Input: Find x for x^3 - 61/14x^2 + 5/7x + 8 = 0

Output:
x^3 - 61/14x^2 + 5/7x + 8 = 0
(x - 7/2)(x - -8/7)(x - 2) = 0
x - 7/2 = 0
x - -8/7 = 0
x - 2 = 0
x = 7/2
x = -8/7
x = 2


Input: Determine x in x^3 - 2/5x^2 - 191/5x - 56 = 0

Output:
x^3 - 2/5x^2 - 191/5x - 56 = 0
(x - -5)(x - 7)(x - -8/5) = 0
x - -5 = 0
x - 7 = 0
x - -8/5 = 0
x = -5
x = 7
x = -8/5


Input: What value of x satisfies x^3 - 29/2x^2 + 37/2x + 13 = 0

Output:
x^3 - 29/2x^2 + 37/2x + 13 = 0
(x - -1/2)(x - 13)(x - 2) = 0
x - -1/2 = 0
x - 13 = 0
x - 2 = 0
x = -1/2
x = 13
x = 2


Input: Solve the equation 10x - 140 = 0

Output:
10x - 140 = 0
10x = 140
x = 140 / 10
x = 14


Input: Solve the equation x^2 - 221/30x + 289/30 = 0

Output:
x^2 - 221/30x + 289/30 = 0
(x - 17/10)(x - 17/3) = 0
x - 17/10 = 0  or  x - 17/3 = 0
x = 17/10
x = 17/3


Input: Compute the solution of x^2 - 8/15x - 11/3 = 0

Output:
x^2 - 8/15x - 11/3 = 0
(x - 11/5)(x - -5/3) = 0
x - 11/5 = 0  or  x - -5/3 = 0
x = 11/5
x = -5/3


Input: Compute the solution of x^3 + 221/60x^2 + 229/120x - 17/12 = 0

Output:
x^3 + 221/60x^2 + 229/120x - 17/12 = 0
(x - 2/5)(x - -5/4)(x - -17/6) = 0
x - 2/5 = 0
x - -5/4 = 0
x - -17/6 = 0
x = 2/5
x = -5/4
x = -17/6


Input: Solve quickly: x^3 - 11/8x^2 - 17/16x + 21/16 = 0

Output:
x^3 - 11/8x^2 - 17/16x + 21/16 = 0
(x - 7/8)(x - -1)(x - 3/2) = 0
x - 7/8 = 0
x - -1 = 0
x - 3/2 = 0
x = 7/8
x = -1
x = 3/2


Input: What value of x satisfies x^3 - 101/5x^2 + 2083/25x - 399/5 = 0

Output:
x^3 - 101/5x^2 + 2083/25x - 399/5 = 0
(x - 7/5)(x - 19/5)(x - 15) = 0
x - 7/5 = 0
x - 19/5 = 0
x - 15 = 0
x = 7/5
x = 19/5
x = 15


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

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


Input: Compute the solution of 4x + 12/5 = 0

Output:
4x + 12/5 = 0
4x = -12/5
x = -12/5 / 4
x = -3/5


Input: Determine x in 2x + 16 = 0

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


Input: Find x for 2x + 40/7 = 0

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


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

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


Input: What value of x satisfies x^2 + 4x + 3 = 0

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


Input:
Solve the system:
6x + 5y = 14
6x + 10y = 28

Output:
6x + 5y = 14
6x + 10y = 28

Using elimination
6*(6x + 5y = 14)
6*(6x + 10y = 28)
36x + 30y = 84
36x + 60y = 168
Subtract equations
-30y = -84
y = -84/-30
y = 14/5

Substitute y
6x + 5(14/5) = 14
6x = 0
x = 0/6
x = 0


Input:
Solve the equations:
10x + 1y = 193/35
10x + 9y = 137/35

Output:
10x + 1y = 193/35
10x + 9y = 137/35

Using elimination
10*(10x + 1y = 193/35)
10*(10x + 9y = 137/35)
100x + 10y = 386/7
100x + 90y = 274/7
Subtract equations
-80y = 16
y = 16/-80
y = -1/5

Substitute y
10x + 1(-1/5) = 193/35
10x = 40/7
x = 40/7/10
x = 4/7


Input: Find the solution to x^3 - 125/28x^2 - 183/28x + 135/7 = 0

Output:
x^3 - 125/28x^2 - 183/28x + 135/7 = 0
(x - 12/7)(x - 5)(x - -9/4) = 0
x - 12/7 = 0
x - 5 = 0
x - -9/4 = 0
x = 12/7
x = 5
x = -9/4


Input:
Find x and y such that
7x + 3y = 1/8
5x + 7y = -95/24

Output:
7x + 3y = 1/8
5x + 7y = -95/24

Using elimination
5*(7x + 3y = 1/8)
7*(5x + 7y = -95/24)
35x + 15y = 5/8
35x + 49y = -665/24
Subtract equations
-34y = 85/3
y = 85/3/-34
y = -5/6

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


Input: Find x for x^3 + 83/24x^2 + 21/8x  = 0

Output:
x^3 + 83/24x^2 + 21/8x  = 0
(x - -7/3)(x - 0)(x - -9/8) = 0
x - -7/3 = 0
x - 0 = 0
x - -9/8 = 0
x = -7/3
x = 0
x = -9/8


Input: Find x in x^3 + 301/30x^2 + 301/10x + 117/5 = 0

Output:
x^3 + 301/30x^2 + 301/10x + 117/5 = 0
(x - -13/3)(x - -9/2)(x - -6/5) = 0
x - -13/3 = 0
x - -9/2 = 0
x - -6/5 = 0
x = -13/3
x = -9/2
x = -6/5


Input: Solve x^2 - 5/2x + 63/50 = 0

Output:
x^2 - 5/2x + 63/50 = 0
(x - 9/5)(x - 7/10) = 0
x - 9/5 = 0  or  x - 7/10 = 0
x = 9/5
x = 7/10


Input: Find x for x^3 + 200/63x^2 - 1/9x - 40/21 = 0

Output:
x^3 + 200/63x^2 - 1/9x - 40/21 = 0
(x - 5/7)(x - -3)(x - -8/9) = 0
x - 5/7 = 0
x - -3 = 0
x - -8/9 = 0
x = 5/7
x = -3
x = -8/9


Input: Solve x^2 + 19/6x + 5/3 = 0

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


Input: Solve quickly: x^3 - 10/3x^2 + 16/9x  = 0

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


Input:
Solve simultaneously:
7x + 10y = 9
10x + 2y = -23/35

Output:
7x + 10y = 9
10x + 2y = -23/35

Using elimination
10*(7x + 10y = 9)
7*(10x + 2y = -23/35)
70x + 100y = 90
70x + 14y = -23/5
Subtract equations
86y = 473/5
y = 473/5/86
y = 11/10

Substitute y
7x + 10(11/10) = 9
7x = -2
x = -2/7
x = -2/7


Input:
Solve the equations:
6x + 9y = 20
7x + 7y = 70/3

Output:
6x + 9y = 20
7x + 7y = 70/3

Using elimination
7*(6x + 9y = 20)
6*(7x + 7y = 70/3)
42x + 63y = 140
42x + 42y = 140
Subtract equations
21y = 0
y = 0/21
y = 0

Substitute y
6x + 9(0) = 20
6x = 20
x = 20/6
x = 10/3


Input: Determine x in x^2 - 59/90x - 22/45 = 0

Output:
x^2 - 59/90x - 22/45 = 0
(x - 11/10)(x - -4/9) = 0
x - 11/10 = 0  or  x - -4/9 = 0
x = 11/10
x = -4/9


Input: Compute the solution of x^2 + 10/3x + 17/12 = 0

Output:
x^2 + 10/3x + 17/12 = 0
(x - -1/2)(x - -17/6) = 0
x - -1/2 = 0  or  x - -17/6 = 0
x = -1/2
x = -17/6


Input:
Solve simultaneously:
2x + 5y = 46
9x + 2y = 166

Output:
2x + 5y = 46
9x + 2y = 166

Using elimination
9*(2x + 5y = 46)
2*(9x + 2y = 166)
18x + 45y = 414
18x + 4y = 332
Subtract equations
41y = 82
y = 82/41
y = 2

Substitute y
2x + 5(2) = 46
2x = 36
x = 36/2
x = 18


Input: Find the solution to x^3 + 297/28x^2 + 755/28x - 57/14 = 0

Output:
x^3 + 297/28x^2 + 755/28x - 57/14 = 0
(x - -6)(x - 1/7)(x - -19/4) = 0
x - -6 = 0
x - 1/7 = 0
x - -19/4 = 0
x = -6
x = 1/7
x = -19/4


Input: Find x in x^2 - 125/7x - 300/7 = 0

Output:
x^2 - 125/7x - 300/7 = 0
(x - -15/7)(x - 20) = 0
x - -15/7 = 0  or  x - 20 = 0
x = -15/7
x = 20


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

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


Input: Find the solution to x^2 - 17/3x + 22/3 = 0

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


Input:
Solve the system:
1x + 1y = 53/4
7x + 10y = 169/2

Output:
1x + 1y = 53/4
7x + 10y = 169/2

Using elimination
7*(1x + 1y = 53/4)
1*(7x + 10y = 169/2)
7x + 7y = 371/4
7x + 10y = 169/2
Subtract equations
-3y = 33/4
y = 33/4/-3
y = -11/4

Substitute y
1x + 1(-11/4) = 53/4
1x = 16
x = 16/1
x = 16


Input: Solve x^3 - 5x^2 + 3/4x + 63/4 = 0

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


Input: Solve 5x - 95/4 = 0

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


Input: Find x for x^2 - 134/35x + 17/5 = 0

Output:
x^2 - 134/35x + 17/5 = 0
(x - 7/5)(x - 17/7) = 0
x - 7/5 = 0  or  x - 17/7 = 0
x = 7/5
x = 17/7


Input: Compute the solution of 2x - 26/7 = 0

Output:
2x - 26/7 = 0
2x = 26/7
x = 26/7 / 2
x = 13/7


Input: What value of x satisfies x^3 - 84/5x^2 - 209/5x  = 0

Output:
x^3 - 84/5x^2 - 209/5x  = 0
(x - -11/5)(x - 19)(x - 0) = 0
x - -11/5 = 0
x - 19 = 0
x - 0 = 0
x = -11/5
x = 19
x = 0


Input: Solve the equation x^3 + 7x^2 + 275/36x - 425/36 = 0

Output:
x^3 + 7x^2 + 275/36x - 425/36 = 0
(x - -5)(x - 5/6)(x - -17/6) = 0
x - -5 = 0
x - 5/6 = 0
x - -17/6 = 0
x = -5
x = 5/6
x = -17/6


Input: Solve quickly: 5x + 25/8 = 0

Output:
5x + 25/8 = 0
5x = -25/8
x = -25/8 / 5
x = -5/8


Input: Find the solution to x^2 + 32/15x + 11/20 = 0

Output:
x^2 + 32/15x + 11/20 = 0
(x - -3/10)(x - -11/6) = 0
x - -3/10 = 0  or  x - -11/6 = 0
x = -3/10
x = -11/6


Input: Find x for 4x + 12 = 0

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


Input: Solve quickly: x^2 + 31/9x + 76/27 = 0

Output:
x^2 + 31/9x + 76/27 = 0
(x - -19/9)(x - -4/3) = 0
x - -19/9 = 0  or  x - -4/3 = 0
x = -19/9
x = -4/3


Input: What value of x satisfies x^2 + 7/10x - 13/5 = 0

Output:
x^2 + 7/10x - 13/5 = 0
(x - -2)(x - 13/10) = 0
x - -2 = 0  or  x - 13/10 = 0
x = -2
x = 13/10


Input: Compute the solution of x^2 + 21/2x + 55/2 = 0

Output:
x^2 + 21/2x + 55/2 = 0
(x - -5)(x - -11/2) = 0
x - -5 = 0  or  x - -11/2 = 0
x = -5
x = -11/2


Input: Find the solution to 1x + 17/7 = 0

Output:
1x + 17/7 = 0
1x = -17/7
x = -17/7 / 1
x = -17/7


Input: Solve quickly: x^3 + 77/24x^2 - 305/48x - 475/24 = 0

Output:
x^3 + 77/24x^2 - 305/48x - 475/24 = 0
(x - -19/8)(x - 5/2)(x - -10/3) = 0
x - -19/8 = 0
x - 5/2 = 0
x - -10/3 = 0
x = -19/8
x = 5/2
x = -10/3


Input:
Solve the equations:
8x + 10y = 808/15
10x + 4y = 32/3

Output:
8x + 10y = 808/15
10x + 4y = 32/3

Using elimination
10*(8x + 10y = 808/15)
8*(10x + 4y = 32/3)
80x + 100y = 1616/3
80x + 32y = 256/3
Subtract equations
68y = 1360/3
y = 1360/3/68
y = 20/3

Substitute y
8x + 10(20/3) = 808/15
8x = -64/5
x = -64/5/8
x = -8/5


Input:
Solve the system:
1x + 9y = 144/5
6x + 6y = 48/5

Output:
1x + 9y = 144/5
6x + 6y = 48/5

Using elimination
6*(1x + 9y = 144/5)
1*(6x + 6y = 48/5)
6x + 54y = 864/5
6x + 6y = 48/5
Subtract equations
48y = 816/5
y = 816/5/48
y = 17/5

Substitute y
1x + 9(17/5) = 144/5
1x = -9/5
x = -9/5/1
x = -9/5


Input: Solve the equation x^3 - 33/8x^2 + 31/32x + 195/32 = 0

Output:
x^3 - 33/8x^2 + 31/32x + 195/32 = 0
(x - 15/8)(x - -1)(x - 13/4) = 0
x - 15/8 = 0
x - -1 = 0
x - 13/4 = 0
x = 15/8
x = -1
x = 13/4


Input:
Solve the equations:
7x + 2y = -32/5
9x + 10y = -134/5

Output:
7x + 2y = -32/5
9x + 10y = -134/5

Using elimination
9*(7x + 2y = -32/5)
7*(9x + 10y = -134/5)
63x + 18y = -288/5
63x + 70y = -938/5
Subtract equations
-52y = 130
y = 130/-52
y = -5/2

Substitute y
7x + 2(-5/2) = -32/5
7x = -7/5
x = -7/5/7
x = -1/5


Input:
Solve simultaneously:
5x + 8y = -117
4x + 3y = -213/5

Output:
5x + 8y = -117
4x + 3y = -213/5

Using elimination
4*(5x + 8y = -117)
5*(4x + 3y = -213/5)
20x + 32y = -468
20x + 15y = -213
Subtract equations
17y = -255
y = -255/17
y = -15

Substitute y
5x + 8(-15) = -117
5x = 3
x = 3/5
x = 3/5


Input: Solve the equation x^2 - 22/5x + 8/5 = 0

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


Input:
Find x and y such that
6x + 10y = -6
9x + 2y = -19/5

Output:
6x + 10y = -6
9x + 2y = -19/5

Using elimination
9*(6x + 10y = -6)
6*(9x + 2y = -19/5)
54x + 90y = -54
54x + 12y = -114/5
Subtract equations
78y = -156/5
y = -156/5/78
y = -2/5

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


Input: Find x in x^3 - 102/7x^2 + 333/7x + 162/7 = 0

Output:
x^3 - 102/7x^2 + 333/7x + 162/7 = 0
(x - 9)(x - 6)(x - -3/7) = 0
x - 9 = 0
x - 6 = 0
x - -3/7 = 0
x = 9
x = 6
x = -3/7


Input: Find x in 2x - 20/7 = 0

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


Input:
Find x and y such that
7x + 4y = 101/2
6x + 6y = 51

Output:
7x + 4y = 101/2
6x + 6y = 51

Using elimination
6*(7x + 4y = 101/2)
7*(6x + 6y = 51)
42x + 24y = 303
42x + 42y = 357
Subtract equations
-18y = -54
y = -54/-18
y = 3

Substitute y
7x + 4(3) = 101/2
7x = 77/2
x = 77/2/7
x = 11/2


Input: Solve quickly: x^2 + 2x + 1 = 0

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


Input: Determine x in x^3 + 29/10x^2 - 12/5x - 63/10 = 0

Output:
x^3 + 29/10x^2 - 12/5x - 63/10 = 0
(x - -3)(x - -7/5)(x - 3/2) = 0
x - -3 = 0
x - -7/5 = 0
x - 3/2 = 0
x = -3
x = -7/5
x = 3/2


Input: Find x for 8x - 72 = 0

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


Input:
Solve simultaneously:
6x + 5y = 63/2
3x + 4y = 27

Output:
6x + 5y = 63/2
3x + 4y = 27

Using elimination
3*(6x + 5y = 63/2)
6*(3x + 4y = 27)
18x + 15y = 189/2
18x + 24y = 162
Subtract equations
-9y = -135/2
y = -135/2/-9
y = 15/2

Substitute y
6x + 5(15/2) = 63/2
6x = -6
x = -6/6
x = -1


Input: Find x in x^3 - 15/4x^2 - 139/64x + 1365/128 = 0

Output:
x^3 - 15/4x^2 - 139/64x + 1365/128 = 0
(x - 7/2)(x - 15/8)(x - -13/8) = 0
x - 7/2 = 0
x - 15/8 = 0
x - -13/8 = 0
x = 7/2
x = 15/8
x = -13/8


