2 - 267/98x + 11/28 = 0

Output:
x^3 - 9/28x^2 - 267/98x + 11/28 = 0
(x - 7/4)(x - 1/7)(x - -11/7) = 0
x - 7/4 = 0
x - 1/7 = 0
x - -11/7 = 0
x = 7/4
x = 1/7
x = -11/7


Input:
Solve the system:
5x + 7y = -59/10
8x + 8y = -28/5

Output:
5x + 7y = -59/10
8x + 8y = -28/5

Using elimination
8*(5x + 7y = -59/10)
5*(8x + 8y = -28/5)
40x + 56y = -236/5
40x + 40y = -28
Subtract equations
16y = -96/5
y = -96/5/16
y = -6/5

Substitute y
5x + 7(-6/5) = -59/10
5x = 5/2
x = 5/2/5
x = 1/2


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

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


Input: Determine x in x^2 + 14/5x - 19/5 = 0

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


Input: Find the solution to x^2 + 37/2x + 143/2 = 0

Output:
x^2 + 37/2x + 143/2 = 0
(x - -11/2)(x - -13) = 0
x - -11/2 = 0  or  x - -13 = 0
x = -11/2
x = -13


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

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


Input: Compute the solution of 4x - 24/7 = 0

Output:
4x - 24/7 = 0
4x = 24/7
x = 24/7 / 4
x = 6/7


Input: Compute the solution of x^2 - 73/14x + 45/14 = 0

Output:
x^2 - 73/14x + 45/14 = 0
(x - 5/7)(x - 9/2) = 0
x - 5/7 = 0  or  x - 9/2 = 0
x = 5/7
x = 9/2


Input: Find the solution to x^2 - 199/56x + 85/28 = 0

Output:
x^2 - 199/56x + 85/28 = 0
(x - 10/7)(x - 17/8) = 0
x - 10/7 = 0  or  x - 17/8 = 0
x = 10/7
x = 17/8


Input: What value of x satisfies 7x + 91 = 0

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


Input: Determine x in 7x + 19 = 0

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


Input: Find x for x^3 - 2/5x^2 - 63/25x  = 0

Output:
x^3 - 2/5x^2 - 63/25x  = 0
(x - -7/5)(x - 9/5)(x - 0) = 0
x - -7/5 = 0
x - 9/5 = 0
x - 0 = 0
x = -7/5
x = 9/5
x = 0


Input: Find the solution to x^3 - 15x^2 - 73x - 57 = 0

Output:
x^3 - 15x^2 - 73x - 57 = 0
(x - 19)(x - -1)(x - -3) = 0
x - 19 = 0
x - -1 = 0
x - -3 = 0
x = 19
x = -1
x = -3


Input:
Find x and y such that
9x + 5y = -136/3
9x + 3y = -38

Output:
9x + 5y = -136/3
9x + 3y = -38

Using elimination
9*(9x + 5y = -136/3)
9*(9x + 3y = -38)
81x + 45y = -408
81x + 27y = -342
Subtract equations
18y = -66
y = -66/18
y = -11/3

Substitute y
9x + 5(-11/3) = -136/3
9x = -27
x = -27/9
x = -3


Input: Find the solution to x^3 + 33/20x^2 - 73/40x - 9/4 = 0

Output:
x^3 + 33/20x^2 - 73/40x - 9/4 = 0
(x - -9/10)(x - 5/4)(x - -2) = 0
x - -9/10 = 0
x - 5/4 = 0
x - -2 = 0
x = -9/10
x = 5/4
x = -2


Input: Solve 10x + 10 = 0

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


Input: What value of x satisfies x^3 + 497/90x^2 + 29/15x - 12 = 0

Output:
x^3 + 497/90x^2 + 29/15x - 12 = 0
(x - -9/2)(x - -20/9)(x - 6/5) = 0
x - -9/2 = 0
x - -20/9 = 0
x - 6/5 = 0
x = -9/2
x = -20/9
x = 6/5


Input: Compute the solution of 1x  = 0

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


Input:
Solve simultaneously:
3x + 9y = -53/2
10x + 6y = -97/3

Output:
3x + 9y = -53/2
10x + 6y = -97/3

Using elimination
10*(3x + 9y = -53/2)
3*(10x + 6y = -97/3)
30x + 90y = -265
30x + 18y = -97
Subtract equations
72y = -168
y = -168/72
y = -7/3

Substitute y
3x + 9(-7/3) = -53/2
3x = -11/2
x = -11/2/3
x = -11/6


Input:
Solve the system:
10x + 8y = -16/3
4x + 10y = 116/3

Output:
10x + 8y = -16/3
4x + 10y = 116/3

Using elimination
4*(10x + 8y = -16/3)
10*(4x + 10y = 116/3)
40x + 32y = -64/3
40x + 100y = 1160/3
Subtract equations
-68y = -408
y = -408/-68
y = 6

Substitute y
10x + 8(6) = -16/3
10x = -160/3
x = -160/3/10
x = -16/3


Input: What value of x satisfies x^3 - 37/8x^2 + 151/32x + 95/64 = 0

Output:
x^3 - 37/8x^2 + 151/32x + 95/64 = 0
(x - -1/4)(x - 5/2)(x - 19/8) = 0
x - -1/4 = 0
x - 5/2 = 0
x - 19/8 = 0
x = -1/4
x = 5/2
x = 19/8


Input: Find x in x^3 - 23/10x^2 - 34/5x  = 0

Output:
x^3 - 23/10x^2 - 34/5x  = 0
(x - -17/10)(x - 0)(x - 4) = 0
x - -17/10 = 0
x - 0 = 0
x - 4 = 0
x = -17/10
x = 0
x = 4


Input: Find x in x^3 - 11/8x^2 - 717/32x - 513/16 = 0

Output:
x^3 - 11/8x^2 - 717/32x - 513/16 = 0
(x - -19/8)(x - -9/4)(x - 6) = 0
x - -19/8 = 0
x - -9/4 = 0
x - 6 = 0
x = -19/8
x = -9/4
x = 6


Input: What value of x satisfies x^3 + 21/4x^2 + 607/72x + 91/24 = 0

Output:
x^3 + 21/4x^2 + 607/72x + 91/24 = 0
(x - -3/4)(x - -13/6)(x - -7/3) = 0
x - -3/4 = 0
x - -13/6 = 0
x - -7/3 = 0
x = -3/4
x = -13/6
x = -7/3


Input:
Solve the system:
2x + 4y = -94/3
1x + 4y = -101/3

Output:
2x + 4y = -94/3
1x + 4y = -101/3

Using elimination
1*(2x + 4y = -94/3)
2*(1x + 4y = -101/3)
2x + 4y = -94/3
2x + 8y = -202/3
Subtract equations
-4y = 36
y = 36/-4
y = -9

Substitute y
2x + 4(-9) = -94/3
2x = 14/3
x = 14/3/2
x = 7/3


Input: Solve x^2 + 53/24x + 55/48 = 0

Output:
x^2 + 53/24x + 55/48 = 0
(x - -5/6)(x - -11/8) = 0
x - -5/6 = 0  or  x - -11/8 = 0
x = -5/6
x = -11/8


Input: Find the solution to x^3 - 185/28x^2 + 53/7x + 65/28 = 0

Output:
x^3 - 185/28x^2 + 53/7x + 65/28 = 0
(x - -1/4)(x - 13/7)(x - 5) = 0
x - -1/4 = 0
x - 13/7 = 0
x - 5 = 0
x = -1/4
x = 13/7
x = 5


Input:
Solve simultaneously:
3x + 3y = -123/7
9x + 2y = 23/7

Output:
3x + 3y = -123/7
9x + 2y = 23/7

Using elimination
9*(3x + 3y = -123/7)
3*(9x + 2y = 23/7)
27x + 27y = -1107/7
27x + 6y = 69/7
Subtract equations
21y = -168
y = -168/21
y = -8

Substitute y
3x + 3(-8) = -123/7
3x = 45/7
x = 45/7/3
x = 15/7


Input: Find x for 7x + 42 = 0

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


Input: Solve quickly: x^2 - 10x - 39 = 0

Output:
x^2 - 10x - 39 = 0
(x - 13)(x - -3) = 0
x - 13 = 0  or  x - -3 = 0
x = 13
x = -3


Input: Find x in 1x + 4/5 = 0

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


Input:
Solve the equations:
5x + 3y = 309/10
9x + 4y = 517/10

Output:
5x + 3y = 309/10
9x + 4y = 517/10

Using elimination
9*(5x + 3y = 309/10)
5*(9x + 4y = 517/10)
45x + 27y = 2781/10
45x + 20y = 517/2
Subtract equations
7y = 98/5
y = 98/5/7
y = 14/5

Substitute y
5x + 3(14/5) = 309/10
5x = 45/2
x = 45/2/5
x = 9/2


Input: Find x in 9x + 117 = 0

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


Input:
Solve simultaneously:
1x + 9y = 49/40
5x + 1y = 421/40

Output:
1x + 9y = 49/40
5x + 1y = 421/40

Using elimination
5*(1x + 9y = 49/40)
1*(5x + 1y = 421/40)
5x + 45y = 49/8
5x + 1y = 421/40
Subtract equations
44y = -22/5
y = -22/5/44
y = -1/10

Substitute y
1x + 9(-1/10) = 49/40
1x = 17/8
x = 17/8/1
x = 17/8


Input: What value of x satisfies x^3 + 5/6x^2 - 299/6x - 95 = 0

Output:
x^3 + 5/6x^2 - 299/6x - 95 = 0
(x - -19/3)(x - -2)(x - 15/2) = 0
x - -19/3 = 0
x - -2 = 0
x - 15/2 = 0
x = -19/3
x = -2
x = 15/2


Input:
Find x and y such that
5x + 4y = -27
9x + 8y = -149/3

Output:
5x + 4y = -27
9x + 8y = -149/3

Using elimination
9*(5x + 4y = -27)
5*(9x + 8y = -149/3)
45x + 36y = -243
45x + 40y = -745/3
Subtract equations
-4y = 16/3
y = 16/3/-4
y = -4/3

Substitute y
5x + 4(-4/3) = -27
5x = -65/3
x = -65/3/5
x = -13/3


Input:
Solve the system:
6x + 6y = -24/7
7x + 8y = -20/7

Output:
6x + 6y = -24/7
7x + 8y = -20/7

Using elimination
7*(6x + 6y = -24/7)
6*(7x + 8y = -20/7)
42x + 42y = -24
42x + 48y = -120/7
Subtract equations
-6y = -48/7
y = -48/7/-6
y = 8/7

Substitute y
6x + 6(8/7) = -24/7
6x = -72/7
x = -72/7/6
x = -12/7


Input: Solve 10x - 70 = 0

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


Input:
Solve the equations:
1x + 3y = 3
4x + 4y = 28

Output:
1x + 3y = 3
4x + 4y = 28

Using elimination
4*(1x + 3y = 3)
1*(4x + 4y = 28)
4x + 12y = 12
4x + 4y = 28
Subtract equations
8y = -16
y = -16/8
y = -2

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


Input: Find the solution to 10x + 160/7 = 0

Output:
10x + 160/7 = 0
10x = -160/7
x = -160/7 / 10
x = -16/7


Input:
Find x and y such that
1x + 8y = 157/3
10x + 3y = 10

Output:
1x + 8y = 157/3
10x + 3y = 10

Using elimination
10*(1x + 8y = 157/3)
1*(10x + 3y = 10)
10x + 80y = 1570/3
10x + 3y = 10
Subtract equations
77y = 1540/3
y = 1540/3/77
y = 20/3

Substitute y
1x + 8(20/3) = 157/3
1x = -1
x = -1/1
x = -1


Input:
Find x and y such that
9x + 1y = 1369/9
6x + 10y = 838/9

Output:
9x + 1y = 1369/9
6x + 10y = 838/9

Using elimination
6*(9x + 1y = 1369/9)
9*(6x + 10y = 838/9)
54x + 6y = 2738/3
54x + 90y = 838
Subtract equations
-84y = 224/3
y = 224/3/-84
y = -8/9

Substitute y
9x + 1(-8/9) = 1369/9
9x = 153
x = 153/9
x = 17


Input: Find x for 9x + 72/5 = 0

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


Input: Find x for x^3 + 146/15x^2 - 136/15x - 64 = 0

Output:
x^3 + 146/15x^2 - 136/15x - 64 = 0
(x - -12/5)(x - -10)(x - 8/3) = 0
x - -12/5 = 0
x - -10 = 0
x - 8/3 = 0
x = -12/5
x = -10
x = 8/3


Input:
Solve the equations:
7x + 7y = 175/6
4x + 3y = 21

Output:
7x + 7y = 175/6
4x + 3y = 21

Using elimination
4*(7x + 7y = 175/6)
7*(4x + 3y = 21)
28x + 28y = 350/3
28x + 21y = 147
Subtract equations
7y = -91/3
y = -91/3/7
y = -13/3

Substitute y
7x + 7(-13/3) = 175/6
7x = 119/2
x = 119/2/7
x = 17/2


Input: Solve quickly: x^2 - 1/20x - 13/8 = 0

Output:
x^2 - 1/20x - 13/8 = 0
(x - 13/10)(x - -5/4) = 0
x - 13/10 = 0  or  x - -5/4 = 0
x = 13/10
x = -5/4


Input:
Find x and y such that
5x + 9y = -17
9x + 1y = 301/15

Output:
5x + 9y = -17
9x + 1y = 301/15

Using elimination
9*(5x + 9y = -17)
5*(9x + 1y = 301/15)
45x + 81y = -153
45x + 5y = 301/3
Subtract equations
76y = -760/3
y = -760/3/76
y = -10/3

Substitute y
5x + 9(-10/3) = -17
5x = 13
x = 13/5
x = 13/5


Input:
Find x and y such that
1x + 10y = 292/21
5x + 8y = 284/21

Output:
1x + 10y = 292/21
5x + 8y = 284/21

Using elimination
5*(1x + 10y = 292/21)
1*(5x + 8y = 284/21)
5x + 50y = 1460/21
5x + 8y = 284/21
Subtract equations
42y = 56
y = 56/42
y = 4/3

Substitute y
1x + 10(4/3) = 292/21
1x = 4/7
x = 4/7/1
x = 4/7


Input: Find x in x^3 + 81/4x^2 + 89/4x - 57/2 = 0

Output:
x^3 + 81/4x^2 + 89/4x - 57/2 = 0
(x - -19)(x - -2)(x - 3/4) = 0
x - -19 = 0
x - -2 = 0
x - 3/4 = 0
x = -19
x = -2
x = 3/4


Input: What value of x satisfies 4x - 6 = 0

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


Input: Determine x in 1x + 17/8 = 0

Output:
1x + 17/8 = 0
1x = -17/8
x = -17/8 / 1
x = -17/8


Input: Find the solution to 7x + 77/5 = 0

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


Input: Find x in x^2 - 104/63x + 20/63 = 0

Output:
x^2 - 104/63x + 20/63 = 0
(x - 2/9)(x - 10/7) = 0
x - 2/9 = 0  or  x - 10/7 = 0
x = 2/9
x = 10/7


Input: Solve quickly: 1x + 2 = 0

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


Input:
Find x and y such that
10x + 3y = 193/8
9x + 8y = 29

Output:
10x + 3y = 193/8
9x + 8y = 29

Using elimination
9*(10x + 3y = 193/8)
10*(9x + 8y = 29)
90x + 27y = 1737/8
90x + 80y = 290
Subtract equations
-53y = -583/8
y = -583/8/-53
y = 11/8