Input: Compute the solution of 4x - 80 = 0

Output:
4x - 80 = 0
4x = 80
x = 80 / 4
x = 20


Input: What value of x satisfies x^2 + 22/5x - 91/5 = 0

Output:
x^2 + 22/5x - 91/5 = 0
(x - 13/5)(x - -7) = 0
x - 13/5 = 0  or  x - -7 = 0
x = 13/5
x = -7


Input:
Solve the equations:
2x + 8y = 38/9
9x + 7y = -1/3

Output:
2x + 8y = 38/9
9x + 7y = -1/3

Using elimination
9*(2x + 8y = 38/9)
2*(9x + 7y = -1/3)
18x + 72y = 38
18x + 14y = -2/3
Subtract equations
58y = 116/3
y = 116/3/58
y = 2/3

Substitute y
2x + 8(2/3) = 38/9
2x = -10/9
x = -10/9/2
x = -5/9


Input: Find x for 1x  = 0

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


Input: What value of x satisfies x^3 - 21/4x^2 + 9/8x + 135/8 = 0

Output:
x^3 - 21/4x^2 + 9/8x + 135/8 = 0
(x - -3/2)(x - 3)(x - 15/4) = 0
x - -3/2 = 0
x - 3 = 0
x - 15/4 = 0
x = -3/2
x = 3
x = 15/4


Input: Find x in 2x - 22/5 = 0

Output:
2x - 22/5 = 0
2x = 22/5
x = 22/5 / 2
x = 11/5


Input: Solve quickly: 7x + 56 = 0

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


Input: Solve the equation 3x + 33/8 = 0

Output:
3x + 33/8 = 0
3x = -33/8
x = -33/8 / 3
x = -11/8


Input: Determine x in 3x - 18 = 0

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


Input: Find x for x^2 + 16/3x + 20/3 = 0

Output:
x^2 + 16/3x + 20/3 = 0
(x - -2)(x - -10/3) = 0
x - -2 = 0  or  x - -10/3 = 0
x = -2
x = -10/3


Input:
Solve simultaneously:
9x + 8y = 41/2
2x + 9y = 1/24

Output:
9x + 8y = 41/2
2x + 9y = 1/24

Using elimination
2*(9x + 8y = 41/2)
9*(2x + 9y = 1/24)
18x + 16y = 41
18x + 81y = 3/8
Subtract equations
-65y = 325/8
y = 325/8/-65
y = -5/8

Substitute y
9x + 8(-5/8) = 41/2
9x = 51/2
x = 51/2/9
x = 17/6


Input: Solve x^3 + 4x^2 + 1x - 6 = 0

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


Input:
Solve the equations:
9x + 10y = -88
5x + 3y = -31

Output:
9x + 10y = -88
5x + 3y = -31

Using elimination
5*(9x + 10y = -88)
9*(5x + 3y = -31)
45x + 50y = -440
45x + 27y = -279
Subtract equations
23y = -161
y = -161/23
y = -7

Substitute y
9x + 10(-7) = -88
9x = -18
x = -18/9
x = -2


Input:
Solve the system:
5x + 5y = 179/14
9x + 3y = 1251/70

Output:
5x + 5y = 179/14
9x + 3y = 1251/70

Using elimination
9*(5x + 5y = 179/14)
5*(9x + 3y = 1251/70)
45x + 45y = 1611/14
45x + 15y = 1251/14
Subtract equations
30y = 180/7
y = 180/7/30
y = 6/7

Substitute y
5x + 5(6/7) = 179/14
5x = 17/2
x = 17/2/5
x = 17/10


Input: Find x in x^2 - 26/9x - 1/3 = 0

Output:
x^2 - 26/9x - 1/3 = 0
(x - -1/9)(x - 3) = 0
x - -1/9 = 0  or  x - 3 = 0
x = -1/9
x = 3


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

Output:
x^2 - 2/5x - 24/5 = 0
(x - 12/5)(x - -2) = 0
x - 12/5 = 0  or  x - -2 = 0
x = 12/5
x = -2


Input:
Solve the equations:
10x + 4y = 188/7
8x + 4y = 160/7

Output:
10x + 4y = 188/7
8x + 4y = 160/7

Using elimination
8*(10x + 4y = 188/7)
10*(8x + 4y = 160/7)
80x + 32y = 1504/7
80x + 40y = 1600/7
Subtract equations
-8y = -96/7
y = -96/7/-8
y = 12/7

Substitute y
10x + 4(12/7) = 188/7
10x = 20
x = 20/10
x = 2


Input: Find the solution to 10x - 36 = 0

Output:
10x - 36 = 0
10x = 36
x = 36 / 10
x = 18/5


Input: Find x in x^3 + 19/2x^2 - 153/2x + 90 = 0

Output:
x^3 + 19/2x^2 - 153/2x + 90 = 0
(x - -15)(x - 4)(x - 3/2) = 0
x - -15 = 0
x - 4 = 0
x - 3/2 = 0
x = -15
x = 4
x = 3/2


Input: What value of x satisfies x^2 + 1/2x - 15/2 = 0

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


Input: Compute the solution of x^2 - 41/7x + 52/7 = 0

Output:
x^2 - 41/7x + 52/7 = 0
(x - 4)(x - 13/7) = 0
x - 4 = 0  or  x - 13/7 = 0
x = 4
x = 13/7


Input: Find x for x^2 + 15/2x + 27/2 = 0

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


Input: Find the solution to 10x - 95/2 = 0

Output:
10x - 95/2 = 0
10x = 95/2
x = 95/2 / 10
x = 19/4


Input: Find x for 10x - 35/4 = 0

Output:
10x - 35/4 = 0
10x = 35/4
x = 35/4 / 10
x = 7/8


Input: Solve the equation x^2 + 10x + 221/9 = 0

Output:
x^2 + 10x + 221/9 = 0
(x - -17/3)(x - -13/3) = 0
x - -17/3 = 0  or  x - -13/3 = 0
x = -17/3
x = -13/3


Input: What value of x satisfies x^3 - 74/45x^2 + 11/15x - 4/45 = 0

Output:
x^3 - 74/45x^2 + 11/15x - 4/45 = 0
(x - 4/9)(x - 1/5)(x - 1) = 0
x - 4/9 = 0
x - 1/5 = 0
x - 1 = 0
x = 4/9
x = 1/5
x = 1


Input: Solve quickly: 6x + 14 = 0

Output:
6x + 14 = 0
6x = -14
x = -14 / 6
x = -7/3


Input:
Solve the system:
2x + 9y = 114/5
1x + 7y = 47/5

Output:
2x + 9y = 114/5
1x + 7y = 47/5

Using elimination
1*(2x + 9y = 114/5)
2*(1x + 7y = 47/5)
2x + 9y = 114/5
2x + 14y = 94/5
Subtract equations
-5y = 4
y = 4/-5
y = -4/5

Substitute y
2x + 9(-4/5) = 114/5
2x = 30
x = 30/2
x = 15


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

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


Input: Solve x^2 - 61/20x + 9/5 = 0

Output:
x^2 - 61/20x + 9/5 = 0
(x - 9/4)(x - 4/5) = 0
x - 9/4 = 0  or  x - 4/5 = 0
x = 9/4
x = 4/5


Input: Find x in x^3 + 83/21x^2 - 2/7x - 8/21 = 0

Output:
x^3 + 83/21x^2 - 2/7x - 8/21 = 0
(x - -2/7)(x - -4)(x - 1/3) = 0
x - -2/7 = 0
x - -4 = 0
x - 1/3 = 0
x = -2/7
x = -4
x = 1/3


Input: What value of x satisfies x^3 - 35/6x^2 + 59/6x - 5 = 0

Output:
x^3 - 35/6x^2 + 59/6x - 5 = 0
(x - 3/2)(x - 10/3)(x - 1) = 0
x - 3/2 = 0
x - 10/3 = 0
x - 1 = 0
x = 3/2
x = 10/3
x = 1


Input:
Solve the equations:
1x + 5y = 47
1x + 3y = 29

Output:
1x + 5y = 47
1x + 3y = 29

Using elimination
1*(1x + 5y = 47)
1*(1x + 3y = 29)
1x + 5y = 47
1x + 3y = 29
Subtract equations
2y = 18
y = 18/2
y = 9

Substitute y
1x + 5(9) = 47
1x = 2
x = 2/1
x = 2


Input:
Solve simultaneously:
6x + 3y = 183/7
2x + 10y = 106/7

Output:
6x + 3y = 183/7
2x + 10y = 106/7

Using elimination
2*(6x + 3y = 183/7)
6*(2x + 10y = 106/7)
12x + 6y = 366/7
12x + 60y = 636/7
Subtract equations
-54y = -270/7
y = -270/7/-54
y = 5/7

Substitute y
6x + 3(5/7) = 183/7
6x = 24
x = 24/6
x = 4


Input: Solve the equation x^2 + 9/10x - 7/10 = 0

Output:
x^2 + 9/10x - 7/10 = 0
(x - -7/5)(x - 1/2) = 0
x - -7/5 = 0  or  x - 1/2 = 0
x = -7/5
x = 1/2


Input: Find the solution to x^2 - 33/7x + 20/7 = 0

Output:
x^2 - 33/7x + 20/7 = 0
(x - 4)(x - 5/7) = 0
x - 4 = 0  or  x - 5/7 = 0
x = 4
x = 5/7


Input: Compute the solution of x^2 + 32/9x - 65/9 = 0

Output:
x^2 + 32/9x - 65/9 = 0
(x - 13/9)(x - -5) = 0
x - 13/9 = 0  or  x - -5 = 0
x = 13/9
x = -5


Input: Solve the equation 4x + 38/5 = 0

Output:
4x + 38/5 = 0
4x = -38/5
x = -38/5 / 4
x = -19/10


Input: Find x in 7x - 133/3 = 0

Output:
7x - 133/3 = 0
7x = 133/3
x = 133/3 / 7
x = 19/3


Input: Compute the solution of x^3 + 21/5x^2 + 104/25x + 84/125 = 0

Output:
x^3 + 21/5x^2 + 104/25x + 84/125 = 0
(x - -14/5)(x - -1/5)(x - -6/5) = 0
x - -14/5 = 0
x - -1/5 = 0
x - -6/5 = 0
x = -14/5
x = -1/5
x = -6/5


Input: Solve x^2 + 17/3x + 14/3 = 0

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


Input: Solve the equation x^2 + 29/2x - 15/2 = 0

Output:
x^2 + 29/2x - 15/2 = 0
(x - 1/2)(x - -15) = 0
x - 1/2 = 0  or  x - -15 = 0
x = 1/2
x = -15


Input:
Solve the equations:
4x + 1y = 11
4x + 8y = 60

Output:
4x + 1y = 11
4x + 8y = 60

Using elimination
4*(4x + 1y = 11)
4*(4x + 8y = 60)
16x + 4y = 44
16x + 32y = 240
Subtract equations
-28y = -196
y = -196/-28
y = 7

Substitute y
4x + 1(7) = 11
4x = 4
x = 4/4
x = 1


Input:
Solve simultaneously:
4x + 7y = -348/5
4x + 5y = -248/5

Output:
4x + 7y = -348/5
4x + 5y = -248/5

Using elimination
4*(4x + 7y = -348/5)
4*(4x + 5y = -248/5)
16x + 28y = -1392/5
16x + 20y = -992/5
Subtract equations
8y = -80
y = -80/8
y = -10

Substitute y
4x + 7(-10) = -348/5
4x = 2/5
x = 2/5/4
x = 1/10


Input:
Solve the equations:
3x + 2y = 61/7
6x + 8y = 262/7

Output:
3x + 2y = 61/7
6x + 8y = 262/7

Using elimination
6*(3x + 2y = 61/7)
3*(6x + 8y = 262/7)
18x + 12y = 366/7
18x + 24y = 786/7
Subtract equations
-12y = -60
y = -60/-12
y = 5

Substitute y
3x + 2(5) = 61/7
3x = -9/7
x = -9/7/3
x = -3/7


Input:
Solve simultaneously:
10x + 9y = -163/10
1x + 10y = -8

Output:
10x + 9y = -163/10
1x + 10y = -8

Using elimination
1*(10x + 9y = -163/10)
10*(1x + 10y = -8)
10x + 9y = -163/10
10x + 100y = -80
Subtract equations
-91y = 637/10
y = 637/10/-91
y = -7/10

Substitute y
10x + 9(-7/10) = -163/10
10x = -10
x = -10/10
x = -1


Input: Find x for 2x - 2 = 0

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


Input: Compute the solution of x^2 - 25/6x + 13/3 = 0

Output:
x^2 - 25/6x + 13/3 = 0
(x - 2)(x - 13/6) = 0
x - 2 = 0  or  x - 13/6 = 0
x = 2
x = 13/6


Input: Solve the equation x^3 + 5/6x^2 - 22/3x + 10/3 = 0

Output:
x^3 + 5/6x^2 - 22/3x + 10/3 = 0
(x - -10/3)(x - 1/2)(x - 2) = 0
x - -10/3 = 0
x - 1/2 = 0
x - 2 = 0
x = -10/3
x = 1/2
x = 2


Input: Determine x in 9x + 27/10 = 0

Output:
9x + 27/10 = 0
9x = -27/10
x = -27/10 / 9
x = -3/10


Input: Determine x in x^3 - 339/35x^2 - 162/5x + 1944/35 = 0

Output:
x^3 - 339/35x^2 - 162/5x + 1944/35 = 0
(x - 9/7)(x - 12)(x - -18/5) = 0
x - 9/7 = 0
x - 12 = 0
x - -18/5 = 0
x = 9/7
x = 12
x = -18/5


Input: Find x in 7x - 35/4 = 0

Output:
7x - 35/4 = 0
7x = 35/4
x = 35/4 / 7
x = 5/4


Input: Determine x in x^3 + 41/30x^2 - 347/150x + 2/5 = 0

Output:
x^3 + 41/30x^2 - 347/150x + 2/5 = 0
(x - 5/6)(x - 1/5)(x - -12/5) = 0
x - 5/6 = 0
x - 1/5 = 0
x - -12/5 = 0
x = 5/6
x = 1/5
x = -12/5


Input: Solve 9x - 10 = 0

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


Input: Find the solution to 5x + 100 = 0

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


Input: Solve x^2 + 34/7x - 48/7 = 0

Output:
x^2 + 34/7x - 48/7 = 0
(x - -6)(x - 8/7) = 0
x - -6 = 0  or  x - 8/7 = 0
x = -6
x = 8/7


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

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


Input: Solve the equation x^2 + 23/14x + 3/14 = 0

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


Input: Find x for x^2 + 27/10x + 38/25 = 0

Output:
x^2 + 27/10x + 38/25 = 0
(x - -4/5)(x - -19/10) = 0
x - -4/5 = 0  or  x - -19/10 = 0
x = -4/5
x = -19/10


Input:
Solve simultaneously:
10x + 10y = -205/9
2x + 1y = -73/18

Output:
10x + 10y = -205/9
2x + 1y = -73/18

Using elimination
2*(10x + 10y = -205/9)
10*(2x + 1y = -73/18)
20x + 20y = -410/9
20x + 10y = -365/9
Subtract equations
10y = -5
y = -5/10
y = -1/2

Substitute y
10x + 10(-1/2) = -205/9
10x = -160/9
x = -160/9/10
x = -16/9


Input: Compute the solution of x^2 + 47/3x + 10 = 0

Output:
x^2 + 47/3x + 10 = 0
(x - -15)(x - -2/3) = 0
x - -15 = 0  or  x - -2/3 = 0
x = -15
x = -2/3


Input: What value of x satisfies x^3 - 151/7x^2 + 32x - 80/7 = 0

Output:
x^3 - 151/7x^2 + 32x - 80/7 = 0
(x - 1)(x - 20)(x - 4/7) = 0
x - 1 = 0
x - 20 = 0
x - 4/7 = 0
x = 1
x = 20
x = 4/7


Input: Find x for x^3 - 8x^2 + 1251/100x - 153/50 = 0

Output:
x^3 - 8x^2 + 1251/100x - 153/50 = 0
(x - 3/10)(x - 6)(x - 17/10) = 0
x - 3/10 = 0
x - 6 = 0
x - 17/10 = 0
x = 3/10
x = 6
x = 17/10


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

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


Input: Determine x in 5x - 3 = 0

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


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

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


Input: Compute the solution of 9x + 36/7 = 0

Output:
9x + 36/7 = 0
9x = -36/7
x = -36/7 / 9
x = -4/7


Input: Solve the equation x^3 + 37/12x^2 + 1/3x - 17/16 = 0

Output:
x^3 + 37/12x^2 + 1/3x - 17/16 = 0
(x - -17/6)(x - 1/2)(x - -3/4) = 0
x - -17/6 = 0
x - 1/2 = 0
x - -3/4 = 0
x = -17/6
x = 1/2
x = -3/4


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

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


Input: Solve quickly: 4x + 16/7 = 0

Output:
4x + 16/7 = 0
4x = -16/7
x = -16/7 / 4
x = -4/7


Input: Determine x in 5x + 45/4 = 0

Output:
5x + 45/4 = 0
5x = -45/4
x = -45/4 / 5
x = -9/4


Input: Find x for x^2 + 21/4x + 49/8 = 0

Output:
x^2 + 21/4x + 49/8 = 0
(x - -7/2)(x - -7/4) = 0
x - -7/2 = 0  or  x - -7/4 = 0
x = -7/2
x = -7/4


Input:
Solve simultaneously:
6x + 9y = 21
6x + 3y = 33

Output:
6x + 9y = 21
6x + 3y = 33

Using elimination
6*(6x + 9y = 21)
6*(6x + 3y = 33)
36x + 54y = 126
36x + 18y = 198
Subtract equations
36y = -72
y = -72/36
y = -2

Substitute y
6x + 9(-2) = 21
6x = 39
x = 39/6
x = 13/2


Input: Find x for x^3 - 353/30x^2 + 239/30x + 77/15 = 0

Output:
x^3 - 353/30x^2 + 239/30x + 77/15 = 0
(x - 11)(x - 7/6)(x - -2/5) = 0
x - 11 = 0
x - 7/6 = 0
x - -2/5 = 0
x = 11
x = 7/6
x = -2/5


Input:
Solve simultaneously:
6x + 9y = -40/7
8x + 6y = -304/21

Output:
6x + 9y = -40/7
8x + 6y = -304/21

Using elimination
8*(6x + 9y = -40/7)
6*(8x + 6y = -304/21)
48x + 72y = -320/7
48x + 36y = -608/7
Subtract equations
36y = 288/7
y = 288/7/36
y = 8/7

Substitute y
6x + 9(8/7) = -40/7
6x = -16
x = -16/6
x = -8/3


Input: Solve 3x + 15 = 0

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


Input: Find x for 6x - 3 = 0

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


Input:
Find x and y such that
1x + 4y = 1/5
6x + 8y = -18/5

Output:
1x + 4y = 1/5
6x + 8y = -18/5

Using elimination
6*(1x + 4y = 1/5)
1*(6x + 8y = -18/5)
6x + 24y = 6/5
6x + 8y = -18/5
Subtract equations
16y = 24/5
y = 24/5/16
y = 3/10

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


Input:
Solve simultaneously:
2x + 10y = 44
1x + 6y = 23

Output:
2x + 10y = 44
1x + 6y = 23

Using elimination
1*(2x + 10y = 44)
2*(1x + 6y = 23)
2x + 10y = 44
2x + 12y = 46
Subtract equations
-2y = -2
y = -2/-2
y = 1

Substitute y
2x + 10(1) = 44
2x = 34
x = 34/2
x = 17


Input: Compute the solution of x^2 - 23/20x + 9/40 = 0

Output:
x^2 - 23/20x + 9/40 = 0
(x - 1/4)(x - 9/10) = 0
x - 1/4 = 0  or  x - 9/10 = 0
x = 1/4
x = 9/10


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

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

Using elimination
4*(9x + 7y = -9/2)
9*(4x + 2y = -7)
36x + 28y = -18
36x + 18y = -63
Subtract equations
10y = 45
y = 45/10
y = 9/2

Substitute y
9x + 7(9/2) = -9/2
9x = -36
x = -36/9
x = -4


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

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


Input:
Solve simultaneously:
3x + 1y = -177/35
8x + 3y = -447/35

Output:
3x + 1y = -177/35
8x + 3y = -447/35

Using elimination
8*(3x + 1y = -177/35)
3*(8x + 3y = -447/35)
24x + 8y = -1416/35
24x + 9y = -1341/35
Subtract equations
-1y = -15/7
y = -15/7/-1
y = 15/7

Substitute y
3x + 1(15/7) = -177/35
3x = -36/5
x = -36/5/3
x = -12/5


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

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


Input: Find x for x^3 - 109/21x^2 + 560/81x - 400/567 = 0

Output:
x^3 - 109/21x^2 + 560/81x - 400/567 = 0
(x - 20/9)(x - 1/9)(x - 20/7) = 0
x - 20/9 = 0
x - 1/9 = 0
x - 20/7 = 0
x = 20/9
x = 1/9
x = 20/7


Input: Find x in 5x + 1 = 0

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


Input:
Find x and y such that
7x + 5y = 157/9
9x + 3y = 11

Output:
7x + 5y = 157/9
9x + 3y = 11

Using elimination
9*(7x + 5y = 157/9)
7*(9x + 3y = 11)
63x + 45y = 157
63x + 21y = 77
Subtract equations
24y = 80
y = 80/24
y = 10/3

Substitute y
7x + 5(10/3) = 157/9
7x = 7/9
x = 7/9/7
x = 1/9


Input: Compute the solution of x^3 - 23/10x^2 - 837/50x + 81/5 = 0

Output:
x^3 - 23/10x^2 - 837/50x + 81/5 = 0
(x - 5)(x - 9/10)(x - -18/5) = 0
x - 5 = 0
x - 9/10 = 0
x - -18/5 = 0
x = 5
x = 9/10
x = -18/5


Input:
Find x and y such that
10x + 10y = -1030/21
8x + 6y = -242/7

Output:
10x + 10y = -1030/21
8x + 6y = -242/7

Using elimination
8*(10x + 10y = -1030/21)
10*(8x + 6y = -242/7)
80x + 80y = -8240/21
80x + 60y = -2420/7
Subtract equations
20y = -140/3
y = -140/3/20
y = -7/3

Substitute y
10x + 10(-7/3) = -1030/21
10x = -180/7
x = -180/7/10
x = -18/7


Input: Find the solution to x^3 - 5/6x^2 - 41/2x - 56/3 = 0

Output:
x^3 - 5/6x^2 - 41/2x - 56/3 = 0
(x - 16/3)(x - -1)(x - -7/2) = 0
x - 16/3 = 0
x - -1 = 0
x - -7/2 = 0
x = 16/3
x = -1
x = -7/2


Input: What value of x satisfies 9x - 63/5 = 0

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


Input:
Solve simultaneously:
3x + 9y = 621/56
10x + 10y = 265/28

Output:
3x + 9y = 621/56
10x + 10y = 265/28

Using elimination
10*(3x + 9y = 621/56)
3*(10x + 10y = 265/28)
30x + 90y = 3105/28
30x + 30y = 795/28
Subtract equations
60y = 165/2
y = 165/2/60
y = 11/8

Substitute y
3x + 9(11/8) = 621/56
3x = -9/7
x = -9/7/3
x = -3/7


Input: Solve the equation x^2 - 67/30x - 7/30 = 0

Output:
x^2 - 67/30x - 7/30 = 0
(x - -1/10)(x - 7/3) = 0
x - -1/10 = 0  or  x - 7/3 = 0
x = -1/10
x = 7/3


Input: Solve quickly: x^3 - 77/10x^2 + 25/2x - 11/5 = 0

Output:
x^3 - 77/10x^2 + 25/2x - 11/5 = 0
(x - 2)(x - 1/5)(x - 11/2) = 0
x - 2 = 0
x - 1/5 = 0
x - 11/2 = 0
x = 2
x = 1/5
x = 11/2


Input:
Solve the equations:
10x + 1y = -86/7
2x + 10y = 120/7

Output:
10x + 1y = -86/7
2x + 10y = 120/7

Using elimination
2*(10x + 1y = -86/7)
10*(2x + 10y = 120/7)
20x + 2y = -172/7
20x + 100y = 1200/7
Subtract equations
-98y = -196
y = -196/-98
y = 2

Substitute y
10x + 1(2) = -86/7
10x = -100/7
x = -100/7/10
x = -10/7


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

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


Input:
Solve simultaneously:
2x + 8y = -34
4x + 2y = -12

Output:
2x + 8y = -34
4x + 2y = -12

Using elimination
4*(2x + 8y = -34)
2*(4x + 2y = -12)
8x + 32y = -136
8x + 4y = -24
Subtract equations
28y = -112
y = -112/28
y = -4

Substitute y
2x + 8(-4) = -34
2x = -2
x = -2/2
x = -1


Input: Solve the equation x^2 + 19/6x - 85/6 = 0

Output:
x^2 + 19/6x - 85/6 = 0
(x - 5/2)(x - -17/3) = 0
x - 5/2 = 0  or  x - -17/3 = 0
x = 5/2
x = -17/3


Input: Solve x^2 + 9/10x - 19/10 = 0

Output:
x^2 + 9/10x - 19/10 = 0
(x - -19/10)(x - 1) = 0
x - -19/10 = 0  or  x - 1 = 0
x = -19/10
x = 1


Input:
Solve the equations:
2x + 7y = -159/8
9x + 6y = -243/4

Output:
2x + 7y = -159/8
9x + 6y = -243/4

Using elimination
9*(2x + 7y = -159/8)
2*(9x + 6y = -243/4)
18x + 63y = -1431/8
18x + 12y = -243/2
Subtract equations
51y = -459/8
y = -459/8/51
y = -9/8

Substitute y
2x + 7(-9/8) = -159/8
2x = -12
x = -12/2
x = -6


Input: Find the solution to x^3 - 28/9x^2 - 361/27x - 170/27 = 0

Output:
x^3 - 28/9x^2 - 361/27x - 170/27 = 0
(x - -2)(x - -5/9)(x - 17/3) = 0
x - -2 = 0
x - -5/9 = 0
x - 17/3 = 0
x = -2
x = -5/9
x = 17/3


Input: Find x for x^3 + 55/18x^2 + 7/3x  = 0

Output:
x^3 + 55/18x^2 + 7/3x  = 0
(x - -14/9)(x - 0)(x - -3/2) = 0
x - -14/9 = 0
x - 0 = 0
x - -3/2 = 0
x = -14/9
x = 0
x = -3/2


Input:
Find x and y such that
6x + 1y = 187/15
10x + 4y = 32/3

Output:
6x + 1y = 187/15
10x + 4y = 32/3

Using elimination
10*(6x + 1y = 187/15)
6*(10x + 4y = 32/3)
60x + 10y = 374/3
60x + 24y = 64
Subtract equations
-14y = 182/3
y = 182/3/-14
y = -13/3

Substitute y
6x + 1(-13/3) = 187/15
6x = 84/5
x = 84/5/6
x = 14/5


Input:
Solve the equations:
4x + 7y = -13
3x + 6y = -21/2

Output:
4x + 7y = -13
3x + 6y = -21/2

Using elimination
3*(4x + 7y = -13)
4*(3x + 6y = -21/2)
12x + 21y = -39
12x + 24y = -42
Subtract equations
-3y = 3
y = 3/-3
y = -1

Substitute y
4x + 7(-1) = -13
4x = -6
x = -6/4
x = -3/2


Input: Solve x^2 + 4/35x - 3/7 = 0

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


Input: Solve x^2 + 23/3x + 34/3 = 0

Output:
x^2 + 23/3x + 34/3 = 0
(x - -17/3)(x - -2) = 0
x - -17/3 = 0  or  x - -2 = 0
x = -17/3
x = -2


Input: Solve the equation x^2 + 44/7x - 96/7 = 0

Output:
x^2 + 44/7x - 96/7 = 0
(x - 12/7)(x - -8) = 0
x - 12/7 = 0  or  x - -8 = 0
x = 12/7
x = -8


Input:
Solve simultaneously:
10x + 6y = -79/2
7x + 2y = -93/4

Output:
10x + 6y = -79/2
7x + 2y = -93/4

Using elimination
7*(10x + 6y = -79/2)
10*(7x + 2y = -93/4)
70x + 42y = -553/2
70x + 20y = -465/2
Subtract equations
22y = -44
y = -44/22
y = -2

Substitute y
10x + 6(-2) = -79/2
10x = -55/2
x = -55/2/10
x = -11/4


Input: Solve quickly: x^2 - 1/2x - 5/18 = 0

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


Input:
Solve the equations:
9x + 2y = 19
1x + 3y = 7/2

Output:
9x + 2y = 19
1x + 3y = 7/2

Using elimination
1*(9x + 2y = 19)
9*(1x + 3y = 7/2)
9x + 2y = 19
9x + 27y = 63/2
Subtract equations
-25y = -25/2
y = -25/2/-25
y = 1/2

Substitute y
9x + 2(1/2) = 19
9x = 18
x = 18/9
x = 2


Input: What value of x satisfies x^3 + 283/210x^2 - 369/70x - 104/15 = 0

Output:
x^3 + 283/210x^2 - 369/70x - 104/15 = 0
(x - 16/7)(x - -13/10)(x - -7/3) = 0
x - 16/7 = 0
x - -13/10 = 0
x - -7/3 = 0
x = 16/7
x = -13/10
x = -7/3


Input: Solve quickly: 3x - 21/4 = 0

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


Input: Compute the solution of 6x + 15/2 = 0

Output:
6x + 15/2 = 0
6x = -15/2
x = -15/2 / 6
x = -5/4


Input: Find the solution to x^2 + 89/14x - 255/14 = 0

Output:
x^2 + 89/14x - 255/14 = 0
(x - 15/7)(x - -17/2) = 0
x - 15/7 = 0  or  x - -17/2 = 0
x = 15/7
x = -17/2


Input: Compute the solution of x^2 + 65/8x - 51/16 = 0

Output:
x^2 + 65/8x - 51/16 = 0
(x - 3/8)(x - -17/2) = 0
x - 3/8 = 0  or  x - -17/2 = 0
x = 3/8
x = -17/2


Input: Determine x in x^2 - 22/35x - 153/35 = 0

Output:
x^2 - 22/35x - 153/35 = 0
(x - -9/5)(x - 17/7) = 0
x - -9/5 = 0  or  x - 17/7 = 0
x = -9/5
x = 17/7


Input: Compute the solution of 7x + 133/2 = 0

Output:
7x + 133/2 = 0
7x = -133/2
x = -133/2 / 7
x = -19/2


Input:
Find x and y such that
6x + 6y = 17/2
6x + 5y = 37/4

Output:
6x + 6y = 17/2
6x + 5y = 37/4

Using elimination
6*(6x + 6y = 17/2)
6*(6x + 5y = 37/4)
36x + 36y = 51
36x + 30y = 111/2
Subtract equations
6y = -9/2
y = -9/2/6
y = -3/4

Substitute y
6x + 6(-3/4) = 17/2
6x = 13
x = 13/6
x = 13/6


Input: Find the solution to x^2 + 89/5x - 18/5 = 0

Output:
x^2 + 89/5x - 18/5 = 0
(x - 1/5)(x - -18) = 0
x - 1/5 = 0  or  x - -18 = 0
x = 1/5
x = -18


Input:
Solve the equations:
7x + 8y = 46
4x + 4y = 20

Output:
7x + 8y = 46
4x + 4y = 20

Using elimination
4*(7x + 8y = 46)
7*(4x + 4y = 20)
28x + 32y = 184
28x + 28y = 140
Subtract equations
4y = 44
y = 44/4
y = 11

Substitute y
7x + 8(11) = 46
7x = -42
x = -42/7
x = -6


Input: Determine x in 3x + 10 = 0

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


Input: Solve x^2 - 157/30x + 19/3 = 0

Output:
x^2 - 157/30x + 19/3 = 0
(x - 19/10)(x - 10/3) = 0
x - 19/10 = 0  or  x - 10/3 = 0
x = 19/10
x = 10/3


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

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


Input:
Solve the equations:
3x + 6y = -13/3
3x + 1y = -8/3

Output:
3x + 6y = -13/3
3x + 1y = -8/3

Using elimination
3*(3x + 6y = -13/3)
3*(3x + 1y = -8/3)
9x + 18y = -13
9x + 3y = -8
Subtract equations
15y = -5
y = -5/15
y = -1/3

Substitute y
3x + 6(-1/3) = -13/3
3x = -7/3
x = -7/3/3
x = -7/9


Input: Find x for 2x + 1 = 0

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


Input: Solve quickly: 7x + 20 = 0

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


Input:
Find x and y such that
10x + 4y = 87/2
5x + 6y = 121/4

Output:
10x + 4y = 87/2
5x + 6y = 121/4

Using elimination
5*(10x + 4y = 87/2)
10*(5x + 6y = 121/4)
50x + 20y = 435/2
50x + 60y = 605/2
Subtract equations
-40y = -85
y = -85/-40
y = 17/8

Substitute y
10x + 4(17/8) = 87/2
10x = 35
x = 35/10
x = 7/2


Input:
Solve the system:
5x + 7y = 97/72
4x + 4y = -35/18

Output:
5x + 7y = 97/72
4x + 4y = -35/18

Using elimination
4*(5x + 7y = 97/72)
5*(4x + 4y = -35/18)
20x + 28y = 97/18
20x + 20y = -175/18
Subtract equations
8y = 136/9
y = 136/9/8
y = 17/9

Substitute y
5x + 7(17/9) = 97/72
5x = -95/8
x = -95/8/5
x = -19/8


Input: Solve the equation x^3 - 399/40x^2 + 1597/80x - 21/2 = 0

Output:
x^3 - 399/40x^2 + 1597/80x - 21/2 = 0
(x - 8/5)(x - 7/8)(x - 15/2) = 0
x - 8/5 = 0
x - 7/8 = 0
x - 15/2 = 0
x = 8/5
x = 7/8
x = 15/2


Input:
Solve simultaneously:
1x + 2y = -74/5
3x + 7y = -219/5

Output:
1x + 2y = -74/5
3x + 7y = -219/5

Using elimination
3*(1x + 2y = -74/5)
1*(3x + 7y = -219/5)
3x + 6y = -222/5
3x + 7y = -219/5
Subtract equations
-1y = -3/5
y = -3/5/-1
y = 3/5