Substitute y
10x + 3(11/8) = 193/8
10x = 20
x = 20/10
x = 2


Input: What value of x satisfies x^3 - 7/6x^2 - 53/3x + 12 = 0

Output:
x^3 - 7/6x^2 - 53/3x + 12 = 0
(x - 9/2)(x - -4)(x - 2/3) = 0
x - 9/2 = 0
x - -4 = 0
x - 2/3 = 0
x = 9/2
x = -4
x = 2/3


Input:
Find x and y such that
5x + 2y = 12
6x + 10y = 148/5

Output:
5x + 2y = 12
6x + 10y = 148/5

Using elimination
6*(5x + 2y = 12)
5*(6x + 10y = 148/5)
30x + 12y = 72
30x + 50y = 148
Subtract equations
-38y = -76
y = -76/-38
y = 2

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


Input:
Solve the system:
10x + 10y = 275/6
8x + 3y = 30

Output:
10x + 10y = 275/6
8x + 3y = 30

Using elimination
8*(10x + 10y = 275/6)
10*(8x + 3y = 30)
80x + 80y = 1100/3
80x + 30y = 300
Subtract equations
50y = 200/3
y = 200/3/50
y = 4/3

Substitute y
10x + 10(4/3) = 275/6
10x = 65/2
x = 65/2/10
x = 13/4


Input: Determine x in x^3 - 13/15x^2 - 706/15x + 56 = 0

Output:
x^3 - 13/15x^2 - 706/15x + 56 = 0
(x - 20/3)(x - 6/5)(x - -7) = 0
x - 20/3 = 0
x - 6/5 = 0
x - -7 = 0
x = 20/3
x = 6/5
x = -7


Input: Find the solution to x^3 - 121/40x^2 + 353/200x + 663/800 = 0

Output:
x^3 - 121/40x^2 + 353/200x + 663/800 = 0
(x - -3/10)(x - 13/8)(x - 17/10) = 0
x - -3/10 = 0
x - 13/8 = 0
x - 17/10 = 0
x = -3/10
x = 13/8
x = 17/10


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

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


Input: Find x in x^2 - 21/5x - 152/5 = 0

Output:
x^2 - 21/5x - 152/5 = 0
(x - -19/5)(x - 8) = 0
x - -19/5 = 0  or  x - 8 = 0
x = -19/5
x = 8


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

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


Input: Find the solution to x^3 + 7/10x^2 - 3/10x  = 0

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


Input: Find the solution to x^3 + 332/63x^2 + 1591/189x + 760/189 = 0

Output:
x^3 + 332/63x^2 + 1591/189x + 760/189 = 0
(x - -8/9)(x - -19/7)(x - -5/3) = 0
x - -8/9 = 0
x - -19/7 = 0
x - -5/3 = 0
x = -8/9
x = -19/7
x = -5/3


Input: Find x for x^3 + 51/4x^2 + 149/4x + 63/2 = 0

Output:
x^3 + 51/4x^2 + 149/4x + 63/2 = 0
(x - -2)(x - -9)(x - -7/4) = 0
x - -2 = 0
x - -9 = 0
x - -7/4 = 0
x = -2
x = -9
x = -7/4


Input: Solve quickly: x^2 - 15/2x - 27/2 = 0

Output:
x^2 - 15/2x - 27/2 = 0
(x - -3/2)(x - 9) = 0
x - -3/2 = 0  or  x - 9 = 0
x = -3/2
x = 9


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

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


Input:
Find x and y such that
10x + 10y = 1
1x + 8y = 39/5

Output:
10x + 10y = 1
1x + 8y = 39/5

Using elimination
1*(10x + 10y = 1)
10*(1x + 8y = 39/5)
10x + 10y = 1
10x + 80y = 78
Subtract equations
-70y = -77
y = -77/-70
y = 11/10

Substitute y
10x + 10(11/10) = 1
10x = -10
x = -10/10
x = -1


Input: Determine x in x^3 + 59/6x^2 + 31/2x - 15 = 0

Output:
x^3 + 59/6x^2 + 31/2x - 15 = 0
(x - -15/2)(x - -3)(x - 2/3) = 0
x - -15/2 = 0
x - -3 = 0
x - 2/3 = 0
x = -15/2
x = -3
x = 2/3


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

Output:
2x - 20/3 = 0
2x = 20/3
x = 20/3 / 2
x = 10/3


Input:
Solve the system:
3x + 10y = 30
1x + 7y = 115/6

Output:
3x + 10y = 30
1x + 7y = 115/6

Using elimination
1*(3x + 10y = 30)
3*(1x + 7y = 115/6)
3x + 10y = 30
3x + 21y = 115/2
Subtract equations
-11y = -55/2
y = -55/2/-11
y = 5/2

Substitute y
3x + 10(5/2) = 30
3x = 5
x = 5/3
x = 5/3


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

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


Input: Find x in x^3 + 17x^2 + 44x + 28 = 0

Output:
x^3 + 17x^2 + 44x + 28 = 0
(x - -2)(x - -14)(x - -1) = 0
x - -2 = 0
x - -14 = 0
x - -1 = 0
x = -2
x = -14
x = -1


Input: Find the solution to x^3 + 37/10x^2 + 8/5x  = 0

Output:
x^3 + 37/10x^2 + 8/5x  = 0
(x - -1/2)(x - -16/5)(x - 0) = 0
x - -1/2 = 0
x - -16/5 = 0
x - 0 = 0
x = -1/2
x = -16/5
x = 0


Input: Solve the equation x^3 - 44/3x^2 + 3539/81x - 2992/81 = 0

Output:
x^3 - 44/3x^2 + 3539/81x - 2992/81 = 0
(x - 17/9)(x - 11)(x - 16/9) = 0
x - 17/9 = 0
x - 11 = 0
x - 16/9 = 0
x = 17/9
x = 11
x = 16/9


Input:
Solve the equations:
10x + 5y = -40
6x + 5y = -44

Output:
10x + 5y = -40
6x + 5y = -44

Using elimination
6*(10x + 5y = -40)
10*(6x + 5y = -44)
60x + 30y = -240
60x + 50y = -440
Subtract equations
-20y = 200
y = 200/-20
y = -10

Substitute y
10x + 5(-10) = -40
10x = 10
x = 10/10
x = 1


Input:
Solve the system:
5x + 1y = 37/2
6x + 5y = 317/10

Output:
5x + 1y = 37/2
6x + 5y = 317/10

Using elimination
6*(5x + 1y = 37/2)
5*(6x + 5y = 317/10)
30x + 6y = 111
30x + 25y = 317/2
Subtract equations
-19y = -95/2
y = -95/2/-19
y = 5/2

Substitute y
5x + 1(5/2) = 37/2
5x = 16
x = 16/5
x = 16/5


Input: Find x in x^3 + 17/3x^2 + 94/9x + 56/9 = 0

Output:
x^3 + 17/3x^2 + 94/9x + 56/9 = 0
(x - -7/3)(x - -4/3)(x - -2) = 0
x - -7/3 = 0
x - -4/3 = 0
x - -2 = 0
x = -7/3
x = -4/3
x = -2


Input:
Solve the equations:
8x + 6y = 77
3x + 4y = 42

Output:
8x + 6y = 77
3x + 4y = 42

Using elimination
3*(8x + 6y = 77)
8*(3x + 4y = 42)
24x + 18y = 231
24x + 32y = 336
Subtract equations
-14y = -105
y = -105/-14
y = 15/2

Substitute y
8x + 6(15/2) = 77
8x = 32
x = 32/8
x = 4


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

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


Input: Solve 10x - 12 = 0

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


Input:
Solve the system:
4x + 10y = -604/5
2x + 6y = -362/5

Output:
4x + 10y = -604/5
2x + 6y = -362/5

Using elimination
2*(4x + 10y = -604/5)
4*(2x + 6y = -362/5)
8x + 20y = -1208/5
8x + 24y = -1448/5
Subtract equations
-4y = 48
y = 48/-4
y = -12

Substitute y
4x + 10(-12) = -604/5
4x = -4/5
x = -4/5/4
x = -1/5


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

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


Input: Determine x in x^2 - 3/2x + 7/18 = 0

Output:
x^2 - 3/2x + 7/18 = 0
(x - 7/6)(x - 1/3) = 0
x - 7/6 = 0  or  x - 1/3 = 0
x = 7/6
x = 1/3


Input: Find x for x^3 + 65/18x^2 + 23/18x - 5/3 = 0

Output:
x^3 + 65/18x^2 + 23/18x - 5/3 = 0
(x - 1/2)(x - -10/9)(x - -3) = 0
x - 1/2 = 0
x - -10/9 = 0
x - -3 = 0
x = 1/2
x = -10/9
x = -3


Input: Solve quickly: x^3 - 77/10x^2 + 73/5x - 11/2 = 0

Output:
x^3 - 77/10x^2 + 73/5x - 11/2 = 0
(x - 5)(x - 1/2)(x - 11/5) = 0
x - 5 = 0
x - 1/2 = 0
x - 11/5 = 0
x = 5
x = 1/2
x = 11/5


Input: Find x for x^2 + 186/35x + 216/35 = 0

Output:
x^2 + 186/35x + 216/35 = 0
(x - -18/5)(x - -12/7) = 0
x - -18/5 = 0  or  x - -12/7 = 0
x = -18/5
x = -12/7


Input: Find x for x^3 - 61/10x^2 + 129/50x + 99/25 = 0

Output:
x^3 - 61/10x^2 + 129/50x + 99/25 = 0
(x - 6/5)(x - -3/5)(x - 11/2) = 0
x - 6/5 = 0
x - -3/5 = 0
x - 11/2 = 0
x = 6/5
x = -3/5
x = 11/2


Input:
Solve the equations:
9x + 2y = -93/2
5x + 6y = -35

Output:
9x + 2y = -93/2
5x + 6y = -35

Using elimination
5*(9x + 2y = -93/2)
9*(5x + 6y = -35)
45x + 10y = -465/2
45x + 54y = -315
Subtract equations
-44y = 165/2
y = 165/2/-44
y = -15/8

Substitute y
9x + 2(-15/8) = -93/2
9x = -171/4
x = -171/4/9
x = -19/4


Input:
Solve simultaneously:
5x + 2y = 23
5x + 4y = 53/3

Output:
5x + 2y = 23
5x + 4y = 53/3

Using elimination
5*(5x + 2y = 23)
5*(5x + 4y = 53/3)
25x + 10y = 115
25x + 20y = 265/3
Subtract equations
-10y = 80/3
y = 80/3/-10
y = -8/3

Substitute y
5x + 2(-8/3) = 23
5x = 85/3
x = 85/3/5
x = 17/3


Input: Determine x in x^2 - 38/21x + 5/21 = 0

Output:
x^2 - 38/21x + 5/21 = 0
(x - 1/7)(x - 5/3) = 0
x - 1/7 = 0  or  x - 5/3 = 0
x = 1/7
x = 5/3


Input: Solve quickly: x^2 - 16/7x - 57/49 = 0

Output:
x^2 - 16/7x - 57/49 = 0
(x - -3/7)(x - 19/7) = 0
x - -3/7 = 0  or  x - 19/7 = 0
x = -3/7
x = 19/7


Input: Determine x in x^3 + 127/56x^2 - 2617/392x - 2907/196 = 0

Output:
x^3 + 127/56x^2 - 2617/392x - 2907/196 = 0
(x - 18/7)(x - -19/7)(x - -17/8) = 0
x - 18/7 = 0
x - -19/7 = 0
x - -17/8 = 0
x = 18/7
x = -19/7
x = -17/8


Input: Solve x^3 - 2/9x^2 - 359/36x + 385/36 = 0

Output:
x^3 - 2/9x^2 - 359/36x + 385/36 = 0
(x - 11/9)(x - -7/2)(x - 5/2) = 0
x - 11/9 = 0
x - -7/2 = 0
x - 5/2 = 0
x = 11/9
x = -7/2
x = 5/2


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

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


Input: Find the solution to 1x  = 0

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


Input: Solve 10x - 70 = 0

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


Input:
Solve the equations:
4x + 7y = -7
1x + 7y = -55/4

Output:
4x + 7y = -7
1x + 7y = -55/4

Using elimination
1*(4x + 7y = -7)
4*(1x + 7y = -55/4)
4x + 7y = -7
4x + 28y = -55
Subtract equations
-21y = 48
y = 48/-21
y = -16/7

Substitute y
4x + 7(-16/7) = -7
4x = 9
x = 9/4
x = 9/4


Input:
Solve simultaneously:
4x + 7y = -2/3
2x + 8y = -10/3

Output:
4x + 7y = -2/3
2x + 8y = -10/3

Using elimination
2*(4x + 7y = -2/3)
4*(2x + 8y = -10/3)
8x + 14y = -4/3
8x + 32y = -40/3
Subtract equations
-18y = 12
y = 12/-18
y = -2/3

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


Input:
Solve the equations:
3x + 10y = -421/21
8x + 2y = 628/63

Output:
3x + 10y = -421/21
8x + 2y = 628/63

Using elimination
8*(3x + 10y = -421/21)
3*(8x + 2y = 628/63)
24x + 80y = -3368/21
24x + 6y = 628/21
Subtract equations
74y = -1332/7
y = -1332/7/74
y = -18/7

Substitute y
3x + 10(-18/7) = -421/21
3x = 17/3
x = 17/3/3
x = 17/9


Input: Find x in x^3 + 5/6x^2 - 26/9x  = 0

Output:
x^3 + 5/6x^2 - 26/9x  = 0
(x - 4/3)(x - 0)(x - -13/6) = 0
x - 4/3 = 0
x - 0 = 0
x - -13/6 = 0
x = 4/3
x = 0
x = -13/6


Input: Compute the solution of x^3 - 25/2x^2 + 2423/64x - 4199/128 = 0

Output:
x^3 - 25/2x^2 + 2423/64x - 4199/128 = 0
(x - 13/8)(x - 17/2)(x - 19/8) = 0
x - 13/8 = 0
x - 17/2 = 0
x - 19/8 = 0
x = 13/8
x = 17/2
x = 19/8


Input: Solve the equation x^3 + 59/4x^2 + 173/8x - 117/8 = 0

Output:
x^3 + 59/4x^2 + 173/8x - 117/8 = 0
(x - 1/2)(x - -9/4)(x - -13) = 0
x - 1/2 = 0
x - -9/4 = 0
x - -13 = 0
x = 1/2
x = -9/4
x = -13


Input: Find x for 5x - 15/8 = 0

Output:
5x - 15/8 = 0
5x = 15/8
x = 15/8 / 5
x = 3/8


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

Output:
6x - 6/5 = 0
6x = 6/5
x = 6/5 / 6
x = 1/5


Input:
Solve simultaneously:
10x + 5y = 125/7
10x + 7y = 17

Output:
10x + 5y = 125/7
10x + 7y = 17

Using elimination
10*(10x + 5y = 125/7)
10*(10x + 7y = 17)
100x + 50y = 1250/7
100x + 70y = 170
Subtract equations
-20y = 60/7
y = 60/7/-20
y = -3/7

Substitute y
10x + 5(-3/7) = 125/7
10x = 20
x = 20/10
x = 2


Input: Solve quickly: x^3 + 59/63x^2 - 1157/189x - 95/27 = 0

Output:
x^3 + 59/63x^2 - 1157/189x - 95/27 = 0
(x - -19/7)(x - 7/3)(x - -5/9) = 0
x - -19/7 = 0
x - 7/3 = 0
x - -5/9 = 0
x = -19/7
x = 7/3
x = -5/9


Input: Find the solution to x^2 + 25/2x - 247/2 = 0

Output:
x^2 + 25/2x - 247/2 = 0
(x - 13/2)(x - -19) = 0
x - 13/2 = 0  or  x - -19 = 0
x = 13/2
x = -19


Input: Solve the equation 8x + 12 = 0

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


Input: Solve quickly: x^3 - 699/56x^2 + 1455/56x - 325/28 = 0

Output:
x^3 - 699/56x^2 + 1455/56x - 325/28 = 0
(x - 5/8)(x - 13/7)(x - 10) = 0
x - 5/8 = 0
x - 13/7 = 0
x - 10 = 0
x = 5/8
x = 13/7
x = 10


Input: Find x for x^2 - 12x + 27 = 0

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


Input: Find x for x^3 + 35/4x^2 + 181/8x + 119/8 = 0

Output:
x^3 + 35/4x^2 + 181/8x + 119/8 = 0
(x - -1)(x - -7/2)(x - -17/4) = 0
x - -1 = 0
x - -7/2 = 0
x - -17/4 = 0
x = -1
x = -7/2
x = -17/4


Input: Determine x in x^3 + 69/7x^2 - 843/7x + 17 = 0

Output:
x^3 + 69/7x^2 - 843/7x + 17 = 0
(x - -17)(x - 7)(x - 1/7) = 0
x - -17 = 0
x - 7 = 0
x - 1/7 = 0
x = -17
x = 7
x = 1/7


Input: Solve quickly: x^3 - 9/2x^2 - 15/2x + 11 = 0

Output:
x^3 - 9/2x^2 - 15/2x + 11 = 0
(x - -2)(x - 1)(x - 11/2) = 0
x - -2 = 0
x - 1 = 0
x - 11/2 = 0
x = -2
x = 1
x = 11/2


Input: Determine x in x^2 + 41/10x - 9/2 = 0

Output:
x^2 + 41/10x - 9/2 = 0
(x - -5)(x - 9/10) = 0
x - -5 = 0  or  x - 9/10 = 0
x = -5
x = 9/10


Input: Find the solution to x^3 - 128/45x^2 + 343/135x - 98/135 = 0

Output:
x^3 - 128/45x^2 + 343/135x - 98/135 = 0
(x - 2/3)(x - 7/9)(x - 7/5) = 0
x - 2/3 = 0
x - 7/9 = 0
x - 7/5 = 0
x = 2/3
x = 7/9
x = 7/5


Input:
Solve simultaneously:
1x + 4y = 65
5x + 3y = 70

Output:
1x + 4y = 65
5x + 3y = 70

Using elimination
5*(1x + 4y = 65)
1*(5x + 3y = 70)
5x + 20y = 325
5x + 3y = 70
Subtract equations
17y = 255
y = 255/17
y = 15

Substitute y
1x + 4(15) = 65
1x = 5
x = 5/1
x = 5


Input: Compute the solution of x^3 + 119/12x^2 + 91/24x - 19/12 = 0

Output:
x^3 + 119/12x^2 + 91/24x - 19/12 = 0
(x - 1/4)(x - -19/2)(x - -2/3) = 0
x - 1/4 = 0
x - -19/2 = 0
x - -2/3 = 0
x = 1/4
x = -19/2
x = -2/3


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

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


Input:
Find x and y such that
6x + 6y = -98/5
3x + 9y = -97/5

Output:
6x + 6y = -98/5
3x + 9y = -97/5

Using elimination
3*(6x + 6y = -98/5)
6*(3x + 9y = -97/5)
18x + 18y = -294/5
18x + 54y = -582/5
Subtract equations
-36y = 288/5
y = 288/5/-36
y = -8/5

Substitute y
6x + 6(-8/5) = -98/5
6x = -10
x = -10/6
x = -5/3


Input: Find the solution to x^3 - 5/9x^2 - 122/9x + 56/3 = 0

Output:
x^3 - 5/9x^2 - 122/9x + 56/3 = 0
(x - 3)(x - -4)(x - 14/9) = 0
x - 3 = 0
x - -4 = 0
x - 14/9 = 0
x = 3
x = -4
x = 14/9


Input: Find x for x^3 + 3x^2 - 70x - 144 = 0

Output:
x^3 + 3x^2 - 70x - 144 = 0
(x - -2)(x - -9)(x - 8) = 0
x - -2 = 0
x - -9 = 0
x - 8 = 0
x = -2
x = -9
x = 8


Input: Solve the equation 6x - 42/5 = 0

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


Input: Solve the equation 4x - 68/9 = 0

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


Input:
Solve the equations:
3x + 9y = 183/10
4x + 4y = 134/5

Output:
3x + 9y = 183/10
4x + 4y = 134/5

Using elimination
4*(3x + 9y = 183/10)
3*(4x + 4y = 134/5)
12x + 36y = 366/5
12x + 12y = 402/5
Subtract equations
24y = -36/5
y = -36/5/24
y = -3/10

Substitute y
3x + 9(-3/10) = 183/10
3x = 21
x = 21/3
x = 7


Input: Find the solution to x^2 + 5/3x - 50/3 = 0

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


Input: What value of x satisfies x^3 + 14/9x^2 - 37/12x - 65/36 = 0

Output:
x^3 + 14/9x^2 - 37/12x - 65/36 = 0
(x - -1/2)(x - 13/9)(x - -5/2) = 0
x - -1/2 = 0
x - 13/9 = 0
x - -5/2 = 0
x = -1/2
x = 13/9
x = -5/2


Input: Find x for x^2 + 10/21x - 200/21 = 0

Output:
x^2 + 10/21x - 200/21 = 0
(x - -10/3)(x - 20/7) = 0
x - -10/3 = 0  or  x - 20/7 = 0
x = -10/3
x = 20/7


Input: Find the solution to x^2 + 4/15x - 7/3 = 0

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


Input: What value of x satisfies x^3 + 9/8x^2 - 21/16x - 13/16 = 0

Output:
x^3 + 9/8x^2 - 21/16x - 13/16 = 0
(x - 1)(x - -1/2)(x - -13/8) = 0
x - 1 = 0
x - -1/2 = 0
x - -13/8 = 0
x = 1
x = -1/2
x = -13/8


Input: Solve the equation x^3 + 141/35x^2 + 29/7x + 39/35 = 0

Output:
x^3 + 141/35x^2 + 29/7x + 39/35 = 0
(x - -13/5)(x - -1)(x - -3/7) = 0
x - -13/5 = 0
x - -1 = 0
x - -3/7 = 0
x = -13/5
x = -1
x = -3/7


Input: Find x in x^3 - 47/6x^2 - 211/18x + 11 = 0

Output:
x^3 - 47/6x^2 - 211/18x + 11 = 0
(x - -11/6)(x - 2/3)(x - 9) = 0
x - -11/6 = 0
x - 2/3 = 0
x - 9 = 0
x = -11/6
x = 2/3
x = 9


Input: Solve 6x - 42 = 0

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


Input: Solve quickly: x^2 - 55/63x - 34/9 = 0

Output:
x^2 - 55/63x - 34/9 = 0
(x - 17/7)(x - -14/9) = 0
x - 17/7 = 0  or  x - -14/9 = 0
x = 17/7
x = -14/9


Input: Solve x^2 + 61/10x + 9 = 0

Output:
x^2 + 61/10x + 9 = 0
(x - -5/2)(x - -18/5) = 0
x - -5/2 = 0  or  x - -18/5 = 0
x = -5/2
x = -18/5


Input: Find x in x^3 - 7/2x^2 - 84x - 216 = 0

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


Input: Compute the solution of x^3 - 23/63x^2 - 164/63x - 4/3 = 0

Output:
x^3 - 23/63x^2 - 164/63x - 4/3 = 0
(x - -7/9)(x - 2)(x - -6/7) = 0
x - -7/9 = 0
x - 2 = 0
x - -6/7 = 0
x = -7/9
x = 2
x = -6/7


Input: What value of x satisfies x^2 - 31/6x + 20/3 = 0

Output:
x^2 - 31/6x + 20/3 = 0
(x - 8/3)(x - 5/2) = 0
x - 8/3 = 0  or  x - 5/2 = 0
x = 8/3
x = 5/2


Input: Determine x in x^3 + 154/45x^2 + 79/75x - 84/25 = 0

Output:
x^3 + 154/45x^2 + 79/75x - 84/25 = 0
(x - -9/5)(x - -12/5)(x - 7/9) = 0
x - -9/5 = 0
x - -12/5 = 0
x - 7/9 = 0
x = -9/5
x = -12/5
x = 7/9


Input:
Solve the equations:
8x + 10y = 163/12
8x + 1y = -25/24

Output:
8x + 10y = 163/12
8x + 1y = -25/24

Using elimination
8*(8x + 10y = 163/12)
8*(8x + 1y = -25/24)
64x + 80y = 326/3
64x + 8y = -25/3
Subtract equations
72y = 117
y = 117/72
y = 13/8

Substitute y
8x + 10(13/8) = 163/12
8x = -8/3
x = -8/3/8
x = -1/3


Input:
Solve the equations:
10x + 5y = 440/21
9x + 3y = 139/7

Output:
10x + 5y = 440/21
9x + 3y = 139/7

Using elimination
9*(10x + 5y = 440/21)
10*(9x + 3y = 139/7)
90x + 45y = 1320/7
90x + 30y = 1390/7
Subtract equations
15y = -10
y = -10/15
y = -2/3

Substitute y
10x + 5(-2/3) = 440/21
10x = 170/7
x = 170/7/10
x = 17/7


Input: What value of x satisfies x^3 + 53/20x^2 + 8/5x - 3/16 = 0

Output:
x^3 + 53/20x^2 + 8/5x - 3/16 = 0
(x - 1/10)(x - -3/2)(x - -5/4) = 0
x - 1/10 = 0
x - -3/2 = 0
x - -5/4 = 0
x = 1/10
x = -3/2
x = -5/4


Input:
Solve the system:
9x + 5y = -53/8
8x + 10y = -9/2

Output:
9x + 5y = -53/8
8x + 10y = -9/2

Using elimination
8*(9x + 5y = -53/8)
9*(8x + 10y = -9/2)
72x + 40y = -53
72x + 90y = -81/2
Subtract equations
-50y = -25/2
y = -25/2/-50
y = 1/4

Substitute y
9x + 5(1/4) = -53/8
9x = -63/8
x = -63/8/9
x = -7/8


Input: Solve x^3 + 109/60x^2 - 1109/120x + 187/40 = 0

Output:
x^3 + 109/60x^2 - 1109/120x + 187/40 = 0
(x - 11/6)(x - -17/4)(x - 3/5) = 0
x - 11/6 = 0
x - -17/4 = 0
x - 3/5 = 0
x = 11/6
x = -17/4
x = 3/5


Input:
Solve the system:
4x + 2y = 172/9
9x + 7y = 422/9

Output:
4x + 2y = 172/9
9x + 7y = 422/9

Using elimination
9*(4x + 2y = 172/9)
4*(9x + 7y = 422/9)
36x + 18y = 172
36x + 28y = 1688/9
Subtract equations
-10y = -140/9
y = -140/9/-10
y = 14/9

Substitute y
4x + 2(14/9) = 172/9
4x = 16
x = 16/4
x = 4


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

Output:
6x + 6/5 = 0
6x = -6/5
x = -6/5 / 6
x = -1/5


Input: Solve quickly: x^3 - 1x^2 - 71/4x + 9 = 0

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


Input:
Solve the system:
2x + 8y = 8/3
3x + 1y = -7

Output:
2x + 8y = 8/3
3x + 1y = -7

Using elimination
3*(2x + 8y = 8/3)
2*(3x + 1y = -7)
6x + 24y = 8
6x + 2y = -14
Subtract equations
22y = 22
y = 22/22
y = 1

Substitute y
2x + 8(1) = 8/3
2x = -16/3
x = -16/3/2
x = -8/3


Input: Find x in x^3 + 581/90x^2 + 1127/90x + 343/45 = 0

Output:
x^3 + 581/90x^2 + 1127/90x + 343/45 = 0
(x - -7/2)(x - -7/5)(x - -14/9) = 0
x - -7/2 = 0
x - -7/5 = 0
x - -14/9 = 0
x = -7/2
x = -7/5
x = -14/9


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

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


Input: What value of x satisfies x^2 + 37/7x + 36/7 = 0

Output:
x^2 + 37/7x + 36/7 = 0
(x - -4)(x - -9/7) = 0
x - -4 = 0  or  x - -9/7 = 0
x = -4
x = -9/7


Input: Compute the solution of x^3 - 163/35x^2 - 559/35x - 3 = 0

Output:
x^3 - 163/35x^2 - 559/35x - 3 = 0
(x - 7)(x - -15/7)(x - -1/5) = 0
x - 7 = 0
x - -15/7 = 0
x - -1/5 = 0
x = 7
x = -15/7
x = -1/5


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

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


Input: What value of x satisfies x^2 - 77/15x + 76/15 = 0

Output:
x^2 - 77/15x + 76/15 = 0
(x - 19/5)(x - 4/3) = 0
x - 19/5 = 0  or  x - 4/3 = 0
x = 19/5
x = 4/3


Input: Compute the solution of 6x + 78 = 0

Output:
6x + 78 = 0
6x = -78
x = -78 / 6
x = -13


Input: Find the solution to x^2 + 173/72x + 91/72 = 0

Output:
x^2 + 173/72x + 91/72 = 0
(x - -7/9)(x - -13/8) = 0
x - -7/9 = 0  or  x - -13/8 = 0
x = -7/9
x = -13/8


Input: Find x in x^2 - 17/5x - 38/25 = 0

Output:
x^2 - 17/5x - 38/25 = 0
(x - 19/5)(x - -2/5) = 0
x - 19/5 = 0  or  x - -2/5 = 0
x = 19/5
x = -2/5


Input: Find the solution to x^3 + 53/8x^2 + 327/32x + 189/64 = 0

Output:
x^3 + 53/8x^2 + 327/32x + 189/64 = 0
(x - -9/2)(x - -7/4)(x - -3/8) = 0
x - -9/2 = 0
x - -7/4 = 0
x - -3/8 = 0
x = -9/2
x = -7/4
x = -3/8


Input: Find x in 3x + 9/2 = 0

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


Input: Determine x in x^2 + 4/7x - 11/7 = 0

Output:
x^2 + 4/7x - 11/7 = 0
(x - -11/7)(x - 1) = 0
x - -11/7 = 0  or  x - 1 = 0
x = -11/7
x = 1


Input: Solve quickly: x^2 - 11/56x - 3/14 = 0

Output:
x^2 - 11/56x - 3/14 = 0
(x - 4/7)(x - -3/8) = 0
x - 4/7 = 0  or  x - -3/8 = 0
x = 4/7
x = -3/8


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

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


Input: Find x for x^3 - 629/252x^2 + 305/252x + 1/6 = 0

Output:
x^3 - 629/252x^2 + 305/252x + 1/6 = 0
(x - 6/7)(x - 7/4)(x - -1/9) = 0
x - 6/7 = 0
x - 7/4 = 0
x - -1/9 = 0
x = 6/7
x = 7/4
x = -1/9


Input: Find x for x^2 + 12x - 64 = 0

Output:
x^2 + 12x - 64 = 0
(x - -16)(x - 4) = 0
x - -16 = 0  or  x - 4 = 0
x = -16
x = 4


Input: Solve the equation x^3 - 15x^2 - 54x  = 0

Output:
x^3 - 15x^2 - 54x  = 0
(x - 18)(x - -3)(x - 0) = 0
x - 18 = 0
x - -3 = 0
x - 0 = 0
x = 18
x = -3
x = 0