Substitute y
1x + 2(3/5) = -74/5
1x = -16
x = -16/1
x = -16


Input: What value of x satisfies x^2 + 149/90x + 11/18 = 0

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


Input: What value of x satisfies 8x  = 0

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


Input:
Solve the equations:
2x + 10y = 407/35
5x + 6y = 103/14

Output:
2x + 10y = 407/35
5x + 6y = 103/14

Using elimination
5*(2x + 10y = 407/35)
2*(5x + 6y = 103/14)
10x + 50y = 407/7
10x + 12y = 103/7
Subtract equations
38y = 304/7
y = 304/7/38
y = 8/7

Substitute y
2x + 10(8/7) = 407/35
2x = 1/5
x = 1/5/2
x = 1/10


Input: Find x in x^3 + 191/36x^2 + 4769/576x + 1805/576 = 0

Output:
x^3 + 191/36x^2 + 4769/576x + 1805/576 = 0
(x - -19/8)(x - -19/8)(x - -5/9) = 0
x - -19/8 = 0
x - -19/8 = 0
x - -5/9 = 0
x = -19/8
x = -19/8
x = -5/9


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

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


Input: What value of x satisfies x^2 - 121/12x + 95/4 = 0

Output:
x^2 - 121/12x + 95/4 = 0
(x - 15/4)(x - 19/3) = 0
x - 15/4 = 0  or  x - 19/3 = 0
x = 15/4
x = 19/3


Input:
Find x and y such that
8x + 6y = 26
7x + 9y = 19

Output:
8x + 6y = 26
7x + 9y = 19

Using elimination
7*(8x + 6y = 26)
8*(7x + 9y = 19)
56x + 42y = 182
56x + 72y = 152
Subtract equations
-30y = 30
y = 30/-30
y = -1

Substitute y
8x + 6(-1) = 26
8x = 32
x = 32/8
x = 4


Input: What value of x satisfies x^3 - 193/60x^2 + 101/30x - 91/80 = 0

Output:
x^3 - 193/60x^2 + 101/30x - 91/80 = 0
(x - 3/4)(x - 7/6)(x - 13/10) = 0
x - 3/4 = 0
x - 7/6 = 0
x - 13/10 = 0
x = 3/4
x = 7/6
x = 13/10


Input: Solve quickly: 6x - 28 = 0

Output:
6x - 28 = 0
6x = 28
x = 28 / 6
x = 14/3


Input: Solve the equation x^3 + 170/9x^2 - 712/27x - 2240/27 = 0

Output:
x^3 + 170/9x^2 - 712/27x - 2240/27 = 0
(x - 8/3)(x - -14/9)(x - -20) = 0
x - 8/3 = 0
x - -14/9 = 0
x - -20 = 0
x = 8/3
x = -14/9
x = -20


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

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


Input: Solve the equation x^3 - 14/3x^2 - 155/12x + 275/6 = 0

Output:
x^3 - 14/3x^2 - 155/12x + 275/6 = 0
(x - 11/2)(x - 5/2)(x - -10/3) = 0
x - 11/2 = 0
x - 5/2 = 0
x - -10/3 = 0
x = 11/2
x = 5/2
x = -10/3


Input: Solve quickly: 8x - 16 = 0

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


Input: What value of x satisfies x^2 - 55/6x + 21 = 0

Output:
x^2 - 55/6x + 21 = 0
(x - 14/3)(x - 9/2) = 0
x - 14/3 = 0  or  x - 9/2 = 0
x = 14/3
x = 9/2


Input: Find x for 10x - 120 = 0

Output:
10x - 120 = 0
10x = 120
x = 120 / 10
x = 12


Input: Compute the solution of x^3 - 37/15x^2 - 166/75x + 112/25 = 0

Output:
x^3 - 37/15x^2 - 166/75x + 112/25 = 0
(x - 6/5)(x - -7/5)(x - 8/3) = 0
x - 6/5 = 0
x - -7/5 = 0
x - 8/3 = 0
x = 6/5
x = -7/5
x = 8/3


Input:
Solve the system:
7x + 2y = -129/7
3x + 4y = -27/7

Output:
7x + 2y = -129/7
3x + 4y = -27/7

Using elimination
3*(7x + 2y = -129/7)
7*(3x + 4y = -27/7)
21x + 6y = -387/7
21x + 28y = -27
Subtract equations
-22y = -198/7
y = -198/7/-22
y = 9/7

Substitute y
7x + 2(9/7) = -129/7
7x = -21
x = -21/7
x = -3


Input:
Solve the equations:
8x + 9y = 421/35
4x + 8y = 298/35

Output:
8x + 9y = 421/35
4x + 8y = 298/35

Using elimination
4*(8x + 9y = 421/35)
8*(4x + 8y = 298/35)
32x + 36y = 1684/35
32x + 64y = 2384/35
Subtract equations
-28y = -20
y = -20/-28
y = 5/7

Substitute y
8x + 9(5/7) = 421/35
8x = 28/5
x = 28/5/8
x = 7/10


Input: Compute the solution of x^2 - 1/6x - 5/2 = 0

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


Input: Solve 4x - 4 = 0

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


Input:
Solve simultaneously:
5x + 7y = 79/9
2x + 3y = 10/3

Output:
5x + 7y = 79/9
2x + 3y = 10/3

Using elimination
2*(5x + 7y = 79/9)
5*(2x + 3y = 10/3)
10x + 14y = 158/9
10x + 15y = 50/3
Subtract equations
-1y = 8/9
y = 8/9/-1
y = -8/9

Substitute y
5x + 7(-8/9) = 79/9
5x = 15
x = 15/5
x = 3


Input: Determine x in x^2 + 121/24x - 85/24 = 0

Output:
x^2 + 121/24x - 85/24 = 0
(x - 5/8)(x - -17/3) = 0
x - 5/8 = 0  or  x - -17/3 = 0
x = 5/8
x = -17/3


Input: Find x for x^2 + 73/35x + 18/35 = 0

Output:
x^2 + 73/35x + 18/35 = 0
(x - -9/5)(x - -2/7) = 0
x - -9/5 = 0  or  x - -2/7 = 0
x = -9/5
x = -2/7


Input: Determine x in x^3 - 11/4x^2 - 237/2x + 90 = 0

Output:
x^3 - 11/4x^2 - 237/2x + 90 = 0
(x - -10)(x - 3/4)(x - 12) = 0
x - -10 = 0
x - 3/4 = 0
x - 12 = 0
x = -10
x = 3/4
x = 12


Input: Compute the solution of 9x + 42 = 0

Output:
9x + 42 = 0
9x = -42
x = -42 / 9
x = -14/3


Input: Solve the equation x^3 - 73/12x^2 - 1/3x + 95/3 = 0

Output:
x^3 - 73/12x^2 - 1/3x + 95/3 = 0
(x - 19/4)(x - -2)(x - 10/3) = 0
x - 19/4 = 0
x - -2 = 0
x - 10/3 = 0
x = 19/4
x = -2
x = 10/3


Input: Find x in 9x - 63 = 0

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


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

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


Input: Find the solution to x^2 - 43/15x + 8/15 = 0

Output:
x^2 - 43/15x + 8/15 = 0
(x - 1/5)(x - 8/3) = 0
x - 1/5 = 0  or  x - 8/3 = 0
x = 1/5
x = 8/3


Input: Find the solution to x^3 - 281/45x^2 + 88/9x - 16/5 = 0

Output:
x^3 - 281/45x^2 + 88/9x - 16/5 = 0
(x - 4)(x - 4/9)(x - 9/5) = 0
x - 4 = 0
x - 4/9 = 0
x - 9/5 = 0
x = 4
x = 4/9
x = 9/5


Input:
Solve simultaneously:
7x + 4y = 749/40
10x + 8y = 599/20

Output:
7x + 4y = 749/40
10x + 8y = 599/20

Using elimination
10*(7x + 4y = 749/40)
7*(10x + 8y = 599/20)
70x + 40y = 749/4
70x + 56y = 4193/20
Subtract equations
-16y = -112/5
y = -112/5/-16
y = 7/5

Substitute y
7x + 4(7/5) = 749/40
7x = 105/8
x = 105/8/7
x = 15/8


Input: Find x for 6x + 60 = 0

Output:
6x + 60 = 0
6x = -60
x = -60 / 6
x = -10


Input: Solve the equation x^2 + 25/12x + 7/12 = 0

Output:
x^2 + 25/12x + 7/12 = 0
(x - -7/4)(x - -1/3) = 0
x - -7/4 = 0  or  x - -1/3 = 0
x = -7/4
x = -1/3


Input: Solve 5x + 5/8 = 0

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


Input: Find x in 9x - 153/7 = 0

Output:
9x - 153/7 = 0
9x = 153/7
x = 153/7 / 9
x = 17/7


Input: Find x for x^3 + 53/10x^2 + 11/5x - 12 = 0

Output:
x^3 + 53/10x^2 + 11/5x - 12 = 0
(x - -5/2)(x - 6/5)(x - -4) = 0
x - -5/2 = 0
x - 6/5 = 0
x - -4 = 0
x = -5/2
x = 6/5
x = -4


Input: What value of x satisfies x^2 + 22/15x - 56/15 = 0

Output:
x^2 + 22/15x - 56/15 = 0
(x - -14/5)(x - 4/3) = 0
x - -14/5 = 0  or  x - 4/3 = 0
x = -14/5
x = 4/3


Input:
Find x and y such that
4x + 10y = 160/9
2x + 1y = 16/9

Output:
4x + 10y = 160/9
2x + 1y = 16/9

Using elimination
2*(4x + 10y = 160/9)
4*(2x + 1y = 16/9)
8x + 20y = 320/9
8x + 4y = 64/9
Subtract equations
16y = 256/9
y = 256/9/16
y = 16/9

Substitute y
4x + 10(16/9) = 160/9
4x = 0
x = 0/4
x = 0


Input: What value of x satisfies 6x - 9 = 0

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


Input: Solve the equation x^3 - 73/14x^2 - 81/14x + 45/7 = 0

Output:
x^3 - 73/14x^2 - 81/14x + 45/7 = 0
(x - -3/2)(x - 5/7)(x - 6) = 0
x - -3/2 = 0
x - 5/7 = 0
x - 6 = 0
x = -3/2
x = 5/7
x = 6


Input:
Solve the system:
8x + 1y = 143
4x + 4y = 12

Output:
8x + 1y = 143
4x + 4y = 12

Using elimination
4*(8x + 1y = 143)
8*(4x + 4y = 12)
32x + 4y = 572
32x + 32y = 96
Subtract equations
-28y = 476
y = 476/-28
y = -17

Substitute y
8x + 1(-17) = 143
8x = 160
x = 160/8
x = 20


Input: Solve quickly: 6x - 72 = 0

Output:
6x - 72 = 0
6x = 72
x = 72 / 6
x = 12


Input: Find x for x^3 + 23/8x^2 - 79/16x - 77/8 = 0

Output:
x^3 + 23/8x^2 - 79/16x - 77/8 = 0
(x - -7/2)(x - -11/8)(x - 2) = 0
x - -7/2 = 0
x - -11/8 = 0
x - 2 = 0
x = -7/2
x = -11/8
x = 2


Input: What value of x satisfies x^3 - 57/14x^2 + 18/7x + 27/14 = 0

Output:
x^3 - 57/14x^2 + 18/7x + 27/14 = 0
(x - -3/7)(x - 3)(x - 3/2) = 0
x - -3/7 = 0
x - 3 = 0
x - 3/2 = 0
x = -3/7
x = 3
x = 3/2


Input: Determine x in 1x + 6/7 = 0

Output:
1x + 6/7 = 0
1x = -6/7
x = -6/7 / 1
x = -6/7


Input:
Find x and y such that
1x + 9y = 16
6x + 8y = -10/9

Output:
1x + 9y = 16
6x + 8y = -10/9

Using elimination
6*(1x + 9y = 16)
1*(6x + 8y = -10/9)
6x + 54y = 96
6x + 8y = -10/9
Subtract equations
46y = 874/9
y = 874/9/46
y = 19/9

Substitute y
1x + 9(19/9) = 16
1x = -3
x = -3/1
x = -3


Input:
Solve simultaneously:
1x + 1y = 47/20
9x + 1y = -177/20

Output:
1x + 1y = 47/20
9x + 1y = -177/20

Using elimination
9*(1x + 1y = 47/20)
1*(9x + 1y = -177/20)
9x + 9y = 423/20
9x + 1y = -177/20
Subtract equations
8y = 30
y = 30/8
y = 15/4

Substitute y
1x + 1(15/4) = 47/20
1x = -7/5
x = -7/5/1
x = -7/5


Input: Find the solution to x^3 + 17/4x^2 - 35/64x - 99/16 = 0

Output:
x^3 + 17/4x^2 - 35/64x - 99/16 = 0
(x - -11/8)(x - 9/8)(x - -4) = 0
x - -11/8 = 0
x - 9/8 = 0
x - -4 = 0
x = -11/8
x = 9/8
x = -4


Input:
Solve the equations:
3x + 2y = -17/8
10x + 9y = -47/4

Output:
3x + 2y = -17/8
10x + 9y = -47/4

Using elimination
10*(3x + 2y = -17/8)
3*(10x + 9y = -47/4)
30x + 20y = -85/4
30x + 27y = -141/4
Subtract equations
-7y = 14
y = 14/-7
y = -2

Substitute y
3x + 2(-2) = -17/8
3x = 15/8
x = 15/8/3
x = 5/8


Input: Compute the solution of x^3 - 148/9x^2 + 569/27x + 80/9 = 0

Output:
x^3 - 148/9x^2 + 569/27x + 80/9 = 0
(x - 15)(x - -1/3)(x - 16/9) = 0
x - 15 = 0
x - -1/3 = 0
x - 16/9 = 0
x = 15
x = -1/3
x = 16/9


Input: Find x for x^3 - 197/63x^2 - 1052/567x + 76/9 = 0

Output:
x^3 - 197/63x^2 - 1052/567x + 76/9 = 0
(x - 19/9)(x - 18/7)(x - -14/9) = 0
x - 19/9 = 0
x - 18/7 = 0
x - -14/9 = 0
x = 19/9
x = 18/7
x = -14/9


Input: Find x for x^2 - 115/18x - 13/18 = 0

Output:
x^2 - 115/18x - 13/18 = 0
(x - 13/2)(x - -1/9) = 0
x - 13/2 = 0  or  x - -1/9 = 0
x = 13/2
x = -1/9


Input:
Solve simultaneously:
10x + 2y = 143/4
9x + 9y = 603/8

Output:
10x + 2y = 143/4
9x + 9y = 603/8

Using elimination
9*(10x + 2y = 143/4)
10*(9x + 9y = 603/8)
90x + 18y = 1287/4
90x + 90y = 3015/4
Subtract equations
-72y = -432
y = -432/-72
y = 6

Substitute y
10x + 2(6) = 143/4
10x = 95/4
x = 95/4/10
x = 19/8


Input:
Solve simultaneously:
9x + 4y = 93/10
1x + 5y = 147/10

Output:
9x + 4y = 93/10
1x + 5y = 147/10

Using elimination
1*(9x + 4y = 93/10)
9*(1x + 5y = 147/10)
9x + 4y = 93/10
9x + 45y = 1323/10
Subtract equations
-41y = -123
y = -123/-41
y = 3

Substitute y
9x + 4(3) = 93/10
9x = -27/10
x = -27/10/9
x = -3/10


Input:
Solve the system:
9x + 1y = -33
2x + 10y = 154/3

Output:
9x + 1y = -33
2x + 10y = 154/3

Using elimination
2*(9x + 1y = -33)
9*(2x + 10y = 154/3)
18x + 2y = -66
18x + 90y = 462
Subtract equations
-88y = -528
y = -528/-88
y = 6

Substitute y
9x + 1(6) = -33
9x = -39
x = -39/9
x = -13/3


Input: Find x for x^2 + 56/9x + 80/9 = 0

Output:
x^2 + 56/9x + 80/9 = 0
(x - -4)(x - -20/9) = 0
x - -4 = 0  or  x - -20/9 = 0
x = -4
x = -20/9


Input: Compute the solution of x^3 + 46/9x^2 + 59/9x + 2/3 = 0

Output:
x^3 + 46/9x^2 + 59/9x + 2/3 = 0
(x - -2)(x - -1/9)(x - -3) = 0
x - -2 = 0
x - -1/9 = 0
x - -3 = 0
x = -2
x = -1/9
x = -3


Input: Compute the solution of 7x - 98 = 0

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


Input: Compute the solution of x^2 - 59/15x - 112/15 = 0

Output:
x^2 - 59/15x - 112/15 = 0
(x - 16/3)(x - -7/5) = 0
x - 16/3 = 0  or  x - -7/5 = 0
x = 16/3
x = -7/5


Input:
Solve the system:
7x + 10y = 355/8
8x + 10y = 45

Output:
7x + 10y = 355/8
8x + 10y = 45

Using elimination
8*(7x + 10y = 355/8)
7*(8x + 10y = 45)
56x + 80y = 355
56x + 70y = 315
Subtract equations
10y = 40
y = 40/10
y = 4

Substitute y
7x + 10(4) = 355/8
7x = 35/8
x = 35/8/7
x = 5/8


Input: Solve the equation x^3 + 5/2x^2 - 107/16x + 51/16 = 0

Output:
x^3 + 5/2x^2 - 107/16x + 51/16 = 0
(x - 1)(x - -17/4)(x - 3/4) = 0
x - 1 = 0
x - -17/4 = 0
x - 3/4 = 0
x = 1
x = -17/4
x = 3/4