Input: Solve quickly: 4x - 76/9 = 0

Output:
4x - 76/9 = 0
4x = 76/9
x = 76/9 / 4
x = 19/9


Input: Solve the equation x^3 + 5/6x^2 - 68/9x + 56/9 = 0

Output:
x^3 + 5/6x^2 - 68/9x + 56/9 = 0
(x - 4/3)(x - 4/3)(x - -7/2) = 0
x - 4/3 = 0
x - 4/3 = 0
x - -7/2 = 0
x = 4/3
x = 4/3
x = -7/2


Input: Solve the equation 2x + 3 = 0

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


Input: Determine x in x^3 - 61/10x^2 - 443/25x + 504/25 = 0

Output:
x^3 - 61/10x^2 - 443/25x + 504/25 = 0
(x - 9/10)(x - -14/5)(x - 8) = 0
x - 9/10 = 0
x - -14/5 = 0
x - 8 = 0
x = 9/10
x = -14/5
x = 8


Input: What value of x satisfies 3x + 36 = 0

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


Input: Find x in x^2 - 6/7x - 1/7 = 0

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


Input: Find x for x^3 - 14x^2 - 95x + 1008 = 0

Output:
x^3 - 14x^2 - 95x + 1008 = 0
(x - 16)(x - -9)(x - 7) = 0
x - 16 = 0
x - -9 = 0
x - 7 = 0
x = 16
x = -9
x = 7


Input: Find x for x^3 + 64/9x^2 + 131/9x + 76/9 = 0

Output:
x^3 + 64/9x^2 + 131/9x + 76/9 = 0
(x - -1)(x - -19/9)(x - -4) = 0
x - -1 = 0
x - -19/9 = 0
x - -4 = 0
x = -1
x = -19/9
x = -4


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

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


Input: Find the solution to x^3 - 47/40x^2 - 2677/400x + 17/25 = 0

Output:
x^3 - 47/40x^2 - 2677/400x + 17/25 = 0
(x - 1/10)(x - 16/5)(x - -17/8) = 0
x - 1/10 = 0
x - 16/5 = 0
x - -17/8 = 0
x = 1/10
x = 16/5
x = -17/8


Input: Find x in x^3 - 37/3x^2 + 467/12x - 34 = 0

Output:
x^3 - 37/3x^2 + 467/12x - 34 = 0
(x - 17/6)(x - 3/2)(x - 8) = 0
x - 17/6 = 0
x - 3/2 = 0
x - 8 = 0
x = 17/6
x = 3/2
x = 8


Input:
Find x and y such that
3x + 4y = -8
8x + 6y = -43/3

Output:
3x + 4y = -8
8x + 6y = -43/3

Using elimination
8*(3x + 4y = -8)
3*(8x + 6y = -43/3)
24x + 32y = -64
24x + 18y = -43
Subtract equations
14y = -21
y = -21/14
y = -3/2

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


Input: Determine x in x^2 - 25/3x + 14 = 0

Output:
x^2 - 25/3x + 14 = 0
(x - 6)(x - 7/3) = 0
x - 6 = 0  or  x - 7/3 = 0
x = 6
x = 7/3


Input:
Solve the system:
5x + 2y = 729/56
9x + 4y = 1325/56

Output:
5x + 2y = 729/56
9x + 4y = 1325/56

Using elimination
9*(5x + 2y = 729/56)
5*(9x + 4y = 1325/56)
45x + 18y = 6561/56
45x + 20y = 6625/56
Subtract equations
-2y = -8/7
y = -8/7/-2
y = 4/7

Substitute y
5x + 2(4/7) = 729/56
5x = 95/8
x = 95/8/5
x = 19/8


Input: Find the solution to x^3 + 63/4x^2 - 15/2x - 56 = 0

Output:
x^3 + 63/4x^2 - 15/2x - 56 = 0
(x - -7/4)(x - 2)(x - -16) = 0
x - -7/4 = 0
x - 2 = 0
x - -16 = 0
x = -7/4
x = 2
x = -16


Input: Solve x^3 + 45/8x^2 + 139/18x + 143/72 = 0

Output:
x^3 + 45/8x^2 + 139/18x + 143/72 = 0
(x - -1/3)(x - -13/8)(x - -11/3) = 0
x - -1/3 = 0
x - -13/8 = 0
x - -11/3 = 0
x = -1/3
x = -13/8
x = -11/3


Input: Solve the equation 10x - 50 = 0

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


Input: Solve x^2 - 160/21x + 256/21 = 0

Output:
x^2 - 160/21x + 256/21 = 0
(x - 16/7)(x - 16/3) = 0
x - 16/7 = 0  or  x - 16/3 = 0
x = 16/7
x = 16/3


Input: What value of x satisfies 6x + 7 = 0

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


Input: Determine x in 2x + 36 = 0

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


Input: Find x in x^2 - 19/2x  = 0

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


Input: Solve x^3 + 13/6x^2 - 151/6x - 13 = 0

Output:
x^3 + 13/6x^2 - 151/6x - 13 = 0
(x - -1/2)(x - -6)(x - 13/3) = 0
x - -1/2 = 0
x - -6 = 0
x - 13/3 = 0
x = -1/2
x = -6
x = 13/3


Input: Solve 10x + 50 = 0

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


Input:
Solve simultaneously:
4x + 1y = 1/6
2x + 3y = 53/6

Output:
4x + 1y = 1/6
2x + 3y = 53/6

Using elimination
2*(4x + 1y = 1/6)
4*(2x + 3y = 53/6)
8x + 2y = 1/3
8x + 12y = 106/3
Subtract equations
-10y = -35
y = -35/-10
y = 7/2

Substitute y
4x + 1(7/2) = 1/6
4x = -10/3
x = -10/3/4
x = -5/6


Input:
Solve the equations:
1x + 2y = 79/5
7x + 3y = 391/10

Output:
1x + 2y = 79/5
7x + 3y = 391/10

Using elimination
7*(1x + 2y = 79/5)
1*(7x + 3y = 391/10)
7x + 14y = 553/5
7x + 3y = 391/10
Subtract equations
11y = 143/2
y = 143/2/11
y = 13/2

Substitute y
1x + 2(13/2) = 79/5
1x = 14/5
x = 14/5/1
x = 14/5


Input: Solve x^2 - 49/20x - 153/20 = 0

Output:
x^2 - 49/20x - 153/20 = 0
(x - 17/4)(x - -9/5) = 0
x - 17/4 = 0  or  x - -9/5 = 0
x = 17/4
x = -9/5


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

Output:
x^2 - 29/9x + 2/3 = 0
(x - 3)(x - 2/9) = 0
x - 3 = 0  or  x - 2/9 = 0
x = 3
x = 2/9


Input: Find x in x^2 - 44/5x - 9/5 = 0

Output:
x^2 - 44/5x - 9/5 = 0
(x - 9)(x - -1/5) = 0
x - 9 = 0  or  x - -1/5 = 0
x = 9
x = -1/5


Input: Solve quickly: x^2 - 111/40x + 19/20 = 0

Output:
x^2 - 111/40x + 19/20 = 0
(x - 19/8)(x - 2/5) = 0
x - 19/8 = 0  or  x - 2/5 = 0
x = 19/8
x = 2/5


Input: Compute the solution of x^3 + 46/15x^2 - 53/15x + 4/5 = 0

Output:
x^3 + 46/15x^2 - 53/15x + 4/5 = 0
(x - -4)(x - 1/3)(x - 3/5) = 0
x - -4 = 0
x - 1/3 = 0
x - 3/5 = 0
x = -4
x = 1/3
x = 3/5


Input: Determine x in x^2 + 135/7x + 38/7 = 0

Output:
x^2 + 135/7x + 38/7 = 0
(x - -2/7)(x - -19) = 0
x - -2/7 = 0  or  x - -19 = 0
x = -2/7
x = -19


Input:
Find x and y such that
10x + 2y = -98
9x + 6y = -84

Output:
10x + 2y = -98
9x + 6y = -84

Using elimination
9*(10x + 2y = -98)
10*(9x + 6y = -84)
90x + 18y = -882
90x + 60y = -840
Subtract equations
-42y = -42
y = -42/-42
y = 1

Substitute y
10x + 2(1) = -98
10x = -100
x = -100/10
x = -10


Input: Find the solution to x^2 - 113/7x - 234/7 = 0

Output:
x^2 - 113/7x - 234/7 = 0
(x - 18)(x - -13/7) = 0
x - 18 = 0  or  x - -13/7 = 0
x = 18
x = -13/7


Input: Compute the solution of x^3 + 3/2x^2 - 135/16x  = 0

Output:
x^3 + 3/2x^2 - 135/16x  = 0
(x - 9/4)(x - 0)(x - -15/4) = 0
x - 9/4 = 0
x - 0 = 0
x - -15/4 = 0
x = 9/4
x = 0
x = -15/4


Input:
Solve the system:
8x + 10y = 84
1x + 7y = 156/5

Output:
8x + 10y = 84
1x + 7y = 156/5

Using elimination
1*(8x + 10y = 84)
8*(1x + 7y = 156/5)
8x + 10y = 84
8x + 56y = 1248/5
Subtract equations
-46y = -828/5
y = -828/5/-46
y = 18/5

Substitute y
8x + 10(18/5) = 84
8x = 48
x = 48/8
x = 6


Input: Find x in 6x + 30 = 0

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


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

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


Input: Compute the solution of 1x + 1/3 = 0

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


Input: Find x for x^2 - 92/9x + 160/9 = 0

Output:
x^2 - 92/9x + 160/9 = 0
(x - 8)(x - 20/9) = 0
x - 8 = 0  or  x - 20/9 = 0
x = 8
x = 20/9


Input: Determine x in 5x + 20/3 = 0

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


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

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


Input: Find x in x^3 - 221/24x^2 + 107/6x + 19/8 = 0

Output:
x^3 - 221/24x^2 + 107/6x + 19/8 = 0
(x - 3)(x - -1/8)(x - 19/3) = 0
x - 3 = 0
x - -1/8 = 0
x - 19/3 = 0
x = 3
x = -1/8
x = 19/3


Input: What value of x satisfies x^3 + 111/10x^2 + 467/25x - 99/50 = 0

Output:
x^3 + 111/10x^2 + 467/25x - 99/50 = 0
(x - -11/5)(x - 1/10)(x - -9) = 0
x - -11/5 = 0
x - 1/10 = 0
x - -9 = 0
x = -11/5
x = 1/10
x = -9


Input: Find x for 7x + 16 = 0

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


Input: What value of x satisfies 10x - 10/9 = 0

Output:
10x - 10/9 = 0
10x = 10/9
x = 10/9 / 10
x = 1/9


Input: Find x for x^3 + 367/168x^2 - 55/21x - 325/56 = 0

Output:
x^3 + 367/168x^2 - 55/21x - 325/56 = 0
(x - -15/7)(x - -5/3)(x - 13/8) = 0
x - -15/7 = 0
x - -5/3 = 0
x - 13/8 = 0
x = -15/7
x = -5/3
x = 13/8


Input: Find x in x^3 + 33/4x^2 + 25/2x - 231/16 = 0

Output:
x^3 + 33/4x^2 + 25/2x - 231/16 = 0
(x - -11/2)(x - -7/2)(x - 3/4) = 0
x - -11/2 = 0
x - -7/2 = 0
x - 3/4 = 0
x = -11/2
x = -7/2
x = 3/4


Input: Find x in x^2 + 2x + 21/25 = 0

Output:
x^2 + 2x + 21/25 = 0
(x - -7/5)(x - -3/5) = 0
x - -7/5 = 0  or  x - -3/5 = 0
x = -7/5
x = -3/5


Input:
Find x and y such that
1x + 10y = 670/21
10x + 7y = 190/21

Output:
1x + 10y = 670/21
10x + 7y = 190/21

Using elimination
10*(1x + 10y = 670/21)
1*(10x + 7y = 190/21)
10x + 100y = 6700/21
10x + 7y = 190/21
Subtract equations
93y = 310
y = 310/93
y = 10/3

Substitute y
1x + 10(10/3) = 670/21
1x = -10/7
x = -10/7/1
x = -10/7


Input: Solve the equation 6x - 16 = 0

Output:
6x - 16 = 0
6x = 16
x = 16 / 6
x = 8/3


Input: Compute the solution of x^2 - 149/21x + 20/7 = 0

Output:
x^2 - 149/21x + 20/7 = 0
(x - 3/7)(x - 20/3) = 0
x - 3/7 = 0  or  x - 20/3 = 0
x = 3/7
x = 20/3


Input: Compute the solution of 5x + 50 = 0

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


Input:
Solve simultaneously:
8x + 4y = -424/5
7x + 8y = -1597/10

Output:
8x + 4y = -424/5
7x + 8y = -1597/10

Using elimination
7*(8x + 4y = -424/5)
8*(7x + 8y = -1597/10)
56x + 28y = -2968/5
56x + 64y = -6388/5
Subtract equations
-36y = 684
y = 684/-36
y = -19

Substitute y
8x + 4(-19) = -424/5
8x = -44/5
x = -44/5/8
x = -11/10


Input: Determine x in 9x - 7 = 0

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


Input: Solve 2x - 14 = 0

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


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

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


Input: Find the solution to 3x + 51/7 = 0

Output:
3x + 51/7 = 0
3x = -51/7
x = -51/7 / 3
x = -17/7


Input:
Find x and y such that
5x + 2y = -81/4
7x + 1y = -99/4

Output:
5x + 2y = -81/4
7x + 1y = -99/4

Using elimination
7*(5x + 2y = -81/4)
5*(7x + 1y = -99/4)
35x + 14y = -567/4
35x + 5y = -495/4
Subtract equations
9y = -18
y = -18/9
y = -2

Substitute y
5x + 2(-2) = -81/4
5x = -65/4
x = -65/4/5
x = -13/4


Input: Find x in x^3 + 9/2x^2 - 35/2x  = 0

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


Input: Solve quickly: 4x - 4 = 0

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


Input:
Solve the system:
5x + 9y = -47/2
6x + 5y = -335/9

Output:
5x + 9y = -47/2
6x + 5y = -335/9

Using elimination
6*(5x + 9y = -47/2)
5*(6x + 5y = -335/9)
30x + 54y = -141
30x + 25y = -1675/9
Subtract equations
29y = 406/9
y = 406/9/29
y = 14/9

Substitute y
5x + 9(14/9) = -47/2
5x = -75/2
x = -75/2/5
x = -15/2


Input:
Find x and y such that
3x + 5y = 103/2
8x + 10y = 317/3

Output:
3x + 5y = 103/2
8x + 10y = 317/3

Using elimination
8*(3x + 5y = 103/2)
3*(8x + 10y = 317/3)
24x + 40y = 412
24x + 30y = 317
Subtract equations
10y = 95
y = 95/10
y = 19/2

Substitute y
3x + 5(19/2) = 103/2
3x = 4
x = 4/3
x = 4/3


Input: Find x in x^3 - 258/35x^2 + 473/28x - 117/10 = 0

Output:
x^3 - 258/35x^2 + 473/28x - 117/10 = 0
(x - 7/2)(x - 18/7)(x - 13/10) = 0
x - 7/2 = 0
x - 18/7 = 0
x - 13/10 = 0
x = 7/2
x = 18/7
x = 13/10


Input: Solve 10x + 14 = 0

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


Input: Find x in x^3 + 69/4x^2 + 757/8x + 165 = 0

Output:
x^3 + 69/4x^2 + 757/8x + 165 = 0
(x - -11/2)(x - -15/4)(x - -8) = 0
x - -11/2 = 0
x - -15/4 = 0
x - -8 = 0
x = -11/2
x = -15/4
x = -8


Input: Find x in x^3 - 452/63x^2 + 223/21x + 80/63 = 0

Output:
x^3 - 452/63x^2 + 223/21x + 80/63 = 0
(x - 5)(x - 16/7)(x - -1/9) = 0
x - 5 = 0
x - 16/7 = 0
x - -1/9 = 0
x = 5
x = 16/7
x = -1/9