Input: Find x for x^2 + 6/5x + 8/25 = 0

Output:
x^2 + 6/5x + 8/25 = 0
(x - -4/5)(x - -2/5) = 0
x - -4/5 = 0  or  x - -2/5 = 0
x = -4/5
x = -2/5


Input: Solve quickly: 3x - 9 = 0

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


Input: Solve the equation x^3 - 110/63x^2 - 32/21x + 128/63 = 0

Output:
x^3 - 110/63x^2 - 32/21x + 128/63 = 0
(x - 8/9)(x - -8/7)(x - 2) = 0
x - 8/9 = 0
x - -8/7 = 0
x - 2 = 0
x = 8/9
x = -8/7
x = 2


Input: Find the solution to 2x + 19/5 = 0

Output:
2x + 19/5 = 0
2x = -19/5
x = -19/5 / 2
x = -19/10


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

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


Input: Compute the solution of 1x - 16 = 0

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


Input:
Solve simultaneously:
6x + 6y = 57
10x + 4y = 35

Output:
6x + 6y = 57
10x + 4y = 35

Using elimination
10*(6x + 6y = 57)
6*(10x + 4y = 35)
60x + 60y = 570
60x + 24y = 210
Subtract equations
36y = 360
y = 360/36
y = 10

Substitute y
6x + 6(10) = 57
6x = -3
x = -3/6
x = -1/2


Input: Find x in x^3 - 4/7x^2 - 97/63x - 10/21 = 0

Output:
x^3 - 4/7x^2 - 97/63x - 10/21 = 0
(x - 5/3)(x - -2/3)(x - -3/7) = 0
x - 5/3 = 0
x - -2/3 = 0
x - -3/7 = 0
x = 5/3
x = -2/3
x = -3/7


Input: Solve quickly: x^2 - 17/5x - 78/5 = 0

Output:
x^2 - 17/5x - 78/5 = 0
(x - -13/5)(x - 6) = 0
x - -13/5 = 0  or  x - 6 = 0
x = -13/5
x = 6


Input: Find the solution to x^2 + 1x - 60/49 = 0

Output:
x^2 + 1x - 60/49 = 0
(x - 5/7)(x - -12/7) = 0
x - 5/7 = 0  or  x - -12/7 = 0
x = 5/7
x = -12/7


Input:
Find x and y such that
6x + 2y = -82/3
1x + 9y = -32

Output:
6x + 2y = -82/3
1x + 9y = -32

Using elimination
1*(6x + 2y = -82/3)
6*(1x + 9y = -32)
6x + 2y = -82/3
6x + 54y = -192
Subtract equations
-52y = 494/3
y = 494/3/-52
y = -19/6

Substitute y
6x + 2(-19/6) = -82/3
6x = -21
x = -21/6
x = -7/2


Input: Compute the solution of x^2 + 11x - 60 = 0

Output:
x^2 + 11x - 60 = 0
(x - 4)(x - -15) = 0
x - 4 = 0  or  x - -15 = 0
x = 4
x = -15


Input: Find the solution to x^3 + 5/24x^2 - 59/24x + 5/4 = 0

Output:
x^3 + 5/24x^2 - 59/24x + 5/4 = 0
(x - 2/3)(x - 1)(x - -15/8) = 0
x - 2/3 = 0
x - 1 = 0
x - -15/8 = 0
x = 2/3
x = 1
x = -15/8


Input: Solve the equation 7x + 84 = 0

Output:
7x + 84 = 0
7x = -84
x = -84 / 7
x = -12


Input:
Solve the system:
10x + 8y = -146
1x + 9y = -103/2

Output:
10x + 8y = -146
1x + 9y = -103/2

Using elimination
1*(10x + 8y = -146)
10*(1x + 9y = -103/2)
10x + 8y = -146
10x + 90y = -515
Subtract equations
-82y = 369
y = 369/-82
y = -9/2

Substitute y
10x + 8(-9/2) = -146
10x = -110
x = -110/10
x = -11


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

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


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

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


Input: Determine x in 4x + 24 = 0

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


Input: Solve 6x + 114/5 = 0

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


Input:
Solve the equations:
7x + 4y = -59/5
6x + 4y = -42/5

Output:
7x + 4y = -59/5
6x + 4y = -42/5

Using elimination
6*(7x + 4y = -59/5)
7*(6x + 4y = -42/5)
42x + 24y = -354/5
42x + 28y = -294/5
Subtract equations
-4y = -12
y = -12/-4
y = 3

Substitute y
7x + 4(3) = -59/5
7x = -119/5
x = -119/5/7
x = -17/5


Input: Solve the equation x^3 - 7/5x^2 - 53/25x + 63/25 = 0

Output:
x^3 - 7/5x^2 - 53/25x + 63/25 = 0
(x - -7/5)(x - 9/5)(x - 1) = 0
x - -7/5 = 0
x - 9/5 = 0
x - 1 = 0
x = -7/5
x = 9/5
x = 1


Input: Solve the equation 7x + 140/9 = 0

Output:
7x + 140/9 = 0
7x = -140/9
x = -140/9 / 7
x = -20/9


Input: Solve quickly: x^2 + 49/5x + 221/20 = 0

Output:
x^2 + 49/5x + 221/20 = 0
(x - -13/10)(x - -17/2) = 0
x - -13/10 = 0  or  x - -17/2 = 0
x = -13/10
x = -17/2


Input: Solve the equation x^2 + 35/12x + 3/2 = 0

Output:
x^2 + 35/12x + 3/2 = 0
(x - -9/4)(x - -2/3) = 0
x - -9/4 = 0  or  x - -2/3 = 0
x = -9/4
x = -2/3


Input: Find x for 5x - 85/8 = 0

Output:
5x - 85/8 = 0
5x = 85/8
x = 85/8 / 5
x = 17/8


Input:
Solve simultaneously:
1x + 7y = -188/7
5x + 8y = -184/7

Output:
1x + 7y = -188/7
5x + 8y = -184/7

Using elimination
5*(1x + 7y = -188/7)
1*(5x + 8y = -184/7)
5x + 35y = -940/7
5x + 8y = -184/7
Subtract equations
27y = -108
y = -108/27
y = -4

Substitute y
1x + 7(-4) = -188/7
1x = 8/7
x = 8/7/1
x = 8/7


Input: Find x in x^2 + 30/7x + 32/7 = 0

Output:
x^2 + 30/7x + 32/7 = 0
(x - -2)(x - -16/7) = 0
x - -2 = 0  or  x - -16/7 = 0
x = -2
x = -16/7


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

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


Input: Solve x^3 - 7/8x^2 - 19/32x + 15/32 = 0

Output:
x^3 - 7/8x^2 - 19/32x + 15/32 = 0
(x - 5/8)(x - 1)(x - -3/4) = 0
x - 5/8 = 0
x - 1 = 0
x - -3/4 = 0
x = 5/8
x = 1
x = -3/4


Input: Find x in x^3 + 194/15x^2 - 769/15x - 176/5 = 0

Output:
x^3 + 194/15x^2 - 769/15x - 176/5 = 0
(x - 11/3)(x - -16)(x - -3/5) = 0
x - 11/3 = 0
x - -16 = 0
x - -3/5 = 0
x = 11/3
x = -16
x = -3/5


Input:
Solve the equations:
9x + 5y = -89/3
3x + 10y = 137/3

Output:
9x + 5y = -89/3
3x + 10y = 137/3

Using elimination
3*(9x + 5y = -89/3)
9*(3x + 10y = 137/3)
27x + 15y = -89
27x + 90y = 411
Subtract equations
-75y = -500
y = -500/-75
y = 20/3

Substitute y
9x + 5(20/3) = -89/3
9x = -63
x = -63/9
x = -7


Input:
Find x and y such that
7x + 3y = -27
4x + 6y = -24

Output:
7x + 3y = -27
4x + 6y = -24

Using elimination
4*(7x + 3y = -27)
7*(4x + 6y = -24)
28x + 12y = -108
28x + 42y = -168
Subtract equations
-30y = 60
y = 60/-30
y = -2

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


Input: Find the solution to x^3 - 11/3x^2 + 1/12x + 19/4 = 0

Output:
x^3 - 11/3x^2 + 1/12x + 19/4 = 0
(x - 3/2)(x - 19/6)(x - -1) = 0
x - 3/2 = 0
x - 19/6 = 0
x - -1 = 0
x = 3/2
x = 19/6
x = -1


Input:
Solve simultaneously:
10x + 3y = 176/5
8x + 1y = 152/5

Output:
10x + 3y = 176/5
8x + 1y = 152/5

Using elimination
8*(10x + 3y = 176/5)
10*(8x + 1y = 152/5)
80x + 24y = 1408/5
80x + 10y = 304
Subtract equations
14y = -112/5
y = -112/5/14
y = -8/5

Substitute y
10x + 3(-8/5) = 176/5
10x = 40
x = 40/10
x = 4


Input:
Solve the system:
5x + 10y = -75/2
2x + 1y = -6

Output:
5x + 10y = -75/2
2x + 1y = -6

Using elimination
2*(5x + 10y = -75/2)
5*(2x + 1y = -6)
10x + 20y = -75
10x + 5y = -30
Subtract equations
15y = -45
y = -45/15
y = -3

Substitute y
5x + 10(-3) = -75/2
5x = -15/2
x = -15/2/5
x = -3/2


Input:
Find x and y such that
10x + 6y = -121
5x + 8y = -53

Output:
10x + 6y = -121
5x + 8y = -53

Using elimination
5*(10x + 6y = -121)
10*(5x + 8y = -53)
50x + 30y = -605
50x + 80y = -530
Subtract equations
-50y = -75
y = -75/-50
y = 3/2

Substitute y
10x + 6(3/2) = -121
10x = -130
x = -130/10
x = -13


Input: Compute the solution of x^2 - 1/8x  = 0

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


Input: Find x in x^2 - 8x + 7 = 0

Output:
x^2 - 8x + 7 = 0
(x - 7)(x - 1) = 0
x - 7 = 0  or  x - 1 = 0
x = 7
x = 1


Input: Solve the equation 4x - 4 = 0

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


Input: Solve the equation 9x + 27 = 0

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


Input: Solve x^3 - 203/45x^2 - 56/27x + 1664/135 = 0

Output:
x^3 - 203/45x^2 - 56/27x + 1664/135 = 0
(x - 16/9)(x - -8/5)(x - 13/3) = 0
x - 16/9 = 0
x - -8/5 = 0
x - 13/3 = 0
x = 16/9
x = -8/5
x = 13/3


Input: What value of x satisfies x^2 - 7/4x - 9/8 = 0

Output:
x^2 - 7/4x - 9/8 = 0
(x - 9/4)(x - -1/2) = 0
x - 9/4 = 0  or  x - -1/2 = 0
x = 9/4
x = -1/2


Input:
Solve simultaneously:
2x + 10y = 191/3
8x + 9y = 79

Output:
2x + 10y = 191/3
8x + 9y = 79

Using elimination
8*(2x + 10y = 191/3)
2*(8x + 9y = 79)
16x + 80y = 1528/3
16x + 18y = 158
Subtract equations
62y = 1054/3
y = 1054/3/62
y = 17/3

Substitute y
2x + 10(17/3) = 191/3
2x = 7
x = 7/2
x = 7/2


Input: Find the solution to x^3 + 21/2x^2 + 49/2x + 15 = 0

Output:
x^3 + 21/2x^2 + 49/2x + 15 = 0
(x - -1)(x - -2)(x - -15/2) = 0
x - -1 = 0
x - -2 = 0
x - -15/2 = 0
x = -1
x = -2
x = -15/2


Input: Solve quickly: 9x - 81/2 = 0

Output:
9x - 81/2 = 0
9x = 81/2
x = 81/2 / 9
x = 9/2


Input: Solve x^2 - 29/15x + 4/5 = 0

Output:
x^2 - 29/15x + 4/5 = 0
(x - 3/5)(x - 4/3) = 0
x - 3/5 = 0  or  x - 4/3 = 0
x = 3/5
x = 4/3


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

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


Input: Compute the solution of x^2 + 55/18x + 50/27 = 0

Output:
x^2 + 55/18x + 50/27 = 0
(x - -20/9)(x - -5/6) = 0
x - -20/9 = 0  or  x - -5/6 = 0
x = -20/9
x = -5/6


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

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


Input: Determine x in 9x - 27 = 0

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


Input: Find x for 1x + 9/5 = 0

Output:
1x + 9/5 = 0
1x = -9/5
x = -9/5 / 1
x = -9/5


Input: Compute the solution of x^3 + 49/4x^2 + 3x  = 0

Output:
x^3 + 49/4x^2 + 3x  = 0
(x - -1/4)(x - 0)(x - -12) = 0
x - -1/4 = 0
x - 0 = 0
x - -12 = 0
x = -1/4
x = 0
x = -12


Input: Find x for x^2 - 23/10x + 28/25 = 0

Output:
x^2 - 23/10x + 28/25 = 0
(x - 7/10)(x - 8/5) = 0
x - 7/10 = 0  or  x - 8/5 = 0
x = 7/10
x = 8/5


Input: Solve the equation 10x  = 0

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


Input: Determine x in x^3 - 14/15x^2 - 49/15x  = 0

Output:
x^3 - 14/15x^2 - 49/15x  = 0
(x - 7/3)(x - 0)(x - -7/5) = 0
x - 7/3 = 0
x - 0 = 0
x - -7/5 = 0
x = 7/3
x = 0
x = -7/5


Input: What value of x satisfies x^2 + 5/3x - 13/12 = 0

Output:
x^2 + 5/3x - 13/12 = 0
(x - 1/2)(x - -13/6) = 0
x - 1/2 = 0  or  x - -13/6 = 0
x = 1/2
x = -13/6


Input: Find x in 5x - 80/7 = 0

Output:
5x - 80/7 = 0
5x = 80/7
x = 80/7 / 5
x = 16/7


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

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


Input: Find x for x^2 + 3/5x - 14/5 = 0

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


Input:
Solve the equations:
2x + 10y = 13/4
6x + 9y = -111/8

Output:
2x + 10y = 13/4
6x + 9y = -111/8

Using elimination
6*(2x + 10y = 13/4)
2*(6x + 9y = -111/8)
12x + 60y = 39/2
12x + 18y = -111/4
Subtract equations
42y = 189/4
y = 189/4/42
y = 9/8

Substitute y
2x + 10(9/8) = 13/4
2x = -8
x = -8/2
x = -4


Input: Compute the solution of x^2 - 47/9x + 44/9 = 0

Output:
x^2 - 47/9x + 44/9 = 0
(x - 4)(x - 11/9) = 0
x - 4 = 0  or  x - 11/9 = 0
x = 4
x = 11/9


Input: Find the solution to x^3 - 59/20x^2 - 96/25x + 63/20 = 0

Output:
x^3 - 59/20x^2 - 96/25x + 63/20 = 0
(x - -7/5)(x - 3/5)(x - 15/4) = 0
x - -7/5 = 0
x - 3/5 = 0
x - 15/4 = 0
x = -7/5
x = 3/5
x = 15/4


Input: Find the solution to x^3 + 35/3x^2 + 107/12x - 665/6 = 0

Output:
x^3 + 35/3x^2 + 107/12x - 665/6 = 0
(x - -19/2)(x - -14/3)(x - 5/2) = 0
x - -19/2 = 0
x - -14/3 = 0
x - 5/2 = 0
x = -19/2
x = -14/3
x = 5/2


Input:
Solve the equations:
3x + 9y = -66/5
1x + 10y = -57/5

Output:
3x + 9y = -66/5
1x + 10y = -57/5

Using elimination
1*(3x + 9y = -66/5)
3*(1x + 10y = -57/5)
3x + 9y = -66/5
3x + 30y = -171/5
Subtract equations
-21y = 21
y = 21/-21
y = -1

Substitute y
3x + 9(-1) = -66/5
3x = -21/5
x = -21/5/3
x = -7/5


Input:
Find x and y such that
6x + 5y = 190/63
4x + 4y = 80/63

Output:
6x + 5y = 190/63
4x + 4y = 80/63

Using elimination
4*(6x + 5y = 190/63)
6*(4x + 4y = 80/63)
24x + 20y = 760/63
24x + 24y = 160/21
Subtract equations
-4y = 40/9
y = 40/9/-4
y = -10/9

Substitute y
6x + 5(-10/9) = 190/63
6x = 60/7
x = 60/7/6
x = 10/7


Input:
Find x and y such that
5x + 9y = 22
5x + 7y = 18

Output:
5x + 9y = 22
5x + 7y = 18

Using elimination
5*(5x + 9y = 22)
5*(5x + 7y = 18)
25x + 45y = 110
25x + 35y = 90
Subtract equations
10y = 20
y = 20/10
y = 2

Substitute y
5x + 9(2) = 22
5x = 4
x = 4/5
x = 4/5


Input:
Solve simultaneously:
4x + 9y = 27
6x + 7y = 21

Output:
4x + 9y = 27
6x + 7y = 21

Using elimination
6*(4x + 9y = 27)
4*(6x + 7y = 21)
24x + 54y = 162
24x + 28y = 84
Subtract equations
26y = 78
y = 78/26
y = 3

Substitute y
4x + 9(3) = 27
4x = 0
x = 0/4
x = 0


Input: Find the solution to 5x - 80 = 0

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


Input: Solve quickly: x^3 - 334/35x^2 + 1259/140x - 153/140 = 0

Output:
x^3 - 334/35x^2 + 1259/140x - 153/140 = 0
(x - 1/7)(x - 9/10)(x - 17/2) = 0
x - 1/7 = 0
x - 9/10 = 0
x - 17/2 = 0
x = 1/7
x = 9/10
x = 17/2


Input: Find x in x^3 - 71/6x^2 + 119/3x - 245/6 = 0

Output:
x^3 - 71/6x^2 + 119/3x - 245/6 = 0
(x - 5/2)(x - 7)(x - 7/3) = 0
x - 5/2 = 0
x - 7 = 0
x - 7/3 = 0
x = 5/2
x = 7
x = 7/3


Input: Solve x^3 + 73/9x^2 + 12x - 160/9 = 0

Output:
x^3 + 73/9x^2 + 12x - 160/9 = 0
(x - -4)(x - 8/9)(x - -5) = 0
x - -4 = 0
x - 8/9 = 0
x - -5 = 0
x = -4
x = 8/9
x = -5


Input:
Solve simultaneously:
4x + 1y = -364/45
9x + 8y = -183/5

Output:
4x + 1y = -364/45
9x + 8y = -183/5

Using elimination
9*(4x + 1y = -364/45)
4*(9x + 8y = -183/5)
36x + 9y = -364/5
36x + 32y = -732/5
Subtract equations
-23y = 368/5
y = 368/5/-23
y = -16/5

Substitute y
4x + 1(-16/5) = -364/45
4x = -44/9
x = -44/9/4
x = -11/9


Input: Solve x^2 + 1/4x - 7/2 = 0

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


Input: Find x in x^2 + 10/9x - 77/27 = 0

Output:
x^2 + 10/9x - 77/27 = 0
(x - 11/9)(x - -7/3) = 0
x - 11/9 = 0  or  x - -7/3 = 0
x = 11/9
x = -7/3


Input:
Find x and y such that
7x + 3y = 9/10
3x + 10y = 76/5

Output:
7x + 3y = 9/10
3x + 10y = 76/5

Using elimination
3*(7x + 3y = 9/10)
7*(3x + 10y = 76/5)
21x + 9y = 27/10
21x + 70y = 532/5
Subtract equations
-61y = -1037/10
y = -1037/10/-61
y = 17/10

Substitute y
7x + 3(17/10) = 9/10
7x = -21/5
x = -21/5/7
x = -3/5


Input: Find x in x^2 + 11x + 28 = 0

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


Input: Solve 2x - 3 = 0

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


Input: Solve x^3 + 153/8x^2 + 229/8x - 255/2 = 0

Output:
x^3 + 153/8x^2 + 229/8x - 255/2 = 0
(x - 15/8)(x - -4)(x - -17) = 0
x - 15/8 = 0
x - -4 = 0
x - -17 = 0
x = 15/8
x = -4
x = -17


Input:
Solve simultaneously:
5x + 3y = -53/28
5x + 1y = -151/28

Output:
5x + 3y = -53/28
5x + 1y = -151/28

Using elimination
5*(5x + 3y = -53/28)
5*(5x + 1y = -151/28)
25x + 15y = -265/28
25x + 5y = -755/28
Subtract equations
10y = 35/2
y = 35/2/10
y = 7/4

Substitute y
5x + 3(7/4) = -53/28
5x = -50/7
x = -50/7/5
x = -10/7


Input:
Solve the system:
7x + 3y = -187/6
10x + 3y = -271/6

Output:
7x + 3y = -187/6
10x + 3y = -271/6

Using elimination
10*(7x + 3y = -187/6)
7*(10x + 3y = -271/6)
70x + 30y = -935/3
70x + 21y = -1897/6
Subtract equations
9y = 9/2
y = 9/2/9
y = 1/2

Substitute y
7x + 3(1/2) = -187/6
7x = -98/3
x = -98/3/7
x = -14/3


Input: Find the solution to x^3 - 31/3x^2 - 48x - 140/3 = 0

Output:
x^3 - 31/3x^2 - 48x - 140/3 = 0
(x - -5/3)(x - 14)(x - -2) = 0
x - -5/3 = 0
x - 14 = 0
x - -2 = 0
x = -5/3
x = 14
x = -2


Input: Determine x in x^3 - 102/5x^2 + 621/25x + 836/25 = 0

Output:
x^3 - 102/5x^2 + 621/25x + 836/25 = 0
(x - 19)(x - -4/5)(x - 11/5) = 0
x - 19 = 0
x - -4/5 = 0
x - 11/5 = 0
x = 19
x = -4/5
x = 11/5


Input: Find x in 2x + 16/9 = 0

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


Input: Find x for x^2 - 11x  = 0

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


Input: Solve the equation x^3 + 23/28x^2 - 747/56x + 405/28 = 0

Output:
x^3 + 23/28x^2 - 747/56x + 405/28 = 0
(x - 10/7)(x - -9/2)(x - 9/4) = 0
x - 10/7 = 0
x - -9/2 = 0
x - 9/4 = 0
x = 10/7
x = -9/2
x = 9/4


Input: Solve the equation 1x - 5/8 = 0

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


Input: Compute the solution of 4x - 4 = 0

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


Input:
Solve simultaneously:
5x + 9y = 44
9x + 4y = 91/5

Output:
5x + 9y = 44
9x + 4y = 91/5

Using elimination
9*(5x + 9y = 44)
5*(9x + 4y = 91/5)
45x + 81y = 396
45x + 20y = 91
Subtract equations
61y = 305
y = 305/61
y = 5

Substitute y
5x + 9(5) = 44
5x = -1
x = -1/5
x = -1/5


Input:
Solve simultaneously:
9x + 3y = 135/8
9x + 9y = 225/8

Output:
9x + 3y = 135/8
9x + 9y = 225/8

Using elimination
9*(9x + 3y = 135/8)
9*(9x + 9y = 225/8)
81x + 27y = 1215/8
81x + 81y = 2025/8
Subtract equations
-54y = -405/4
y = -405/4/-54
y = 15/8

Substitute y
9x + 3(15/8) = 135/8
9x = 45/4
x = 45/4/9
x = 5/4


Input: What value of x satisfies x^3 + 293/36x^2 - 187/18x - 95/4 = 0

Output:
x^3 + 293/36x^2 - 187/18x - 95/4 = 0
(x - 19/9)(x - -5/4)(x - -9) = 0
x - 19/9 = 0
x - -5/4 = 0
x - -9 = 0
x = 19/9
x = -5/4
x = -9


Input: Solve 10x + 8 = 0

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


Input: Find x for 3x - 21/8 = 0

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


Input:
Find x and y such that
2x + 6y = -5/3
10x + 10y = 35/3

Output:
2x + 6y = -5/3
10x + 10y = 35/3

Using elimination
10*(2x + 6y = -5/3)
2*(10x + 10y = 35/3)
20x + 60y = -50/3
20x + 20y = 70/3
Subtract equations
40y = -40
y = -40/40
y = -1

Substitute y
2x + 6(-1) = -5/3
2x = 13/3
x = 13/3/2
x = 13/6


Input:
Solve the system:
6x + 2y = 64/5
3x + 5y = 52/5

Output:
6x + 2y = 64/5
3x + 5y = 52/5

Using elimination
3*(6x + 2y = 64/5)
6*(3x + 5y = 52/5)
18x + 6y = 192/5
18x + 30y = 312/5
Subtract equations
-24y = -24
y = -24/-24
y = 1

Substitute y
6x + 2(1) = 64/5
6x = 54/5
x = 54/5/6
x = 9/5


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

Output:
10x - 5/2 = 0
10x = 5/2
x = 5/2 / 10
x = 1/4


Input: What value of x satisfies 2x + 18 = 0

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


Input: What value of x satisfies x^2 - 21x + 38 = 0

Output:
x^2 - 21x + 38 = 0
(x - 19)(x - 2) = 0
x - 19 = 0  or  x - 2 = 0
x = 19
x = 2


Input: Find the solution to 6x + 102/5 = 0

Output:
6x + 102/5 = 0
6x = -102/5
x = -102/5 / 6
x = -17/5


Input: Solve the equation x^3 + 23/5x^2 - 2/5x - 56/5 = 0

Output:
x^3 + 23/5x^2 - 2/5x - 56/5 = 0
(x - -2)(x - -4)(x - 7/5) = 0
x - -2 = 0
x - -4 = 0
x - 7/5 = 0
x = -2
x = -4
x = 7/5


Input: Solve the equation x^3 - 21/4x^2 - 42x - 55 = 0

Output:
x^3 - 21/4x^2 - 42x - 55 = 0
(x - 10)(x - -11/4)(x - -2) = 0
x - 10 = 0
x - -11/4 = 0
x - -2 = 0
x = 10
x = -11/4
x = -2


Input:
Solve the system:
8x + 10y = 124/7
7x + 2y = 176/7

Output:
8x + 10y = 124/7
7x + 2y = 176/7

Using elimination
7*(8x + 10y = 124/7)
8*(7x + 2y = 176/7)
56x + 70y = 124
56x + 16y = 1408/7
Subtract equations
54y = -540/7
y = -540/7/54
y = -10/7

Substitute y
8x + 10(-10/7) = 124/7
8x = 32
x = 32/8
x = 4


Input: Find x in 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:
Solve simultaneously:
1x + 6y = 31/2
4x + 10y = 114/5

Output:
1x + 6y = 31/2
4x + 10y = 114/5

Using elimination
4*(1x + 6y = 31/2)
1*(4x + 10y = 114/5)
4x + 24y = 62
4x + 10y = 114/5
Subtract equations
14y = 196/5
y = 196/5/14
y = 14/5

Substitute y
1x + 6(14/5) = 31/2
1x = -13/10
x = -13/10/1
x = -13/10


Input: Solve quickly: 6x - 3/5 = 0

Output:
6x - 3/5 = 0
6x = 3/5
x = 3/5 / 6
x = 1/10


Input: Solve the equation x^2 - 23/8x - 117/16 = 0

Output:
x^2 - 23/8x - 117/16 = 0
(x - 9/2)(x - -13/8) = 0
x - 9/2 = 0  or  x - -13/8 = 0
x = 9/2
x = -13/8


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

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


Input: Solve the equation x^2 + 49/8x - 165/16 = 0

Output:
x^2 + 49/8x - 165/16 = 0
(x - 11/8)(x - -15/2) = 0
x - 11/8 = 0  or  x - -15/2 = 0
x = 11/8
x = -15/2


Input: Find x for x^3 - 37/56x^2 - 159/224x - 27/224 = 0

Output:
x^3 - 37/56x^2 - 159/224x - 27/224 = 0
(x - 9/7)(x - -1/4)(x - -3/8) = 0
x - 9/7 = 0
x - -1/4 = 0
x - -3/8 = 0
x = 9/7
x = -1/4
x = -3/8


Input: Compute the solution of 5x - 65 = 0

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


Input:
Solve the system:
9x + 2y = 123/7
3x + 4y = 81/7

Output:
9x + 2y = 123/7
3x + 4y = 81/7

Using elimination
3*(9x + 2y = 123/7)
9*(3x + 4y = 81/7)
27x + 6y = 369/7
27x + 36y = 729/7
Subtract equations
-30y = -360/7
y = -360/7/-30
y = 12/7

Substitute y
9x + 2(12/7) = 123/7
9x = 99/7
x = 99/7/9
x = 11/7


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

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


Input:
Solve simultaneously:
3x + 5y = -109/7
7x + 7y = -33

Output:
3x + 5y = -109/7
7x + 7y = -33

Using elimination
7*(3x + 5y = -109/7)
3*(7x + 7y = -33)
21x + 35y = -109
21x + 21y = -99
Subtract equations
14y = -10
y = -10/14
y = -5/7

Substitute y
3x + 5(-5/7) = -109/7
3x = -12
x = -12/3
x = -4


Input: Find x in x^2 + 116/21x + 160/21 = 0

Output:
x^2 + 116/21x + 160/21 = 0
(x - -8/3)(x - -20/7) = 0
x - -8/3 = 0  or  x - -20/7 = 0
x = -8/3
x = -20/7


Input: Determine x in x^2 - 1/14x - 85/14 = 0

Output:
x^2 - 1/14x - 85/14 = 0
(x - -17/7)(x - 5/2) = 0
x - -17/7 = 0  or  x - 5/2 = 0
x = -17/7
x = 5/2


Input: Solve 10x + 55/3 = 0

Output:
10x + 55/3 = 0
10x = -55/3
x = -55/3 / 10
x = -11/6


Input: Determine x in 7x - 1 = 0

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


Input: Determine x in 2x + 32 = 0

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


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

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


Input: Compute the solution of x^2 - 16/3x - 4 = 0

Output:
x^2 - 16/3x - 4 = 0
(x - -2/3)(x - 6) = 0
x - -2/3 = 0  or  x - 6 = 0
x = -2/3
x = 6


Input:
Solve the equations:
3x + 9y = -69/2
5x + 2y = -37/2

Output:
3x + 9y = -69/2
5x + 2y = -37/2

Using elimination
5*(3x + 9y = -69/2)
3*(5x + 2y = -37/2)
15x + 45y = -345/2
15x + 6y = -111/2
Subtract equations
39y = -117
y = -117/39
y = -3

Substitute y
3x + 9(-3) = -69/2
3x = -15/2
x = -15/2/3
x = -5/2


Input: Find x for x^3 + 17/4x^2 + 33/8x + 9/8 = 0

Output:
x^3 + 17/4x^2 + 33/8x + 9/8 = 0
(x - -1/2)(x - -3/4)(x - -3) = 0
x - -1/2 = 0
x - -3/4 = 0
x - -3 = 0
x = -1/2
x = -3/4
x = -3


Input: Compute the solution of x^3 - 9/4x^2 - 23/8x + 15/8 = 0

Output:
x^3 - 9/4x^2 - 23/8x + 15/8 = 0
(x - -5/4)(x - 3)(x - 1/2) = 0
x - -5/4 = 0
x - 3 = 0
x - 1/2 = 0
x = -5/4
x = 3
x = 1/2


Input: Find x in 8x - 68/3 = 0

Output:
8x - 68/3 = 0
8x = 68/3
x = 68/3 / 8
x = 17/6


Input:
Find x and y such that
8x + 3y = 18
4x + 3y = 18

Output:
8x + 3y = 18
4x + 3y = 18

Using elimination
4*(8x + 3y = 18)
8*(4x + 3y = 18)
32x + 12y = 72
32x + 24y = 144
Subtract equations
-12y = -72
y = -72/-12
y = 6

Substitute y
8x + 3(6) = 18
8x = 0
x = 0/8
x = 0


Input:
Solve the equations:
1x + 2y = 17/9
4x + 9y = 9

Output:
1x + 2y = 17/9
4x + 9y = 9

Using elimination
4*(1x + 2y = 17/9)
1*(4x + 9y = 9)
4x + 8y = 68/9
4x + 9y = 9
Subtract equations
-1y = -13/9
y = -13/9/-1
y = 13/9

Substitute y
1x + 2(13/9) = 17/9
1x = -1
x = -1/1
x = -1


Input:
Solve the system:
3x + 7y = -37/2
10x + 7y = -22

Output:
3x + 7y = -37/2
10x + 7y = -22

Using elimination
10*(3x + 7y = -37/2)
3*(10x + 7y = -22)
30x + 70y = -185
30x + 21y = -66
Subtract equations
49y = -119
y = -119/49
y = -17/7

Substitute y
3x + 7(-17/7) = -37/2
3x = -3/2
x = -3/2/3
x = -1/2


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

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


Input: What value of x satisfies x^2 + 43/35x - 2/7 = 0

Output:
x^2 + 43/35x - 2/7 = 0
(x - -10/7)(x - 1/5) = 0
x - -10/7 = 0  or  x - 1/5 = 0
x = -10/7
x = 1/5


Input:
Solve the equations:
8x + 3y = 8
6x + 1y = 13/3

Output:
8x + 3y = 8
6x + 1y = 13/3

Using elimination
6*(8x + 3y = 8)
8*(6x + 1y = 13/3)
48x + 18y = 48
48x + 8y = 104/3
Subtract equations
10y = 40/3
y = 40/3/10
y = 4/3

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


Input:
Solve the equations:
4x + 8y = -97
3x + 5y = -243/4

Output:
4x + 8y = -97
3x + 5y = -243/4

Using elimination
3*(4x + 8y = -97)
4*(3x + 5y = -243/4)
12x + 24y = -291
12x + 20y = -243
Subtract equations
4y = -48
y = -48/4
y = -12

Substitute y
4x + 8(-12) = -97
4x = -1
x = -1/4
x = -1/4


Input: Compute the solution of 5x - 85 = 0

Output:
5x - 85 = 0
5x = 85
x = 85 / 5
x = 17


Input: Solve x^2 + 2x - 15 = 0

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


Input: Determine x in 8x + 48 = 0

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


Input:
Solve simultaneously:
6x + 10y = 273/5
3x + 3y = 153/10

Output:
6x + 10y = 273/5
3x + 3y = 153/10

Using elimination
3*(6x + 10y = 273/5)
6*(3x + 3y = 153/10)
18x + 30y = 819/5
18x + 18y = 459/5
Subtract equations
12y = 72
y = 72/12
y = 6