Input: Solve the equation x^3 + 52/21x^2 + 32/21x  = 0

Output:
x^3 + 52/21x^2 + 32/21x  = 0
(x - -8/7)(x - -4/3)(x - 0) = 0
x - -8/7 = 0
x - -4/3 = 0
x - 0 = 0
x = -8/7
x = -4/3
x = 0


Input: Solve x^3 + 203/90x^2 + 31/50x - 182/225 = 0

Output:
x^3 + 203/90x^2 + 31/50x - 182/225 = 0
(x - -7/5)(x - 4/9)(x - -13/10) = 0
x - -7/5 = 0
x - 4/9 = 0
x - -13/10 = 0
x = -7/5
x = 4/9
x = -13/10


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

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


Input: Determine x in x^3 + 37/4x^2 + 43/4x - 105/2 = 0

Output:
x^3 + 37/4x^2 + 43/4x - 105/2 = 0
(x - -5)(x - -6)(x - 7/4) = 0
x - -5 = 0
x - -6 = 0
x - 7/4 = 0
x = -5
x = -6
x = 7/4


Input:
Find x and y such that
4x + 5y = -142/21
1x + 1y = -32/21

Output:
4x + 5y = -142/21
1x + 1y = -32/21

Using elimination
1*(4x + 5y = -142/21)
4*(1x + 1y = -32/21)
4x + 5y = -142/21
4x + 4y = -128/21
Subtract equations
1y = -2/3
y = -2/3/1
y = -2/3

Substitute y
4x + 5(-2/3) = -142/21
4x = -24/7
x = -24/7/4
x = -6/7


Input:
Find x and y such that
6x + 5y = 50
10x + 6y = 60

Output:
6x + 5y = 50
10x + 6y = 60

Using elimination
10*(6x + 5y = 50)
6*(10x + 6y = 60)
60x + 50y = 500
60x + 36y = 360
Subtract equations
14y = 140
y = 140/14
y = 10

Substitute y
6x + 5(10) = 50
6x = 0
x = 0/6
x = 0


Input: Determine x in x^3 + 38/21x^2 - 131/21x - 8 = 0

Output:
x^3 + 38/21x^2 - 131/21x - 8 = 0
(x - 7/3)(x - -8/7)(x - -3) = 0
x - 7/3 = 0
x - -8/7 = 0
x - -3 = 0
x = 7/3
x = -8/7
x = -3


Input: What value of x satisfies x^3 - 59/6x^2 + 565/18x - 884/27 = 0

Output:
x^3 - 59/6x^2 + 565/18x - 884/27 = 0
(x - 13/3)(x - 8/3)(x - 17/6) = 0
x - 13/3 = 0
x - 8/3 = 0
x - 17/6 = 0
x = 13/3
x = 8/3
x = 17/6


Input: Find the solution to x^2 + 4x + 15/16 = 0

Output:
x^2 + 4x + 15/16 = 0
(x - -15/4)(x - -1/4) = 0
x - -15/4 = 0  or  x - -1/4 = 0
x = -15/4
x = -1/4


Input: Compute the solution of 4x - 18/5 = 0

Output:
4x - 18/5 = 0
4x = 18/5
x = 18/5 / 4
x = 9/10


Input: Solve x^3 + 51/8x^2 + 45/8x - 25/4 = 0

Output:
x^3 + 51/8x^2 + 45/8x - 25/4 = 0
(x - -2)(x - -5)(x - 5/8) = 0
x - -2 = 0
x - -5 = 0
x - 5/8 = 0
x = -2
x = -5
x = 5/8


Input: Determine x in x^3 - 48/35x^2 - 87/25x + 26/35 = 0

Output:
x^3 - 48/35x^2 - 87/25x + 26/35 = 0
(x - 1/5)(x - 13/5)(x - -10/7) = 0
x - 1/5 = 0
x - 13/5 = 0
x - -10/7 = 0
x = 1/5
x = 13/5
x = -10/7


Input: Compute the solution of 2x + 19/4 = 0

Output:
2x + 19/4 = 0
2x = -19/4
x = -19/4 / 2
x = -19/8


Input: Find x for x^2 + 5/2x - 17/18 = 0

Output:
x^2 + 5/2x - 17/18 = 0
(x - 1/3)(x - -17/6) = 0
x - 1/3 = 0  or  x - -17/6 = 0
x = 1/3
x = -17/6


Input:
Solve the equations:
8x + 3y = -47/10
7x + 7y = -539/30

Output:
8x + 3y = -47/10
7x + 7y = -539/30

Using elimination
7*(8x + 3y = -47/10)
8*(7x + 7y = -539/30)
56x + 21y = -329/10
56x + 56y = -2156/15
Subtract equations
-35y = 665/6
y = 665/6/-35
y = -19/6

Substitute y
8x + 3(-19/6) = -47/10
8x = 24/5
x = 24/5/8
x = 3/5


Input: Determine x in x^2 + 14/5x + 33/25 = 0

Output:
x^2 + 14/5x + 33/25 = 0
(x - -11/5)(x - -3/5) = 0
x - -11/5 = 0  or  x - -3/5 = 0
x = -11/5
x = -3/5


Input: Compute the solution of x^3 - 9/7x^2 - 76/49x + 12/49 = 0

Output:
x^3 - 9/7x^2 - 76/49x + 12/49 = 0
(x - -6/7)(x - 1/7)(x - 2) = 0
x - -6/7 = 0
x - 1/7 = 0
x - 2 = 0
x = -6/7
x = 1/7
x = 2


Input:
Find x and y such that
4x + 3y = -6/5
2x + 2y = 2/5

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

Using elimination
2*(4x + 3y = -6/5)
4*(2x + 2y = 2/5)
8x + 6y = -12/5
8x + 8y = 8/5
Subtract equations
-2y = -4
y = -4/-2
y = 2

Substitute y
4x + 3(2) = -6/5
4x = -36/5
x = -36/5/4
x = -9/5


Input:
Solve the system:
4x + 2y = 14/3
5x + 2y = 17/3

Output:
4x + 2y = 14/3
5x + 2y = 17/3

Using elimination
5*(4x + 2y = 14/3)
4*(5x + 2y = 17/3)
20x + 10y = 70/3
20x + 8y = 68/3
Subtract equations
2y = 2/3
y = 2/3/2
y = 1/3

Substitute y
4x + 2(1/3) = 14/3
4x = 4
x = 4/4
x = 1


Input: Compute the solution of 1x - 17/6 = 0

Output:
1x - 17/6 = 0
1x = 17/6
x = 17/6 / 1
x = 17/6


Input: Determine x in 9x - 20 = 0

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


Input: Compute the solution of x^3 - 106/5x^2 + 2213/25x - 2128/25 = 0

Output:
x^3 - 106/5x^2 + 2213/25x - 2128/25 = 0
(x - 16)(x - 19/5)(x - 7/5) = 0
x - 16 = 0
x - 19/5 = 0
x - 7/5 = 0
x = 16
x = 19/5
x = 7/5


Input: Solve the equation x^3 + 82/3x^2 + 201x + 1292/3 = 0

Output:
x^3 + 82/3x^2 + 201x + 1292/3 = 0
(x - -4)(x - -19/3)(x - -17) = 0
x - -4 = 0
x - -19/3 = 0
x - -17 = 0
x = -4
x = -19/3
x = -17


Input: Determine x in 8x + 4 = 0

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


Input: Compute the solution of x^2 + 11/10x - 57/10 = 0

Output:
x^2 + 11/10x - 57/10 = 0
(x - 19/10)(x - -3) = 0
x - 19/10 = 0  or  x - -3 = 0
x = 19/10
x = -3


Input: Solve x^3 - 259/40x^2 + 759/80x - 27/10 = 0

Output:
x^3 - 259/40x^2 + 759/80x - 27/10 = 0
(x - 8/5)(x - 9/2)(x - 3/8) = 0
x - 8/5 = 0
x - 9/2 = 0
x - 3/8 = 0
x = 8/5
x = 9/2
x = 3/8


Input: Find x in x^3 + 7/5x^2 - 14/5x - 16/5 = 0

Output:
x^3 + 7/5x^2 - 14/5x - 16/5 = 0
(x - -1)(x - -2)(x - 8/5) = 0
x - -1 = 0
x - -2 = 0
x - 8/5 = 0
x = -1
x = -2
x = 8/5


Input: Solve x^3 - 49/36x^2 - 3/4x + 10/9 = 0

Output:
x^3 - 49/36x^2 - 3/4x + 10/9 = 0
(x - 5/4)(x - -8/9)(x - 1) = 0
x - 5/4 = 0
x - -8/9 = 0
x - 1 = 0
x = 5/4
x = -8/9
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 quickly: 5x + 95/4 = 0

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


Input: Find x for x^3 + 24/5x^2 + 37/5x + 18/5 = 0

Output:
x^3 + 24/5x^2 + 37/5x + 18/5 = 0
(x - -9/5)(x - -1)(x - -2) = 0
x - -9/5 = 0
x - -1 = 0
x - -2 = 0
x = -9/5
x = -1
x = -2


Input: Solve quickly: 2x - 32 = 0

Output:
2x - 32 = 0
2x = 32
x = 32 / 2
x = 16


Input: Find the solution to x^2 + 29/10x + 21/10 = 0

Output:
x^2 + 29/10x + 21/10 = 0
(x - -7/5)(x - -3/2) = 0
x - -7/5 = 0  or  x - -3/2 = 0
x = -7/5
x = -3/2


Input:
Solve the equations:
7x + 3y = 63
5x + 1y = 143/3

Output:
7x + 3y = 63
5x + 1y = 143/3

Using elimination
5*(7x + 3y = 63)
7*(5x + 1y = 143/3)
35x + 15y = 315
35x + 7y = 1001/3
Subtract equations
8y = -56/3
y = -56/3/8
y = -7/3

Substitute y
7x + 3(-7/3) = 63
7x = 70
x = 70/7
x = 10


Input: Find x in x^3 + 99/56x^2 - 45/56x  = 0

Output:
x^3 + 99/56x^2 - 45/56x  = 0
(x - 0)(x - 3/8)(x - -15/7) = 0
x - 0 = 0
x - 3/8 = 0
x - -15/7 = 0
x = 0
x = 3/8
x = -15/7


Input:
Solve simultaneously:
5x + 8y = 31/6
7x + 2y = 25/6

Output:
5x + 8y = 31/6
7x + 2y = 25/6

Using elimination
7*(5x + 8y = 31/6)
5*(7x + 2y = 25/6)
35x + 56y = 217/6
35x + 10y = 125/6
Subtract equations
46y = 46/3
y = 46/3/46
y = 1/3

Substitute y
5x + 8(1/3) = 31/6
5x = 5/2
x = 5/2/5
x = 1/2


Input: Solve quickly: x^3 + 18x^2 + 15x - 34 = 0

Output:
x^3 + 18x^2 + 15x - 34 = 0
(x - -2)(x - -17)(x - 1) = 0
x - -2 = 0
x - -17 = 0
x - 1 = 0
x = -2
x = -17
x = 1


Input: Find x in 9x - 18/7 = 0

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


Input: Solve x^2 + 151/30x - 8/5 = 0

Output:
x^2 + 151/30x - 8/5 = 0
(x - 3/10)(x - -16/3) = 0
x - 3/10 = 0  or  x - -16/3 = 0
x = 3/10
x = -16/3


Input:
Solve the system:
4x + 10y = -628/5
8x + 7y = -346/5

Output:
4x + 10y = -628/5
8x + 7y = -346/5

Using elimination
8*(4x + 10y = -628/5)
4*(8x + 7y = -346/5)
32x + 80y = -5024/5
32x + 28y = -1384/5
Subtract equations
52y = -728
y = -728/52
y = -14

Substitute y
4x + 10(-14) = -628/5
4x = 72/5
x = 72/5/4
x = 18/5


Input: Solve the equation x^2 - 23/10x + 9/10 = 0

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


Input:
Solve the equations:
8x + 6y = 336/5
5x + 6y = 246/5

Output:
8x + 6y = 336/5
5x + 6y = 246/5

Using elimination
5*(8x + 6y = 336/5)
8*(5x + 6y = 246/5)
40x + 30y = 336
40x + 48y = 1968/5
Subtract equations
-18y = -288/5
y = -288/5/-18
y = 16/5

Substitute y
8x + 6(16/5) = 336/5
8x = 48
x = 48/8
x = 6


Input:
Find x and y such that
9x + 3y = 981/14
7x + 2y = 759/14

Output:
9x + 3y = 981/14
7x + 2y = 759/14

Using elimination
7*(9x + 3y = 981/14)
9*(7x + 2y = 759/14)
63x + 21y = 981/2
63x + 18y = 6831/14
Subtract equations
3y = 18/7
y = 18/7/3
y = 6/7

Substitute y
9x + 3(6/7) = 981/14
9x = 135/2
x = 135/2/9
x = 15/2


Input: Solve the equation 9x - 72 = 0

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


Input:
Solve simultaneously:
6x + 7y = -16
10x + 5y = -20

Output:
6x + 7y = -16
10x + 5y = -20

Using elimination
10*(6x + 7y = -16)
6*(10x + 5y = -20)
60x + 70y = -160
60x + 30y = -120
Subtract equations
40y = -40
y = -40/40
y = -1

Substitute y
6x + 7(-1) = -16
6x = -9
x = -9/6
x = -3/2


Input: Solve the equation 10x + 15 = 0

Output:
10x + 15 = 0
10x = -15
x = -15 / 10
x = -3/2


Input: Solve quickly: x^3 - 115/21x^2 + 50/7x  = 0

Output:
x^3 - 115/21x^2 + 50/7x  = 0
(x - 15/7)(x - 10/3)(x - 0) = 0
x - 15/7 = 0
x - 10/3 = 0
x - 0 = 0
x = 15/7
x = 10/3
x = 0


Input: Find x in x^3 + 47/10x^2 + 34/5x + 14/5 = 0

Output:
x^3 + 47/10x^2 + 34/5x + 14/5 = 0
(x - -7/10)(x - -2)(x - -2) = 0
x - -7/10 = 0
x - -2 = 0
x - -2 = 0
x = -7/10
x = -2
x = -2


Input: Compute the solution of x^3 + 27/2x^2 - 576/25x - 81/10 = 0

Output:
x^3 + 27/2x^2 - 576/25x - 81/10 = 0
(x - -15)(x - 9/5)(x - -3/10) = 0
x - -15 = 0
x - 9/5 = 0
x - -3/10 = 0
x = -15
x = 9/5
x = -3/10


Input: Find the solution to x^3 + 39/5x^2 + 1711/180x + 247/180 = 0

Output:
x^3 + 39/5x^2 + 1711/180x + 247/180 = 0
(x - -13/10)(x - -1/6)(x - -19/3) = 0
x - -13/10 = 0
x - -1/6 = 0
x - -19/3 = 0
x = -13/10
x = -1/6
x = -19/3


Input: What value of x satisfies x^3 - 15/8x^2 - 71/32x + 99/32 = 0

Output:
x^3 - 15/8x^2 - 71/32x + 99/32 = 0
(x - -11/8)(x - 9/4)(x - 1) = 0
x - -11/8 = 0
x - 9/4 = 0
x - 1 = 0
x = -11/8
x = 9/4
x = 1


Input:
Solve the system:
4x + 9y = 175/4
9x + 2y = 133/2

Output:
4x + 9y = 175/4
9x + 2y = 133/2

Using elimination
9*(4x + 9y = 175/4)
4*(9x + 2y = 133/2)
36x + 81y = 1575/4
36x + 8y = 266
Subtract equations
73y = 511/4
y = 511/4/73
y = 7/4