Substitute y
6x + 10(6) = 273/5
6x = -27/5
x = -27/5/6
x = -9/10


Input: Solve quickly: 6x - 36 = 0

Output:
6x - 36 = 0
6x = 36
x = 36 / 6
x = 6


Input: Determine x in 1x + 5/2 = 0

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


Input:
Solve the system:
10x + 2y = 26
9x + 9y = 9

Output:
10x + 2y = 26
9x + 9y = 9

Using elimination
9*(10x + 2y = 26)
10*(9x + 9y = 9)
90x + 18y = 234
90x + 90y = 90
Subtract equations
-72y = 144
y = 144/-72
y = -2

Substitute y
10x + 2(-2) = 26
10x = 30
x = 30/10
x = 3


Input: Solve 6x - 66/7 = 0

Output:
6x - 66/7 = 0
6x = 66/7
x = 66/7 / 6
x = 11/7


Input: Solve the equation 3x + 1 = 0

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


Input: Find the solution to 8x + 40 = 0

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


Input:
Solve the equations:
10x + 2y = 46
8x + 3y = 48

Output:
10x + 2y = 46
8x + 3y = 48

Using elimination
8*(10x + 2y = 46)
10*(8x + 3y = 48)
80x + 16y = 368
80x + 30y = 480
Subtract equations
-14y = -112
y = -112/-14
y = 8

Substitute y
10x + 2(8) = 46
10x = 30
x = 30/10
x = 3


Input:
Solve the system:
2x + 5y = -301/4
10x + 5y = -305/4

Output:
2x + 5y = -301/4
10x + 5y = -305/4

Using elimination
10*(2x + 5y = -301/4)
2*(10x + 5y = -305/4)
20x + 50y = -1505/2
20x + 10y = -305/2
Subtract equations
40y = -600
y = -600/40
y = -15

Substitute y
2x + 5(-15) = -301/4
2x = -1/4
x = -1/4/2
x = -1/8


Input: Solve 1x - 7 = 0

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


Input: What value of x satisfies x^2 + 178/21x + 95/7 = 0

Output:
x^2 + 178/21x + 95/7 = 0
(x - -15/7)(x - -19/3) = 0
x - -15/7 = 0  or  x - -19/3 = 0
x = -15/7
x = -19/3


Input: Solve the equation x^2 - 29/10x + 9/5 = 0

Output:
x^2 - 29/10x + 9/5 = 0
(x - 2)(x - 9/10) = 0
x - 2 = 0  or  x - 9/10 = 0
x = 2
x = 9/10


Input: Find x in x^3 + 101/14x^2 + 199/14x + 38/7 = 0

Output:
x^3 + 101/14x^2 + 199/14x + 38/7 = 0
(x - -1/2)(x - -19/7)(x - -4) = 0
x - -1/2 = 0
x - -19/7 = 0
x - -4 = 0
x = -1/2
x = -19/7
x = -4


Input:
Solve the system:
9x + 8y = 97/10
3x + 3y = 37/10

Output:
9x + 8y = 97/10
3x + 3y = 37/10

Using elimination
3*(9x + 8y = 97/10)
9*(3x + 3y = 37/10)
27x + 24y = 291/10
27x + 27y = 333/10
Subtract equations
-3y = -21/5
y = -21/5/-3
y = 7/5

Substitute y
9x + 8(7/5) = 97/10
9x = -3/2
x = -3/2/9
x = -1/6


Input: Find x in x^2 + 114/7x + 32 = 0

Output:
x^2 + 114/7x + 32 = 0
(x - -14)(x - -16/7) = 0
x - -14 = 0  or  x - -16/7 = 0
x = -14
x = -16/7


Input: Find the solution to x^2 - 35/6x + 25/3 = 0

Output:
x^2 - 35/6x + 25/3 = 0
(x - 5/2)(x - 10/3) = 0
x - 5/2 = 0  or  x - 10/3 = 0
x = 5/2
x = 10/3


Input:
Solve simultaneously:
6x + 8y = -141/4
10x + 2y = -99/4

Output:
6x + 8y = -141/4
10x + 2y = -99/4

Using elimination
10*(6x + 8y = -141/4)
6*(10x + 2y = -99/4)
60x + 80y = -705/2
60x + 12y = -297/2
Subtract equations
68y = -204
y = -204/68
y = -3

Substitute y
6x + 8(-3) = -141/4
6x = -45/4
x = -45/4/6
x = -15/8


Input:
Solve the system:
9x + 9y = 129/2
6x + 7y = 259/6

Output:
9x + 9y = 129/2
6x + 7y = 259/6

Using elimination
6*(9x + 9y = 129/2)
9*(6x + 7y = 259/6)
54x + 54y = 387
54x + 63y = 777/2
Subtract equations
-9y = -3/2
y = -3/2/-9
y = 1/6

Substitute y
9x + 9(1/6) = 129/2
9x = 63
x = 63/9
x = 7


Input: Determine x in x^3 + 80/9x^2 - 1811/81x + 770/81 = 0

Output:
x^3 + 80/9x^2 - 1811/81x + 770/81 = 0
(x - -11)(x - 5/9)(x - 14/9) = 0
x - -11 = 0
x - 5/9 = 0
x - 14/9 = 0
x = -11
x = 5/9
x = 14/9


Input: Find the solution to x^2 + 31/4x + 55/4 = 0

Output:
x^2 + 31/4x + 55/4 = 0
(x - -5)(x - -11/4) = 0
x - -5 = 0  or  x - -11/4 = 0
x = -5
x = -11/4


Input:
Find x and y such that
1x + 10y = 41/2
4x + 2y = 145/2

Output:
1x + 10y = 41/2
4x + 2y = 145/2

Using elimination
4*(1x + 10y = 41/2)
1*(4x + 2y = 145/2)
4x + 40y = 82
4x + 2y = 145/2
Subtract equations
38y = 19/2
y = 19/2/38
y = 1/4

Substitute y
1x + 10(1/4) = 41/2
1x = 18
x = 18/1
x = 18


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

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


Input: Solve x^3 + 25/4x^2 - 19/4x - 55 = 0

Output:
x^3 + 25/4x^2 - 19/4x - 55 = 0
(x - 11/4)(x - -5)(x - -4) = 0
x - 11/4 = 0
x - -5 = 0
x - -4 = 0
x = 11/4
x = -5
x = -4


Input: Find x in x^3 + 113/8x^2 + 183/8x - 63/2 = 0

Output:
x^3 + 113/8x^2 + 183/8x - 63/2 = 0
(x - -3)(x - 7/8)(x - -12) = 0
x - -3 = 0
x - 7/8 = 0
x - -12 = 0
x = -3
x = 7/8
x = -12


Input:
Solve simultaneously:
8x + 5y = -94/9
5x + 2y = -199/36

Output:
8x + 5y = -94/9
5x + 2y = -199/36

Using elimination
5*(8x + 5y = -94/9)
8*(5x + 2y = -199/36)
40x + 25y = -470/9
40x + 16y = -398/9
Subtract equations
9y = -8
y = -8/9
y = -8/9

Substitute y
8x + 5(-8/9) = -94/9
8x = -6
x = -6/8
x = -3/4


Input: Find x in x^2 + 83/5x + 182/5 = 0

Output:
x^2 + 83/5x + 182/5 = 0
(x - -14)(x - -13/5) = 0
x - -14 = 0  or  x - -13/5 = 0
x = -14
x = -13/5


Input: Find x for 2x - 17 = 0

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


Input:
Solve the system:
8x + 8y = 32
9x + 1y = 116

Output:
8x + 8y = 32
9x + 1y = 116

Using elimination
9*(8x + 8y = 32)
8*(9x + 1y = 116)
72x + 72y = 288
72x + 8y = 928
Subtract equations
64y = -640
y = -640/64
y = -10

Substitute y
8x + 8(-10) = 32
8x = 112
x = 112/8
x = 14


Input: What value of x satisfies 3x - 19/3 = 0

Output:
3x - 19/3 = 0
3x = 19/3
x = 19/3 / 3
x = 19/9


Input:
Solve the equations:
5x + 10y = -130/3
10x + 4y = -172/3

Output:
5x + 10y = -130/3
10x + 4y = -172/3

Using elimination
10*(5x + 10y = -130/3)
5*(10x + 4y = -172/3)
50x + 100y = -1300/3
50x + 20y = -860/3
Subtract equations
80y = -440/3
y = -440/3/80
y = -11/6

Substitute y
5x + 10(-11/6) = -130/3
5x = -25
x = -25/5
x = -5


Input: What value of x satisfies x^2 + 1/8x - 3/16 = 0

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


Input: What value of x satisfies x^2 - 52/9x + 140/27 = 0

Output:
x^2 - 52/9x + 140/27 = 0
(x - 10/9)(x - 14/3) = 0
x - 10/9 = 0  or  x - 14/3 = 0
x = 10/9
x = 14/3


Input: What value of x satisfies x^3 - 25/8x^2 - 83/32x + 665/64 = 0

Output:
x^3 - 25/8x^2 - 83/32x + 665/64 = 0
(x - 5/2)(x - 19/8)(x - -7/4) = 0
x - 5/2 = 0
x - 19/8 = 0
x - -7/4 = 0
x = 5/2
x = 19/8
x = -7/4


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

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


Input:
Solve the system:
9x + 2y = -153
7x + 4y = -119

Output:
9x + 2y = -153
7x + 4y = -119

Using elimination
7*(9x + 2y = -153)
9*(7x + 4y = -119)
63x + 14y = -1071
63x + 36y = -1071
Subtract equations
-22y = 0
y = 0/-22
y = 0

Substitute y
9x + 2(0) = -153
9x = -153
x = -153/9
x = -17


Input: Solve the equation 10x + 16 = 0

Output:
10x + 16 = 0
10x = -16
x = -16 / 10
x = -8/5


Input:
Solve the equations:
2x + 4y = 94/5
10x + 4y = 774/5

Output:
2x + 4y = 94/5
10x + 4y = 774/5

Using elimination
10*(2x + 4y = 94/5)
2*(10x + 4y = 774/5)
20x + 40y = 188
20x + 8y = 1548/5
Subtract equations
32y = -608/5
y = -608/5/32
y = -19/5

Substitute y
2x + 4(-19/5) = 94/5
2x = 34
x = 34/2
x = 17


Input: Solve x^3 + 1/2x^2 - 243/2x - 342 = 0

Output:
x^3 + 1/2x^2 - 243/2x - 342 = 0
(x - -3)(x - 12)(x - -19/2) = 0
x - -3 = 0
x - 12 = 0
x - -19/2 = 0
x = -3
x = 12
x = -19/2


Input:
Solve simultaneously:
1x + 3y = -31/5
6x + 1y = 18/5

Output:
1x + 3y = -31/5
6x + 1y = 18/5

Using elimination
6*(1x + 3y = -31/5)
1*(6x + 1y = 18/5)
6x + 18y = -186/5
6x + 1y = 18/5
Subtract equations
17y = -204/5
y = -204/5/17
y = -12/5

Substitute y
1x + 3(-12/5) = -31/5
1x = 1
x = 1/1
x = 1


Input: Solve quickly: x^3 - 1/2x^2 - 239/16x + 357/16 = 0

Output:
x^3 - 1/2x^2 - 239/16x + 357/16 = 0
(x - 7/4)(x - 3)(x - -17/4) = 0
x - 7/4 = 0
x - 3 = 0
x - -17/4 = 0
x = 7/4
x = 3
x = -17/4


Input: Determine x in 10x + 140 = 0

Output:
10x + 140 = 0
10x = -140
x = -140 / 10
x = -14


Input: Determine x in 3x - 12 = 0

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


Input:
Find x and y such that
10x + 3y = 85/2
2x + 3y = 113/2

Output:
10x + 3y = 85/2
2x + 3y = 113/2

Using elimination
2*(10x + 3y = 85/2)
10*(2x + 3y = 113/2)
20x + 6y = 85
20x + 30y = 565
Subtract equations
-24y = -480
y = -480/-24
y = 20

Substitute y
10x + 3(20) = 85/2
10x = -35/2
x = -35/2/10
x = -7/4


Input:
Solve the equations:
9x + 1y = -335/2
3x + 7y = -65/2

Output:
9x + 1y = -335/2
3x + 7y = -65/2

Using elimination
3*(9x + 1y = -335/2)
9*(3x + 7y = -65/2)
27x + 3y = -1005/2
27x + 63y = -585/2
Subtract equations
-60y = -210
y = -210/-60
y = 7/2

Substitute y
9x + 1(7/2) = -335/2
9x = -171
x = -171/9
x = -19


Input: Find x in x^3 + 155/7x^2 + 300/7x  = 0

Output:
x^3 + 155/7x^2 + 300/7x  = 0
(x - 0)(x - -15/7)(x - -20) = 0
x - 0 = 0
x - -15/7 = 0
x - -20 = 0
x = 0
x = -15/7
x = -20


Input: Find the solution to 8x - 16/3 = 0

Output:
8x - 16/3 = 0
8x = 16/3
x = 16/3 / 8
x = 2/3


Input: Solve 9x + 63/5 = 0

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


Input: Determine x in 10x - 45/2 = 0

Output:
10x - 45/2 = 0
10x = 45/2
x = 45/2 / 10
x = 9/4


Input: Solve the equation x^3 + 11/7x^2 - 312/49x - 540/49 = 0

Output:
x^3 + 11/7x^2 - 312/49x - 540/49 = 0
(x - -15/7)(x - -2)(x - 18/7) = 0
x - -15/7 = 0
x - -2 = 0
x - 18/7 = 0
x = -15/7
x = -2
x = 18/7


Input: Find the solution to x^3 + 37/6x^2 - 137/18x - 770/27 = 0

Output:
x^3 + 37/6x^2 - 137/18x - 770/27 = 0
(x - 7/3)(x - -20/3)(x - -11/6) = 0
x - 7/3 = 0
x - -20/3 = 0
x - -11/6 = 0
x = 7/3
x = -20/3
x = -11/6


Input: Find x in x^3 - 19/120x^2 - 233/30x + 4199/480 = 0

Output:
x^3 - 19/120x^2 - 233/30x + 4199/480 = 0
(x - -19/6)(x - 17/10)(x - 13/8) = 0
x - -19/6 = 0
x - 17/10 = 0
x - 13/8 = 0
x = -19/6
x = 17/10
x = 13/8


Input:
Solve the equations:
2x + 4y = 79/5
9x + 10y = 91/2

Output:
2x + 4y = 79/5
9x + 10y = 91/2

Using elimination
9*(2x + 4y = 79/5)
2*(9x + 10y = 91/2)
18x + 36y = 711/5
18x + 20y = 91
Subtract equations
16y = 256/5
y = 256/5/16
y = 16/5

Substitute y
2x + 4(16/5) = 79/5
2x = 3
x = 3/2
x = 3/2


Input: Solve quickly: x^2 + 8/5x - 4/5 = 0

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


Input: Solve quickly: 3x - 39/5 = 0

Output:
3x - 39/5 = 0
3x = 39/5
x = 39/5 / 3
x = 13/5


Input: Determine x in x^3 - 191/10x^2 + 141/10x + 513/5 = 0

Output:
x^3 - 191/10x^2 + 141/10x + 513/5 = 0
(x - -19/10)(x - 18)(x - 3) = 0
x - -19/10 = 0
x - 18 = 0
x - 3 = 0
x = -19/10
x = 18
x = 3


Input: Find the solution to x^3 - 37/12x^2 + 37/12x - 1 = 0

Output:
x^3 - 37/12x^2 + 37/12x - 1 = 0
(x - 4/3)(x - 1)(x - 3/4) = 0
x - 4/3 = 0
x - 1 = 0
x - 3/4 = 0
x = 4/3
x = 1
x = 3/4


Input: Find x in x^2 + 55/12x + 25/6 = 0

Output:
x^2 + 55/12x + 25/6 = 0
(x - -5/4)(x - -10/3) = 0
x - -5/4 = 0  or  x - -10/3 = 0
x = -5/4
x = -10/3


Input: Determine x in x^3 - 52/35x^2 - 108/35x + 144/35 = 0

Output:
x^3 - 52/35x^2 - 108/35x + 144/35 = 0
(x - -12/7)(x - 6/5)(x - 2) = 0
x - -12/7 = 0
x - 6/5 = 0
x - 2 = 0
x = -12/7
x = 6/5
x = 2


Input: Compute the solution of x^3 + 85/21x^2 - 64/3x - 304/7 = 0

Output:
x^3 + 85/21x^2 - 64/3x - 304/7 = 0
(x - -12/7)(x - -19/3)(x - 4) = 0
x - -12/7 = 0
x - -19/3 = 0
x - 4 = 0
x = -12/7
x = -19/3
x = 4


Input: What value of x satisfies x^2 + 1x + 12/49 = 0

Output:
x^2 + 1x + 12/49 = 0
(x - -4/7)(x - -3/7) = 0
x - -4/7 = 0  or  x - -3/7 = 0
x = -4/7
x = -3/7


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

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


Input: Solve 4x + 76/3 = 0

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


Input: Find x for x^3 + 227/35x^2 - 1154/35x + 152/7 = 0

Output:
x^3 + 227/35x^2 - 1154/35x + 152/7 = 0
(x - -10)(x - 19/7)(x - 4/5) = 0
x - -10 = 0
x - 19/7 = 0
x - 4/5 = 0
x = -10
x = 19/7
x = 4/5