Substitute y
4x + 9(7/4) = 175/4
4x = 28
x = 28/4
x = 7


Input: Find x for x^2 + 13/3x + 40/9 = 0

Output:
x^2 + 13/3x + 40/9 = 0
(x - -5/3)(x - -8/3) = 0
x - -5/3 = 0  or  x - -8/3 = 0
x = -5/3
x = -8/3


Input: Compute the solution of x^3 + 205/36x^2 + 181/36x - 85/18 = 0

Output:
x^3 + 205/36x^2 + 181/36x - 85/18 = 0
(x - -2)(x - -17/4)(x - 5/9) = 0
x - -2 = 0
x - -17/4 = 0
x - 5/9 = 0
x = -2
x = -17/4
x = 5/9


Input: Solve the equation x^3 + 129/20x^2 + 279/40x - 209/40 = 0

Output:
x^3 + 129/20x^2 + 279/40x - 209/40 = 0
(x - 1/2)(x - -11/5)(x - -19/4) = 0
x - 1/2 = 0
x - -11/5 = 0
x - -19/4 = 0
x = 1/2
x = -11/5
x = -19/4


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

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


Input: What value of x satisfies 8x + 32/9 = 0

Output:
8x + 32/9 = 0
8x = -32/9
x = -32/9 / 8
x = -4/9


Input:
Solve the system:
6x + 8y = -45
9x + 2y = -135/2

Output:
6x + 8y = -45
9x + 2y = -135/2

Using elimination
9*(6x + 8y = -45)
6*(9x + 2y = -135/2)
54x + 72y = -405
54x + 12y = -405
Subtract equations
60y = 0
y = 0/60
y = 0

Substitute y
6x + 8(0) = -45
6x = -45
x = -45/6
x = -15/2


Input: Find x in 7x - 21 = 0

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


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

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


Input: Find the solution to x^2 - 67/30x + 6/5 = 0

Output:
x^2 - 67/30x + 6/5 = 0
(x - 4/3)(x - 9/10) = 0
x - 4/3 = 0  or  x - 9/10 = 0
x = 4/3
x = 9/10


Input: Find x in x^2 - 29/8x - 55/8 = 0

Output:
x^2 - 29/8x - 55/8 = 0
(x - 5)(x - -11/8) = 0
x - 5 = 0  or  x - -11/8 = 0
x = 5
x = -11/8


Input: Solve the equation 9x - 162/5 = 0

Output:
9x - 162/5 = 0
9x = 162/5
x = 162/5 / 9
x = 18/5


Input: Solve quickly: 4x + 80/3 = 0

Output:
4x + 80/3 = 0
4x = -80/3
x = -80/3 / 4
x = -20/3


Input: Determine x in 7x + 42 = 0

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


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

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


Input:
Find x and y such that
9x + 2y = -65/8
10x + 7y = -103/4

Output:
9x + 2y = -65/8
10x + 7y = -103/4

Using elimination
10*(9x + 2y = -65/8)
9*(10x + 7y = -103/4)
90x + 20y = -325/4
90x + 63y = -927/4
Subtract equations
-43y = 301/2
y = 301/2/-43
y = -7/2

Substitute y
9x + 2(-7/2) = -65/8
9x = -9/8
x = -9/8/9
x = -1/8


Input: Find x for 1x + 9/5 = 0

Output:
1x + 9/5 = 0
1x = -9/5
x = -9/5 / 1
x = -9/5


Input: Solve the equation x^3 + 14/5x^2 - 49/25x + 34/125 = 0

Output:
x^3 + 14/5x^2 - 49/25x + 34/125 = 0
(x - 1/5)(x - -17/5)(x - 2/5) = 0
x - 1/5 = 0
x - -17/5 = 0
x - 2/5 = 0
x = 1/5
x = -17/5
x = 2/5


Input: What value of x satisfies x^3 - 48/5x^2 + 151/5x - 156/5 = 0

Output:
x^3 - 48/5x^2 + 151/5x - 156/5 = 0
(x - 3)(x - 4)(x - 13/5) = 0
x - 3 = 0
x - 4 = 0
x - 13/5 = 0
x = 3
x = 4
x = 13/5


Input: Compute the solution of x^3 + 13/10x^2 + 1/50x - 7/25 = 0

Output:
x^3 + 13/10x^2 + 1/50x - 7/25 = 0
(x - -1)(x - 2/5)(x - -7/10) = 0
x - -1 = 0
x - 2/5 = 0
x - -7/10 = 0
x = -1
x = 2/5
x = -7/10


Input: Solve the equation 9x + 171/4 = 0

Output:
9x + 171/4 = 0
9x = -171/4
x = -171/4 / 9
x = -19/4


Input:
Solve the equations:
1x + 8y = -173/40
9x + 8y = -533/40

Output:
1x + 8y = -173/40
9x + 8y = -533/40

Using elimination
9*(1x + 8y = -173/40)
1*(9x + 8y = -533/40)
9x + 72y = -1557/40
9x + 8y = -533/40
Subtract equations
64y = -128/5
y = -128/5/64
y = -2/5

Substitute y
1x + 8(-2/5) = -173/40
1x = -9/8
x = -9/8/1
x = -9/8


Input: Solve quickly: x^3 + 76/45x^2 - 49/45x - 8/5 = 0

Output:
x^3 + 76/45x^2 - 49/45x - 8/5 = 0
(x - -8/9)(x - 1)(x - -9/5) = 0
x - -8/9 = 0
x - 1 = 0
x - -9/5 = 0
x = -8/9
x = 1
x = -9/5


Input:
Find x and y such that
3x + 9y = -19
10x + 1y = -193/9

Output:
3x + 9y = -19
10x + 1y = -193/9

Using elimination
10*(3x + 9y = -19)
3*(10x + 1y = -193/9)
30x + 90y = -190
30x + 3y = -193/3
Subtract equations
87y = -377/3
y = -377/3/87
y = -13/9

Substitute y
3x + 9(-13/9) = -19
3x = -6
x = -6/3
x = -2


Input: Solve quickly: 2x + 4/9 = 0

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


Input: Find x in x^3 - 38/9x^2 + 59/12x - 55/36 = 0

Output:
x^3 - 38/9x^2 + 59/12x - 55/36 = 0
(x - 11/9)(x - 1/2)(x - 5/2) = 0
x - 11/9 = 0
x - 1/2 = 0
x - 5/2 = 0
x = 11/9
x = 1/2
x = 5/2


Input: Find the solution to 10x + 200/3 = 0

Output:
10x + 200/3 = 0
10x = -200/3
x = -200/3 / 10
x = -20/3


Input: Solve quickly: 3x + 57/8 = 0

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


Input: Solve quickly: x^2 - 15/2x + 9 = 0

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


Input:
Solve simultaneously:
4x + 6y = 31/7
10x + 5y = -55/14

Output:
4x + 6y = 31/7
10x + 5y = -55/14

Using elimination
10*(4x + 6y = 31/7)
4*(10x + 5y = -55/14)
40x + 60y = 310/7
40x + 20y = -110/7
Subtract equations
40y = 60
y = 60/40
y = 3/2

Substitute y
4x + 6(3/2) = 31/7
4x = -32/7
x = -32/7/4
x = -8/7


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

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


Input: Find x for x^3 + 13/20x^2 - 229/20x + 39/5 = 0

Output:
x^3 + 13/20x^2 - 229/20x + 39/5 = 0
(x - 13/5)(x - -4)(x - 3/4) = 0
x - 13/5 = 0
x - -4 = 0
x - 3/4 = 0
x = 13/5
x = -4
x = 3/4


Input:
Solve simultaneously:
1x + 10y = 95/9
8x + 5y = 385/9

Output:
1x + 10y = 95/9
8x + 5y = 385/9

Using elimination
8*(1x + 10y = 95/9)
1*(8x + 5y = 385/9)
8x + 80y = 760/9
8x + 5y = 385/9
Subtract equations
75y = 125/3
y = 125/3/75
y = 5/9

Substitute y
1x + 10(5/9) = 95/9
1x = 5
x = 5/1
x = 5


Input: What value of x satisfies 7x + 49/8 = 0

Output:
7x + 49/8 = 0
7x = -49/8
x = -49/8 / 7
x = -7/8


Input:
Find x and y such that
7x + 8y = -28
10x + 1y = -87/4

Output:
7x + 8y = -28
10x + 1y = -87/4

Using elimination
10*(7x + 8y = -28)
7*(10x + 1y = -87/4)
70x + 80y = -280
70x + 7y = -609/4
Subtract equations
73y = -511/4
y = -511/4/73
y = -7/4

Substitute y
7x + 8(-7/4) = -28
7x = -14
x = -14/7
x = -2


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

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


Input: What value of x satisfies x^2 - 19/8x - 15/8 = 0

Output:
x^2 - 19/8x - 15/8 = 0
(x - 3)(x - -5/8) = 0
x - 3 = 0  or  x - -5/8 = 0
x = 3
x = -5/8


Input: Find x for 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 6x - 36/5 = 0

Output:
6x - 36/5 = 0
6x = 36/5
x = 36/5 / 6
x = 6/5


Input:
Solve the system:
3x + 7y = -190/9
1x + 7y = -82/9

Output:
3x + 7y = -190/9
1x + 7y = -82/9

Using elimination
1*(3x + 7y = -190/9)
3*(1x + 7y = -82/9)
3x + 7y = -190/9
3x + 21y = -82/3
Subtract equations
-14y = 56/9
y = 56/9/-14
y = -4/9

Substitute y
3x + 7(-4/9) = -190/9
3x = -18
x = -18/3
x = -6


Input: Find x for 9x + 12 = 0

Output:
9x + 12 = 0
9x = -12
x = -12 / 9
x = -4/3


Input: Solve the equation 3x + 33/8 = 0

Output:
3x + 33/8 = 0
3x = -33/8
x = -33/8 / 3
x = -11/8


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

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


Input: Determine x in x^3 - 3/5x^2 - 71/20x + 33/10 = 0

Output:
x^3 - 3/5x^2 - 71/20x + 33/10 = 0
(x - 3/2)(x - -2)(x - 11/10) = 0
x - 3/2 = 0
x - -2 = 0
x - 11/10 = 0
x = 3/2
x = -2
x = 11/10


Input: Compute the solution of x^2 - 151/10x + 3/2 = 0

Output:
x^2 - 151/10x + 3/2 = 0
(x - 15)(x - 1/10) = 0
x - 15 = 0  or  x - 1/10 = 0
x = 15
x = 1/10


Input:
Solve the equations:
1x + 1y = 86/63
8x + 6y = 796/63

Output:
1x + 1y = 86/63
8x + 6y = 796/63

Using elimination
8*(1x + 1y = 86/63)
1*(8x + 6y = 796/63)
8x + 8y = 688/63
8x + 6y = 796/63
Subtract equations
2y = -12/7
y = -12/7/2
y = -6/7

Substitute y
1x + 1(-6/7) = 86/63
1x = 20/9
x = 20/9/1
x = 20/9


Input: Solve x^3 - 302/45x^2 - 29/45x + 442/15 = 0

Output:
x^3 - 302/45x^2 - 29/45x + 442/15 = 0
(x - 13/5)(x - -17/9)(x - 6) = 0
x - 13/5 = 0
x - -17/9 = 0
x - 6 = 0
x = 13/5
x = -17/9
x = 6


Input:
Find x and y such that
9x + 4y = 4
10x + 10y = 145/12

Output:
9x + 4y = 4
10x + 10y = 145/12

Using elimination
10*(9x + 4y = 4)
9*(10x + 10y = 145/12)
90x + 40y = 40
90x + 90y = 435/4
Subtract equations
-50y = -275/4
y = -275/4/-50
y = 11/8

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


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

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


Input: Find x in x^2 + 7/10x - 6/5 = 0

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


Input: Find the solution to 3x - 45/7 = 0

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


Input: Solve the equation 3x - 36/7 = 0

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


Input: Solve x^3 - 19/5x^2 - 16x + 304/5 = 0

Output:
x^3 - 19/5x^2 - 16x + 304/5 = 0
(x - -4)(x - 19/5)(x - 4) = 0
x - -4 = 0
x - 19/5 = 0
x - 4 = 0
x = -4
x = 19/5
x = 4


Input: Solve quickly: x^3 + 61/21x^2 + 272/147x - 16/49 = 0

Output:
x^3 + 61/21x^2 + 272/147x - 16/49 = 0
(x - -4/3)(x - 1/7)(x - -12/7) = 0
x - -4/3 = 0
x - 1/7 = 0
x - -12/7 = 0
x = -4/3
x = 1/7
x = -12/7


Input:
Solve the equations:
3x + 10y = 174
6x + 8y = 132

Output:
3x + 10y = 174
6x + 8y = 132

Using elimination
6*(3x + 10y = 174)
3*(6x + 8y = 132)
18x + 60y = 1044
18x + 24y = 396
Subtract equations
36y = 648
y = 648/36
y = 18

Substitute y
3x + 10(18) = 174
3x = -6
x = -6/3
x = -2


Input:
Solve the system:
2x + 5y = -13
8x + 6y = 11

Output:
2x + 5y = -13
8x + 6y = 11

Using elimination
8*(2x + 5y = -13)
2*(8x + 6y = 11)
16x + 40y = -104
16x + 12y = 22
Subtract equations
28y = -126
y = -126/28
y = -9/2

Substitute y
2x + 5(-9/2) = -13
2x = 19/2
x = 19/2/2
x = 19/4


Input: What value of x satisfies x^3 + 5/6x^2 - 181/6x - 65 = 0

Output:
x^3 + 5/6x^2 - 181/6x - 65 = 0
(x - -5/2)(x - -13/3)(x - 6) = 0
x - -5/2 = 0
x - -13/3 = 0
x - 6 = 0
x = -5/2
x = -13/3
x = 6


Input: What value of x satisfies 10x + 20 = 0

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


Input: Solve the equation x^2 + 113/7x + 120/7 = 0

Output:
x^2 + 113/7x + 120/7 = 0
(x - -8/7)(x - -15) = 0
x - -8/7 = 0  or  x - -15 = 0
x = -8/7
x = -15


Input: Find the solution to x^3 + 55/7x^2 + 409/28x - 9/4 = 0

Output:
x^3 + 55/7x^2 + 409/28x - 9/4 = 0
(x - -7/2)(x - 1/7)(x - -9/2) = 0
x - -7/2 = 0
x - 1/7 = 0
x - -9/2 = 0
x = -7/2
x = 1/7
x = -9/2


Input: Compute the solution of x^2 - 13/5x - 171/20 = 0

Output:
x^2 - 13/5x - 171/20 = 0
(x - 9/2)(x - -19/10) = 0
x - 9/2 = 0  or  x - -19/10 = 0
x = 9/2
x = -19/10


Input: Find the solution to x^2 + 79/4x + 57/4 = 0

Output:
x^2 + 79/4x + 57/4 = 0
(x - -19)(x - -3/4) = 0
x - -19 = 0  or  x - -3/4 = 0
x = -19
x = -3/4


Input:
Solve the equations:
10x + 6y = -49/3
10x + 7y = -154/9

Output:
10x + 6y = -49/3
10x + 7y = -154/9

Using elimination
10*(10x + 6y = -49/3)
10*(10x + 7y = -154/9)
100x + 60y = -490/3
100x + 70y = -1540/9
Subtract equations
-10y = 70/9
y = 70/9/-10
y = -7/9

Substitute y
10x + 6(-7/9) = -49/3
10x = -35/3
x = -35/3/10
x = -7/6


Input: Find the solution to x^2 + 5/18x - 7/18 = 0

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


Input: Solve x^2 + 39/14x + 5/7 = 0

Output:
x^2 + 39/14x + 5/7 = 0
(x - -5/2)(x - -2/7) = 0
x - -5/2 = 0  or  x - -2/7 = 0
x = -5/2
x = -2/7


Input:
Solve simultaneously:
2x + 9y = 201/8
7x + 10y = 169/4

Output:
2x + 9y = 201/8
7x + 10y = 169/4

Using elimination
7*(2x + 9y = 201/8)
2*(7x + 10y = 169/4)
14x + 63y = 1407/8
14x + 20y = 169/2
Subtract equations
43y = 731/8
y = 731/8/43
y = 17/8

Substitute y
2x + 9(17/8) = 201/8
2x = 6
x = 6/2
x = 3


Input:
Solve the system:
3x + 6y = -41/2
8x + 3y = -86/3

Output:
3x + 6y = -41/2
8x + 3y = -86/3

Using elimination
8*(3x + 6y = -41/2)
3*(8x + 3y = -86/3)
24x + 48y = -164
24x + 9y = -86
Subtract equations
39y = -78
y = -78/39
y = -2

Substitute y
3x + 6(-2) = -41/2
3x = -17/2
x = -17/2/3
x = -17/6


Input: Determine x in x^2 + 1/45x - 2/45 = 0

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


Input: Solve 7x + 20 = 0

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


Input: Solve x^3 + 657/40x^2 - 279/10x + 81/10 = 0

Output:
x^3 + 657/40x^2 - 279/10x + 81/10 = 0
(x - 3/8)(x - 6/5)(x - -18) = 0
x - 3/8 = 0
x - 6/5 = 0
x - -18 = 0
x = 3/8
x = 6/5
x = -18


Input: Determine x in x^3 + 41/2x^2 + 125x + 200 = 0

Output:
x^3 + 41/2x^2 + 125x + 200 = 0
(x - -8)(x - -5/2)(x - -10) = 0
x - -8 = 0
x - -5/2 = 0
x - -10 = 0
x = -8
x = -5/2
x = -10


Input: Solve quickly: 7x + 49/5 = 0

Output:
7x + 49/5 = 0
7x = -49/5
x = -49/5 / 7
x = -7/5


Input: Solve the equation x^3 + 113/63x^2 - 404/147x - 1760/441 = 0

Output:
x^3 + 113/63x^2 - 404/147x - 1760/441 = 0
(x - 11/7)(x - -20/9)(x - -8/7) = 0
x - 11/7 = 0
x - -20/9 = 0
x - -8/7 = 0
x = 11/7
x = -20/9
x = -8/7


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

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


Input:
Solve the system:
8x + 6y = -9/4
10x + 7y = -17/8

Output:
8x + 6y = -9/4
10x + 7y = -17/8

Using elimination
10*(8x + 6y = -9/4)
8*(10x + 7y = -17/8)
80x + 60y = -45/2
80x + 56y = -17
Subtract equations
4y = -11/2
y = -11/2/4
y = -11/8

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


Input:
Find x and y such that
3x + 4y = -24
10x + 10y = -65

Output:
3x + 4y = -24
10x + 10y = -65

Using elimination
10*(3x + 4y = -24)
3*(10x + 10y = -65)
30x + 40y = -240
30x + 30y = -195
Subtract equations
10y = -45
y = -45/10
y = -9/2

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


Input: Determine x in 7x - 35/4 = 0

Output:
7x - 35/4 = 0
7x = 35/4
x = 35/4 / 7
x = 5/4


Input: Find x for 4x - 10 = 0

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


Input: Solve x^2 + 22/5x - 3 = 0

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


Input: What value of x satisfies x^3 + 163/42x^2 - 5/6x - 76/7 = 0

Output:
x^3 + 163/42x^2 - 5/6x - 76/7 = 0
(x - -19/7)(x - -8/3)(x - 3/2) = 0
x - -19/7 = 0
x - -8/3 = 0
x - 3/2 = 0
x = -19/7
x = -8/3
x = 3/2


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

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


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

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


Input:
Solve the equations:
2x + 1y = 33/20
3x + 6y = -9/40

Output:
2x + 1y = 33/20
3x + 6y = -9/40

Using elimination
3*(2x + 1y = 33/20)
2*(3x + 6y = -9/40)
6x + 3y = 99/20
6x + 12y = -9/20
Subtract equations
-9y = 27/5
y = 27/5/-9
y = -3/5

Substitute y
2x + 1(-3/5) = 33/20
2x = 9/4
x = 9/4/2
x = 9/8


Input: Find x in 9x + 54/5 = 0

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


Input: Find x for 10x - 190 = 0

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


Input:
Solve the system:
1x + 8y = 184/9
1x + 6y = 52/3

Output:
1x + 8y = 184/9
1x + 6y = 52/3

Using elimination
1*(1x + 8y = 184/9)
1*(1x + 6y = 52/3)
1x + 8y = 184/9
1x + 6y = 52/3
Subtract equations
2y = 28/9
y = 28/9/2
y = 14/9

Substitute y
1x + 8(14/9) = 184/9
1x = 8
x = 8/1
x = 8


Input:
Solve the system:
6x + 1y = -12
6x + 5y = 4

Output:
6x + 1y = -12
6x + 5y = 4

Using elimination
6*(6x + 1y = -12)
6*(6x + 5y = 4)
36x + 6y = -72
36x + 30y = 24
Subtract equations
-24y = -96
y = -96/-24
y = 4

Substitute y
6x + 1(4) = -12
6x = -16
x = -16/6
x = -8/3


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

Output:
x^2 + 23/3x + 10 = 0
(x - -5/3)(x - -6) = 0
x - -5/3 = 0  or  x - -6 = 0
x = -5/3
x = -6


Input: Solve the equation x^2 - 10/3x - 8/3 = 0

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


Input: Find x in x^2 + 33/56x - 27/14 = 0

Output:
x^2 + 33/56x - 27/14 = 0
(x - -12/7)(x - 9/8) = 0
x - -12/7 = 0  or  x - 9/8 = 0
x = -12/7
x = 9/8


Input: What value of x satisfies x^3 - 5x^2 - 12x + 36 = 0

Output:
x^3 - 5x^2 - 12x + 36 = 0
(x - 6)(x - -3)(x - 2) = 0
x - 6 = 0
x - -3 = 0
x - 2 = 0
x = 6
x = -3
x = 2


Input: Determine x in 7x + 21/2 = 0

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


Input: Solve the equation 4x + 72/7 = 0

Output:
4x + 72/7 = 0
4x = -72/7
x = -72/7 / 4
x = -18/7


Input:
Solve simultaneously:
1x + 7y = -389/12
1x + 4y = -221/12

Output:
1x + 7y = -389/12
1x + 4y = -221/12

Using elimination
1*(1x + 7y = -389/12)
1*(1x + 4y = -221/12)
1x + 7y = -389/12
1x + 4y = -221/12
Subtract equations
3y = -14
y = -14/3
y = -14/3

Substitute y
1x + 7(-14/3) = -389/12
1x = 1/4
x = 1/4/1
x = 1/4


Input:
Solve the equations:
10x + 5y = 85
6x + 9y = 105

Output:
10x + 5y = 85
6x + 9y = 105

Using elimination
6*(10x + 5y = 85)
10*(6x + 9y = 105)
60x + 30y = 510
60x + 90y = 1050
Subtract equations
-60y = -540
y = -540/-60
y = 9

Substitute y
10x + 5(9) = 85
10x = 40
x = 40/10
x = 4


Input:
Solve the equations:
4x + 10y = -126
1x + 4y = -45

Output:
4x + 10y = -126
1x + 4y = -45

Using elimination
1*(4x + 10y = -126)
4*(1x + 4y = -45)
4x + 10y = -126
4x + 16y = -180
Subtract equations
-6y = 54
y = 54/-6
y = -9

Substitute y
4x + 10(-9) = -126
4x = -36
x = -36/4
x = -9


Input:
Solve the system:
10x + 5y = -282/7
1x + 5y = -129/7

Output:
10x + 5y = -282/7
1x + 5y = -129/7

Using elimination
1*(10x + 5y = -282/7)
10*(1x + 5y = -129/7)
10x + 5y = -282/7
10x + 50y = -1290/7
Subtract equations
-45y = 144
y = 144/-45
y = -16/5

Substitute y
10x + 5(-16/5) = -282/7
10x = -170/7
x = -170/7/10
x = -17/7


Input:
Solve simultaneously:
9x + 3y = -31/4
9x + 4y = -8

Output:
9x + 3y = -31/4
9x + 4y = -8

Using elimination
9*(9x + 3y = -31/4)
9*(9x + 4y = -8)
81x + 27y = -279/4
81x + 36y = -72
Subtract equations
-9y = 9/4
y = 9/4/-9
y = -1/4

Substitute y
9x + 3(-1/4) = -31/4
9x = -7
x = -7/9
x = -7/9


Input:
Solve the equations:
4x + 5y = -131/8
4x + 4y = -31/2

Output:
4x + 5y = -131/8
4x + 4y = -31/2

Using elimination
4*(4x + 5y = -131/8)
4*(4x + 4y = -31/2)
16x + 20y = -131/2
16x + 16y = -62
Subtract equations
4y = -7/2
y = -7/2/4
y = -7/8

Substitute y
4x + 5(-7/8) = -131/8
4x = -12
x = -12/4
x = -3


Input: Solve the equation x^2 + 19/6x + 35/18 = 0

Output:
x^2 + 19/6x + 35/18 = 0
(x - -5/6)(x - -7/3) = 0
x - -5/6 = 0  or  x - -7/3 = 0
x = -5/6
x = -7/3


Input:
Find x and y such that
9x + 2y = 49/4
3x + 7y = 39/8

Output:
9x + 2y = 49/4
3x + 7y = 39/8

Using elimination
3*(9x + 2y = 49/4)
9*(3x + 7y = 39/8)
27x + 6y = 147/4
27x + 63y = 351/8
Subtract equations
-57y = -57/8
y = -57/8/-57
y = 1/8

Substitute y
9x + 2(1/8) = 49/4
9x = 12
x = 12/9
x = 4/3


Input: Find x for 7x - 105/8 = 0

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


Input: Solve 1x  = 0

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


Input: Find x for x^3 + 499/21x^2 + 960/7x + 4352/21 = 0

Output:
x^3 + 499/21x^2 + 960/7x + 4352/21 = 0
(x - -17/7)(x - -16/3)(x - -16) = 0
x - -17/7 = 0
x - -16/3 = 0
x - -16 = 0
x = -17/7
x = -16/3
x = -16


Input: Find x for x^3 + 1255/56x^2 + 337/4x + 612/7 = 0

Output:
x^3 + 1255/56x^2 + 337/4x + 612/7 = 0
(x - -17/8)(x - -16/7)(x - -18) = 0
x - -17/8 = 0
x - -16/7 = 0
x - -18 = 0
x = -17/8
x = -16/7
x = -18


Input: Find x for 4x - 6 = 0

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


Input:
Find x and y such that
5x + 4y = -176/7
2x + 4y = -188/7

Output:
5x + 4y = -176/7
2x + 4y = -188/7

Using elimination
2*(5x + 4y = -176/7)
5*(2x + 4y = -188/7)
10x + 8y = -352/7
10x + 20y = -940/7
Subtract equations
-12y = 84
y = 84/-12
y = -7

Substitute y
5x + 4(-7) = -176/7
5x = 20/7
x = 20/7/5
x = 4/7


Input: Find x for 1x + 7/2 = 0

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


Input: Find the solution to x^2 + 23/5x - 42/5 = 0

Output:
x^2 + 23/5x - 42/5 = 0
(x - -6)(x - 7/5) = 0
x - -6 = 0  or  x - 7/5 = 0
x = -6
x = 7/5


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

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


Input: Find the solution to x^3 + 1/8x^2 - 1x - 1/8 = 0

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


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

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


Input: Find x for x^3 - 127/12x^2 - 1085/24x - 147/4 = 0

Output:
x^3 - 127/12x^2 - 1085/24x - 147/4 = 0
(x - -9/4)(x - -7/6)(x - 14) = 0
x - -9/4 = 0
x - -7/6 = 0
x - 14 = 0
x = -9/4
x = -7/6
x = 14


Input: What value of x satisfies x^3 + 41/3x^2 - 655/12x + 425/12 = 0

Output:
x^3 + 41/3x^2 - 655/12x + 425/12 = 0
(x - 5/2)(x - -17)(x - 5/6) = 0
x - 5/2 = 0
x - -17 = 0
x - 5/6 = 0
x = 5/2
x = -17
x = 5/6


Input: Solve quickly: x^3 - 67/6x^2 - 334/3x - 210 = 0

Output:
x^3 - 67/6x^2 - 334/3x - 210 = 0
(x - -7/2)(x - -10/3)(x - 18) = 0
x - -7/2 = 0
x - -10/3 = 0
x - 18 = 0
x = -7/2
x = -10/3
x = 18


Input: Find the solution to x^2 - 23/3x + 40/3 = 0

Output:
x^2 - 23/3x + 40/3 = 0
(x - 8/3)(x - 5) = 0
x - 8/3 = 0  or  x - 5 = 0
x = 8/3
x = 5


Input: What value of x satisfies x^2 - 79/28x + 55/28 = 0

Output:
x^2 - 79/28x + 55/28 = 0
(x - 11/7)(x - 5/4) = 0
x - 11/7 = 0  or  x - 5/4 = 0
x = 11/7
x = 5/4


Input:
Solve the equations:
3x + 3y = -144/5
6x + 1y = -13/5

Output:
3x + 3y = -144/5
6x + 1y = -13/5

Using elimination
6*(3x + 3y = -144/5)
3*(6x + 1y = -13/5)
18x + 18y = -864/5
18x + 3y = -39/5
Subtract equations
15y = -165
y = -165/15
y = -11

Substitute y
3x + 3(-11) = -144/5
3x = 21/5
x = 21/5/3
x = 7/5


Input:
Find x and y such that
6x + 3y = -73
2x + 5y = -77/3

Output:
6x + 3y = -73
2x + 5y = -77/3

Using elimination
2*(6x + 3y = -73)
6*(2x + 5y = -77/3)
12x + 6y = -146
12x + 30y = -154
Subtract equations
-24y = 8
y = 8/-24
y = -1/3

Substitute y
6x + 3(-1/3) = -73
6x = -72
x = -72/6
x = -12


Input: Determine x in 6x - 33 = 0

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


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

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


Input:
Solve the equations:
8x + 5y = -7/2
2x + 7y = 27/2

Output:
8x + 5y = -7/2
2x + 7y = 27/2

Using elimination
2*(8x + 5y = -7/2)
8*(2x + 7y = 27/2)
16x + 10y = -7
16x + 56y = 108
Subtract equations
-46y = -115
y = -115/-46
y = 5/2

Substitute y
8x + 5(5/2) = -7/2
8x = -16
x = -16/8
x = -2


Input: Solve quickly: 6x + 33 = 0

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


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

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


Input: Compute the solution of x^2 + 94/15x - 8/3 = 0

Output:
x^2 + 94/15x - 8/3 = 0
(x - -20/3)(x - 2/5) = 0
x - -20/3 = 0  or  x - 2/5 = 0
x = -20/3
x = 2/5


Input: What value of x satisfies x^3 + 46/9x^2 - 49/9x - 2/3 = 0

Output:
x^3 + 46/9x^2 - 49/9x - 2/3 = 0
(x - -1/9)(x - -6)(x - 1) = 0
x - -1/9 = 0
x - -6 = 0
x - 1 = 0
x = -1/9
x = -6
x = 1


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

Output:
5x - 10/3 = 0
5x = 10/3
x = 10/3 / 5
x = 2/3


Input:
Solve the system:
10x + 10y = -172/3
7x + 2y = -202/15

Output:
10x + 10y = -172/3
7x + 2y = -202/15

Using elimination
7*(10x + 10y = -172/3)
10*(7x + 2y = -202/15)
70x + 70y = -1204/3
70x + 20y = -404/3
Subtract equations
50y = -800/3
y = -800/3/50
y = -16/3

Substitute y
10x + 10(-16/3) = -172/3
10x = -4
x = -4/10
x = -2/5


Input: Solve the equation 6x - 20 = 0

Output:
6x - 20 = 0
6x = 20
x = 20 / 6
x = 10/3


Input: Compute the solution of x^2 + 7x + 38/9 = 0

Output:
x^2 + 7x + 38/9 = 0
(x - -2/3)(x - -19/3) = 0
x - -2/3 = 0  or  x - -19/3 = 0
x = -2/3
x = -19/3


Input: Find x for x^2 + 19/14x - 20/7 = 0

Output:
x^2 + 19/14x - 20/7 = 0
(x - -5/2)(x - 8/7) = 0
x - -5/2 = 0  or  x - 8/7 = 0
x = -5/2
x = 8/7


Input: Determine x in x^2 - 51/28x - 27/28 = 0

Output:
x^2 - 51/28x - 27/28 = 0
(x - -3/7)(x - 9/4) = 0
x - -3/7 = 0  or  x - 9/4 = 0
x = -3/7
x = 9/4


Input:
Find x and y such that
8x + 7y = 233/6
3x + 8y = 28

Output:
8x + 7y = 233/6
3x + 8y = 28

Using elimination
3*(8x + 7y = 233/6)
8*(3x + 8y = 28)
24x + 21y = 233/2
24x + 64y = 224
Subtract equations
-43y = -215/2
y = -215/2/-43
y = 5/2

Substitute y
8x + 7(5/2) = 233/6
8x = 64/3
x = 64/3/8
x = 8/3


Input: Find x for x^2 - 53/35x - 12/35 = 0

Output:
x^2 - 53/35x - 12/35 = 0
(x - -1/5)(x - 12/7) = 0
x - -1/5 = 0  or  x - 12/7 = 0
x = -1/5
x = 12/7


Input: Find x in x^2 - 13/12x - 1/3 = 0

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


Input:
Find x and y such that
2x + 5y = -118/5
9x + 3y = -141/5

Output:
2x + 5y = -118/5
9x + 3y = -141/5

Using elimination
9*(2x + 5y = -118/5)
2*(9x + 3y = -141/5)
18x + 45y = -1062/5
18x + 6y = -282/5
Subtract equations
39y = -156
y = -156/39
y = -4

Substitute y
2x + 5(-4) = -118/5
2x = -18/5
x = -18/5/2
x = -9/5


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

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


Input:
Solve simultaneously:
10x + 9y = -205/4
7x + 4y = -195/8

Output:
10x + 9y = -205/4
7x + 4y = -195/8

Using elimination
7*(10x + 9y = -205/4)
10*(7x + 4y = -195/8)
70x + 63y = -1435/4
70x + 40y = -975/4
Subtract equations
23y = -115
y = -115/23
y = -5

Substitute y
10x + 9(-5) = -205/4
10x = -25/4
x = -25/4/10
x = -5/8


Input: Solve quickly: x^2 - 14/3x - 5/3 = 0

Output:
x^2 - 14/3x - 5/3 = 0
(x - -1/3)(x - 5) = 0
x - -1/3 = 0  or  x - 5 = 0
x = -1/3
x = 5


Input: Solve x^2 + 13x + 30 = 0

Output:
x^2 + 13x + 30 = 0
(x - -10)(x - -3) = 0
x - -10 = 0  or  x - -3 = 0
x = -10
x = -3


Input:
Solve simultaneously:
3x + 9y = 51/2
7x + 1y = 59/2

Output:
3x + 9y = 51/2
7x + 1y = 59/2

Using elimination
7*(3x + 9y = 51/2)
3*(7x + 1y = 59/2)
21x + 63y = 357/2
21x + 3y = 177/2
Subtract equations
60y = 90
y = 90/60
y = 3/2

Substitute y
3x + 9(3/2) = 51/2
3x = 12
x = 12/3
x = 4


Input: What value of x satisfies x^2 - 3/5x - 27/20 = 0

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


Input:
Solve the system:
5x + 9y = 571/40
4x + 6y = 101/10

Output:
5x + 9y = 571/40
4x + 6y = 101/10

Using elimination
4*(5x + 9y = 571/40)
5*(4x + 6y = 101/10)
20x + 36y = 571/10
20x + 30y = 101/2
Subtract equations
6y = 33/5
y = 33/5/6
y = 11/10

Substitute y
5x + 9(11/10) = 571/40
5x = 35/8
x = 35/8/5
x = 7/8


Input: Find x in x^3 - 417/40x^2 - 53/5x + 1881/40 = 0

Output:
x^3 - 417/40x^2 - 53/5x + 1881/40 = 0
(x - 9/5)(x - 11)(x - -19/8) = 0
x - 9/5 = 0
x - 11 = 0
x - -19/8 = 0
x = 9/5
x = 11
x = -19/8


Input: Find the solution to x^3 - 17/3x^2 - 1x + 17/3 = 0

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


Input:
Solve the system:
9x + 5y = 1847/70
1x + 2y = 393/70

Output:
9x + 5y = 1847/70
1x + 2y = 393/70

Using elimination
1*(9x + 5y = 1847/70)
9*(1x + 2y = 393/70)
9x + 5y = 1847/70
9x + 18y = 3537/70
Subtract equations
-13y = -169/7
y = -169/7/-13
y = 13/7

Substitute y
9x + 5(13/7) = 1847/70
9x = 171/10
x = 171/10/9
x = 19/10


Input: Solve the equation x^2 - 8/3x + 143/81 = 0

Output:
x^2 - 8/3x + 143/81 = 0
(x - 13/9)(x - 11/9) = 0
x - 13/9 = 0  or  x - 11/9 = 0
x = 13/9
x = 11/9


Input: Find x for x^3 + 1/2x^2 - 37/2x - 18 = 0

Output:
x^3 + 1/2x^2 - 37/2x - 18 = 0
(x - -1)(x - -4)(x - 9/2) = 0
x - -1 = 0
x - -4 = 0
x - 9/2 = 0
x = -1
x = -4
x = 9/2


Input: Solve quickly: x^3 + 274/15x^2 - 23x - 2584/15 = 0

Output:
x^3 + 274/15x^2 - 23x - 2584/15 = 0
(x - 17/5)(x - -8/3)(x - -19) = 0
x - 17/5 = 0
x - -8/3 = 0
x - -19 = 0
x = 17/5
x = -8/3
x = -19


Input: Compute the solution of x^3 - 149/30x^2 + 1/10x + 91/15 = 0

Output:
x^3 - 149/30x^2 + 1/10x + 91/15 = 0
(x - 14/3)(x - -1)(x - 13/10) = 0
x - 14/3 = 0
x - -1 = 0
x - 13/10 = 0
x = 14/3
x = -1
x = 13/10


Input: What value of x satisfies x^3 - 13/18x^2 - 2/3x + 7/18 = 0

Output:
x^3 - 13/18x^2 - 2/3x + 7/18 = 0
(x - -7/9)(x - 1)(x - 1/2) = 0
x - -7/9 = 0
x - 1 = 0
x - 1/2 = 0
x = -7/9
x = 1
x = 1/2


Input:
Solve the system:
4x + 6y = 31/4
8x + 1y = 201/8

Output:
4x + 6y = 31/4
8x + 1y = 201/8

Using elimination
8*(4x + 6y = 31/4)
4*(8x + 1y = 201/8)
32x + 48y = 62
32x + 4y = 201/2
Subtract equations
44y = -77/2
y = -77/2/44
y = -7/8

Substitute y
4x + 6(-7/8) = 31/4
4x = 13
x = 13/4
x = 13/4


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

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


Input: Determine x in x^3 - 59/30x^2 - 13/45x + 44/45 = 0

Output:
x^3 - 59/30x^2 - 13/45x + 44/45 = 0
(x - 4/5)(x - 11/6)(x - -2/3) = 0
x - 4/5 = 0
x - 11/6 = 0
x - -2/3 = 0
x = 4/5
x = 11/6
x = -2/3


Input:
Solve the equations:
10x + 9y = -150/7
4x + 7y = -60/7

Output:
10x + 9y = -150/7
4x + 7y = -60/7

Using elimination
4*(10x + 9y = -150/7)
10*(4x + 7y = -60/7)
40x + 36y = -600/7
40x + 70y = -600/7
Subtract equations
-34y = 0
y = 0/-34
y = 0

Substitute y
10x + 9(0) = -150/7
10x = -150/7
x = -150/7/10
x = -15/7


Input: Determine x in x^2 + 11/6x - 38/9 = 0

Output:
x^2 + 11/6x - 38/9 = 0
(x - -19/6)(x - 4/3) = 0
x - -19/6 = 0  or  x - 4/3 = 0
x = -19/6
x = 4/3


Input:
Solve simultaneously:
3x + 1y = -15/2
1x + 8y = -37

Output:
3x + 1y = -15/2
1x + 8y = -37

Using elimination
1*(3x + 1y = -15/2)
3*(1x + 8y = -37)
3x + 1y = -15/2
3x + 24y = -111
Subtract equations
-23y = 207/2
y = 207/2/-23
y = -9/2

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


Input: Solve the equation 6x - 12 = 0

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


Input:
Solve the equations:
1x + 10y = -89/6
9x + 10y = -161/6

Output:
1x + 10y = -89/6
9x + 10y = -161/6

Using elimination
9*(1x + 10y = -89/6)
1*(9x + 10y = -161/6)
9x + 90y = -267/2
9x + 10y = -161/6
Subtract equations
80y = -320/3
y = -320/3/80
y = -4/3

Substitute y
1x + 10(-4/3) = -89/6
1x = -3/2
x = -3/2/1
x = -3/2


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

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


Input: Compute the solution of x^3 - 7/3x^2 - 131/3x + 455/3 = 0

Output:
x^3 - 7/3x^2 - 131/3x + 455/3 = 0
(x - -7)(x - 13/3)(x - 5) = 0
x - -7 = 0
x - 13/3 = 0
x - 5 = 0
x = -7
x = 13/3
x = 5


Input: What value of x satisfies x^2 + 39/10x - 2/5 = 0

Output:
x^2 + 39/10x - 2/5 = 0
(x - -4)(x - 1/10) = 0
x - -4 = 0  or  x - 1/10 = 0
x = -4
x = 1/10


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

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


Input: Compute the solution of x^2 - 151/24x + 85/24 = 0

Output:
x^2 - 151/24x + 85/24 = 0
(x - 17/3)(x - 5/8) = 0
x - 17/3 = 0  or  x - 5/8 = 0
x = 17/3
x = 5/8


Input: Find x for 8x  = 0

Output:
8x  = 0
8x = 0
x = 0 / 8
x = 0


Input: What value of x satisfies x^3 - 263/70x^2 + 1529/350x - 39/25 = 0

Output:
x^3 - 263/70x^2 + 1529/350x - 39/25 = 0
(x - 6/5)(x - 13/7)(x - 7/10) = 0
x - 6/5 = 0
x - 13/7 = 0
x - 7/10 = 0
x = 6/5
x = 13/7
x = 7/10


Input: Determine x in x^2 - 20/7x  = 0

Output:
x^2 - 20/7x  = 0
(x - 20/7)(x - 0) = 0
x - 20/7 = 0  or  x - 0 = 0
x = 20/7
x = 0


Input: Solve quickly: x^2 - 261/56x + 38/7 = 0

Output:
x^2 - 261/56x + 38/7 = 0
(x - 16/7)(x - 19/8) = 0
x - 16/7 = 0  or  x - 19/8 = 0
x = 16/7
x = 19/8


Input: Solve the equation 7x - 119/3 = 0

Output:
7x - 119/3 = 0
7x = 119/3
x = 119/3 / 7
x = 17/3


Input: Solve quickly: x^3 + 179/72x^2 + 49/96x - 19/32 = 0

Output:
x^3 + 179/72x^2 + 49/96x - 19/32 = 0
(x - -19/9)(x - 3/8)(x - -3/4) = 0
x - -19/9 = 0
x - 3/8 = 0
x - -3/4 = 0
x = -19/9
x = 3/8
x = -3/4


Input: What value of x satisfies x^3 + 22/15x^2 - 721/60x + 147/20 = 0

Output:
x^3 + 22/15x^2 - 721/60x + 147/20 = 0
(x - 7/10)(x - -9/2)(x - 7/3) = 0
x - 7/10 = 0
x - -9/2 = 0
x - 7/3 = 0
x = 7/10
x = -9/2
x = 7/3


Input: Determine x in 4x + 36 = 0

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


Input: What value of x satisfies 7x - 63/4 = 0

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


Input: Find x in 6x - 14 = 0

Output:
6x - 14 = 0
6x = 14
x = 14 / 6
x = 7/3


Input: Find the solution to x^2 - 37/2x - 19/2 = 0

Output:
x^2 - 37/2x - 19/2 = 0
(x - -1/2)(x - 19) = 0
x - -1/2 = 0  or  x - 19 = 0
x = -1/2
x = 19


Input: What value of x satisfies 5x - 75/7 = 0

Output:
5x - 75/7 = 0
5x = 75/7
x = 75/7 / 5
x = 15/7


Input: Solve the equation 4x + 56/3 = 0

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


Input:
Find x and y such that
2x + 10y = 81/4
2x + 9y = 149/8

Output:
2x + 10y = 81/4
2x + 9y = 149/8

Using elimination
2*(2x + 10y = 81/4)
2*(2x + 9y = 149/8)
4x + 20y = 81/2
4x + 18y = 149/4
Subtract equations
2y = 13/4
y = 13/4/2
y = 13/8

Substitute y
2x + 10(13/8) = 81/4
2x = 4
x = 4/2
x = 2


Input: Find the solution to x^2 - 18x + 17 = 0

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


Input:
Solve the equations:
8x + 4y = -19
1x + 7y = -71/8

Output:
8x + 4y = -19
1x + 7y = -71/8

Using elimination
1*(8x + 4y = -19)
8*(1x + 7y = -71/8)
8x + 4y = -19
8x + 56y = -71
Subtract equations
-52y = 52
y = 52/-52
y = -1

Substitute y
8x + 4(-1) = -19
8x = -15
x = -15/8
x = -15/8


Input: Find x in 2x - 19 = 0

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


Input:
Find x and y such that
10x + 8y = 28
6x + 5y = 18

Output:
10x + 8y = 28
6x + 5y = 18

Using elimination
6*(10x + 8y = 28)
10*(6x + 5y = 18)
60x + 48y = 168
60x + 50y = 180
Subtract equations
-2y = -12
y = -12/-2
y = 6

Substitute y
10x + 8(6) = 28
10x = -20
x = -20/10
x = -2


Input: Solve the equation 9x - 99/2 = 0

Output:
9x - 99/2 = 0
9x = 99/2
x = 99/2 / 9
x = 11/2


Input: Find x for x^2 + 41/5x - 36/5 = 0

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


Input: Compute the solution of x^2 + 75/14x + 50/7 = 0

Output:
x^2 + 75/14x + 50/7 = 0
(x - -20/7)(x - -5/2) = 0
x - -20/7 = 0  or  x - -5/2 = 0
x = -20/7
x = -5/2