Input: Determine x in x^3 + 31/12x^2 - 75/8x - 27/8 = 0

Output:
x^3 + 31/12x^2 - 75/8x - 27/8 = 0
(x - -9/2)(x - -1/3)(x - 9/4) = 0
x - -9/2 = 0
x - -1/3 = 0
x - 9/4 = 0
x = -9/2
x = -1/3
x = 9/4


Input: Solve x^2 - 10/9x - 17/3 = 0

Output:
x^2 - 10/9x - 17/3 = 0
(x - -17/9)(x - 3) = 0
x - -17/9 = 0  or  x - 3 = 0
x = -17/9
x = 3


Input: Determine x in x^2 - 7/2x - 36 = 0

Output:
x^2 - 7/2x - 36 = 0
(x - -9/2)(x - 8) = 0
x - -9/2 = 0  or  x - 8 = 0
x = -9/2
x = 8


Input: Determine x in 3x - 27/7 = 0

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


Input: Solve the equation x^3 - 101/90x^2 - 133/90x  = 0

Output:
x^3 - 101/90x^2 - 133/90x  = 0
(x - -7/9)(x - 0)(x - 19/10) = 0
x - -7/9 = 0
x - 0 = 0
x - 19/10 = 0
x = -7/9
x = 0
x = 19/10


Input: Find the solution to x^3 - 57/5x^2 + 38x - 168/5 = 0

Output:
x^3 - 57/5x^2 + 38x - 168/5 = 0
(x - 4)(x - 6)(x - 7/5) = 0
x - 4 = 0
x - 6 = 0
x - 7/5 = 0
x = 4
x = 6
x = 7/5


Input: Find x for x^2 - 13/8x - 105/16 = 0

Output:
x^2 - 13/8x - 105/16 = 0
(x - 7/2)(x - -15/8) = 0
x - 7/2 = 0  or  x - -15/8 = 0
x = 7/2
x = -15/8


Input: Solve x^3 + 11/2x^2 - 40/9x - 350/9 = 0

Output:
x^3 + 11/2x^2 - 40/9x - 350/9 = 0
(x - 5/2)(x - -10/3)(x - -14/3) = 0
x - 5/2 = 0
x - -10/3 = 0
x - -14/3 = 0
x = 5/2
x = -10/3
x = -14/3


Input: Find x in 2x + 10 = 0

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


Input:
Solve simultaneously:
8x + 4y = 73
10x + 8y = 545/4

Output:
8x + 4y = 73
10x + 8y = 545/4

Using elimination
10*(8x + 4y = 73)
8*(10x + 8y = 545/4)
80x + 40y = 730
80x + 64y = 1090
Subtract equations
-24y = -360
y = -360/-24
y = 15

Substitute y
8x + 4(15) = 73
8x = 13
x = 13/8
x = 13/8


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

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


Input:
Solve the system:
5x + 9y = 1/4
5x + 3y = 131/12

Output:
5x + 9y = 1/4
5x + 3y = 131/12

Using elimination
5*(5x + 9y = 1/4)
5*(5x + 3y = 131/12)
25x + 45y = 5/4
25x + 15y = 655/12
Subtract equations
30y = -160/3
y = -160/3/30
y = -16/9

Substitute y
5x + 9(-16/9) = 1/4
5x = 65/4
x = 65/4/5
x = 13/4


Input: Determine x in 6x + 54/5 = 0

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


Input: Find the solution to x^3 - 154/15x^2 + 287/15x - 8 = 0

Output:
x^3 - 154/15x^2 + 287/15x - 8 = 0
(x - 5/3)(x - 8)(x - 3/5) = 0
x - 5/3 = 0
x - 8 = 0
x - 3/5 = 0
x = 5/3
x = 8
x = 3/5


Input:
Solve simultaneously:
10x + 2y = -31/4
4x + 2y = -1/4

Output:
10x + 2y = -31/4
4x + 2y = -1/4

Using elimination
4*(10x + 2y = -31/4)
10*(4x + 2y = -1/4)
40x + 8y = -31
40x + 20y = -5/2
Subtract equations
-12y = -57/2
y = -57/2/-12
y = 19/8

Substitute y
10x + 2(19/8) = -31/4
10x = -25/2
x = -25/2/10
x = -5/4


Input:
Solve the equations:
5x + 9y = 41/9
3x + 3y = 5/3

Output:
5x + 9y = 41/9
3x + 3y = 5/3

Using elimination
3*(5x + 9y = 41/9)
5*(3x + 3y = 5/3)
15x + 27y = 41/3
15x + 15y = 25/3
Subtract equations
12y = 16/3
y = 16/3/12
y = 4/9

Substitute y
5x + 9(4/9) = 41/9
5x = 5/9
x = 5/9/5
x = 1/9


Input:
Solve the equations:
3x + 9y = -477/4
6x + 4y = -85/2

Output:
3x + 9y = -477/4
6x + 4y = -85/2

Using elimination
6*(3x + 9y = -477/4)
3*(6x + 4y = -85/2)
18x + 54y = -1431/2
18x + 12y = -255/2
Subtract equations
42y = -588
y = -588/42
y = -14

Substitute y
3x + 9(-14) = -477/4
3x = 27/4
x = 27/4/3
x = 9/4


Input: Solve the equation x^3 - 383/40x^2 + 1057/80x - 49/10 = 0

Output:
x^3 - 383/40x^2 + 1057/80x - 49/10 = 0
(x - 7/8)(x - 7/10)(x - 8) = 0
x - 7/8 = 0
x - 7/10 = 0
x - 8 = 0
x = 7/8
x = 7/10
x = 8


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

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


Input: Determine x in x^3 + 185/21x^2 + 422/21x + 272/21 = 0

Output:
x^3 + 185/21x^2 + 422/21x + 272/21 = 0
(x - -2)(x - -17/3)(x - -8/7) = 0
x - -2 = 0
x - -17/3 = 0
x - -8/7 = 0
x = -2
x = -17/3
x = -8/7


Input: Solve quickly: x^2 + 13/6x - 22/3 = 0

Output:
x^2 + 13/6x - 22/3 = 0
(x - 11/6)(x - -4) = 0
x - 11/6 = 0  or  x - -4 = 0
x = 11/6
x = -4


Input: Solve quickly: x^2 + 101/24x + 35/12 = 0

Output:
x^2 + 101/24x + 35/12 = 0
(x - -10/3)(x - -7/8) = 0
x - -10/3 = 0  or  x - -7/8 = 0
x = -10/3
x = -7/8


Input: Find the solution to 1x - 15 = 0

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


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

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


Input: Find the solution to 4x + 26/3 = 0

Output:
4x + 26/3 = 0
4x = -26/3
x = -26/3 / 4
x = -13/6


Input: Find x in x^2 - 31/5x - 72/5 = 0

Output:
x^2 - 31/5x - 72/5 = 0
(x - 8)(x - -9/5) = 0
x - 8 = 0  or  x - -9/5 = 0
x = 8
x = -9/5


Input: Solve the equation 2x + 32/5 = 0

Output:
2x + 32/5 = 0
2x = -32/5
x = -32/5 / 2
x = -16/5


Input: Compute the solution of 4x - 32/5 = 0

Output:
4x - 32/5 = 0
4x = 32/5
x = 32/5 / 4
x = 8/5


Input:
Solve the system:
1x + 9y = 181/3
1x + 6y = 118/3

Output:
1x + 9y = 181/3
1x + 6y = 118/3

Using elimination
1*(1x + 9y = 181/3)
1*(1x + 6y = 118/3)
1x + 9y = 181/3
1x + 6y = 118/3
Subtract equations
3y = 21
y = 21/3
y = 7

Substitute y
1x + 9(7) = 181/3
1x = -8/3
x = -8/3/1
x = -8/3


Input: Find x in x^3 - 181/120x^2 - 221/240x + 7/16 = 0

Output:
x^3 - 181/120x^2 - 221/240x + 7/16 = 0
(x - -7/10)(x - 15/8)(x - 1/3) = 0
x - -7/10 = 0
x - 15/8 = 0
x - 1/3 = 0
x = -7/10
x = 15/8
x = 1/3


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

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


Input: Solve quickly: x^2 - 1/30x - 7/5 = 0

Output:
x^2 - 1/30x - 7/5 = 0
(x - -7/6)(x - 6/5) = 0
x - -7/6 = 0  or  x - 6/5 = 0
x = -7/6
x = 6/5


Input: Find the solution to x^3 + 129/10x^2 + 389/10x + 171/5 = 0

Output:
x^3 + 129/10x^2 + 389/10x + 171/5 = 0
(x - -9)(x - -19/10)(x - -2) = 0
x - -9 = 0
x - -19/10 = 0
x - -2 = 0
x = -9
x = -19/10
x = -2


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

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


Input:
Solve simultaneously:
5x + 4y = -101/4
9x + 9y = -225/4

Output:
5x + 4y = -101/4
9x + 9y = -225/4

Using elimination
9*(5x + 4y = -101/4)
5*(9x + 9y = -225/4)
45x + 36y = -909/4
45x + 45y = -1125/4
Subtract equations
-9y = 54
y = 54/-9
y = -6

Substitute y
5x + 4(-6) = -101/4
5x = -5/4
x = -5/4/5
x = -1/4


Input:
Solve the system:
7x + 3y = -12
6x + 6y = -72/7

Output:
7x + 3y = -12
6x + 6y = -72/7

Using elimination
6*(7x + 3y = -12)
7*(6x + 6y = -72/7)
42x + 18y = -72
42x + 42y = -72
Subtract equations
-24y = 0
y = 0/-24
y = 0

Substitute y
7x + 3(0) = -12
7x = -12
x = -12/7
x = -12/7


Input: Solve the equation x^2 + 5/2x - 7/2 = 0

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


Input:
Solve the equations:
1x + 5y = -39/14
6x + 7y = -73/14

Output:
1x + 5y = -39/14
6x + 7y = -73/14

Using elimination
6*(1x + 5y = -39/14)
1*(6x + 7y = -73/14)
6x + 30y = -117/7
6x + 7y = -73/14
Subtract equations
23y = -23/2
y = -23/2/23
y = -1/2

Substitute y
1x + 5(-1/2) = -39/14
1x = -2/7
x = -2/7/1
x = -2/7


Input: Find the solution to 3x - 27/4 = 0

Output:
3x - 27/4 = 0
3x = 27/4
x = 27/4 / 3
x = 9/4


Input:
Solve simultaneously:
1x + 2y = -83/15
9x + 6y = -119/5

Output:
1x + 2y = -83/15
9x + 6y = -119/5

Using elimination
9*(1x + 2y = -83/15)
1*(9x + 6y = -119/5)
9x + 18y = -249/5
9x + 6y = -119/5
Subtract equations
12y = -26
y = -26/12
y = -13/6

Substitute y
1x + 2(-13/6) = -83/15
1x = -6/5
x = -6/5/1
x = -6/5


Input: Find x for x^3 + 67/6x^2 + 39/2x  = 0

Output:
x^3 + 67/6x^2 + 39/2x  = 0
(x - 0)(x - -13/6)(x - -9) = 0
x - 0 = 0
x - -13/6 = 0
x - -9 = 0
x = 0
x = -13/6
x = -9


Input: Solve quickly: 8x - 18 = 0

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


Input:
Find x and y such that
5x + 5y = 69
4x + 3y = 211/5

Output:
5x + 5y = 69
4x + 3y = 211/5

Using elimination
4*(5x + 5y = 69)
5*(4x + 3y = 211/5)
20x + 20y = 276
20x + 15y = 211
Subtract equations
5y = 65
y = 65/5
y = 13

Substitute y
5x + 5(13) = 69
5x = 4
x = 4/5
x = 4/5


Input: Solve quickly: x^3 + 121/8x^2 + 223/8x + 13/4 = 0

Output:
x^3 + 121/8x^2 + 223/8x + 13/4 = 0
(x - -1/8)(x - -2)(x - -13) = 0
x - -1/8 = 0
x - -2 = 0
x - -13 = 0
x = -1/8
x = -2
x = -13


Input:
Solve the equations:
2x + 2y = 418/35
7x + 4y = 1193/35

Output:
2x + 2y = 418/35
7x + 4y = 1193/35

Using elimination
7*(2x + 2y = 418/35)
2*(7x + 4y = 1193/35)
14x + 14y = 418/5
14x + 8y = 2386/35
Subtract equations
6y = 108/7
y = 108/7/6
y = 18/7

Substitute y
2x + 2(18/7) = 418/35
2x = 34/5
x = 34/5/2
x = 17/5


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

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


Input: Solve x^2 - 3x - 10 = 0

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


Input:
Solve simultaneously:
5x + 4y = 22/5
7x + 10y = 0

Output:
5x + 4y = 22/5
7x + 10y = 0

Using elimination
7*(5x + 4y = 22/5)
5*(7x + 10y = 0)
35x + 28y = 154/5
35x + 50y = 0
Subtract equations
-22y = 154/5
y = 154/5/-22
y = -7/5

Substitute y
5x + 4(-7/5) = 22/5
5x = 10
x = 10/5
x = 2


Input: Solve x^2 + 33/8x + 35/16 = 0

Output:
x^2 + 33/8x + 35/16 = 0
(x - -5/8)(x - -7/2) = 0
x - -5/8 = 0  or  x - -7/2 = 0
x = -5/8
x = -7/2


Input: Compute the solution of 10x - 180/7 = 0

Output:
10x - 180/7 = 0
10x = 180/7
x = 180/7 / 10
x = 18/7


Input: Find the solution to x^2 - 6/35x - 8/35 = 0

Output:
x^2 - 6/35x - 8/35 = 0
(x - -2/5)(x - 4/7) = 0
x - -2/5 = 0  or  x - 4/7 = 0
x = -2/5
x = 4/7


Input: Solve quickly: 7x + 21/2 = 0

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


Input: Find x for 5x - 90/7 = 0

Output:
5x - 90/7 = 0
5x = 90/7
x = 90/7 / 5
x = 18/7


Input: Find x for x^2 - 39/5x + 54/5 = 0

Output:
x^2 - 39/5x + 54/5 = 0
(x - 6)(x - 9/5) = 0
x - 6 = 0  or  x - 9/5 = 0
x = 6
x = 9/5


Input:
Solve simultaneously:
5x + 1y = -19/12
8x + 4y = 5/3

Output:
5x + 1y = -19/12
8x + 4y = 5/3

Using elimination
8*(5x + 1y = -19/12)
5*(8x + 4y = 5/3)
40x + 8y = -38/3
40x + 20y = 25/3
Subtract equations
-12y = -21
y = -21/-12
y = 7/4

Substitute y
5x + 1(7/4) = -19/12
5x = -10/3
x = -10/3/5
x = -2/3


Input: What value of x satisfies x^3 + 14/3x^2 + 67/12x + 7/4 = 0

Output:
x^3 + 14/3x^2 + 67/12x + 7/4 = 0
(x - -3)(x - -7/6)(x - -1/2) = 0
x - -3 = 0
x - -7/6 = 0
x - -1/2 = 0
x = -3
x = -7/6
x = -1/2


Input: Find the solution to x^2 - 23/20x - 7/20 = 0

Output:
x^2 - 23/20x - 7/20 = 0
(x - 7/5)(x - -1/4) = 0
x - 7/5 = 0  or  x - -1/4 = 0
x = 7/5
x = -1/4


Input:
Find x and y such that
10x + 5y = 99
7x + 2y = 333/5

Output:
10x + 5y = 99
7x + 2y = 333/5

Using elimination
7*(10x + 5y = 99)
10*(7x + 2y = 333/5)
70x + 35y = 693
70x + 20y = 666
Subtract equations
15y = 27
y = 27/15
y = 9/5

Substitute y
10x + 5(9/5) = 99
10x = 90
x = 90/10
x = 9


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

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


Input: Find x in x^3 + 49/10x^2 + 27/10x - 18/5 = 0

Output:
x^3 + 49/10x^2 + 27/10x - 18/5 = 0
(x - 3/5)(x - -3/2)(x - -4) = 0
x - 3/5 = 0
x - -3/2 = 0
x - -4 = 0
x = 3/5
x = -3/2
x = -4


Input: What value of x satisfies x^2 - 61/40x + 9/20 = 0

Output:
x^2 - 61/40x + 9/20 = 0
(x - 9/8)(x - 2/5) = 0
x - 9/8 = 0  or  x - 2/5 = 0
x = 9/8
x = 2/5


Input:
Solve simultaneously:
3x + 10y = 8
8x + 4y = -52/5

Output:
3x + 10y = 8
8x + 4y = -52/5

Using elimination
8*(3x + 10y = 8)
3*(8x + 4y = -52/5)
24x + 80y = 64
24x + 12y = -156/5
Subtract equations
68y = 476/5
y = 476/5/68
y = 7/5

Substitute y
3x + 10(7/5) = 8
3x = -6
x = -6/3
x = -2


Input: Find x in x^2 + 61/15x - 136/15 = 0

Output:
x^2 + 61/15x - 136/15 = 0
(x - -17/3)(x - 8/5) = 0
x - -17/3 = 0  or  x - 8/5 = 0
x = -17/3
x = 8/5


Input: Solve 5x + 45/2 = 0

Output:
5x + 45/2 = 0
5x = -45/2
x = -45/2 / 5
x = -9/2


Input: Solve quickly: x^2 + 7/9x - 98/27 = 0

Output:
x^2 + 7/9x - 98/27 = 0
(x - 14/9)(x - -7/3) = 0
x - 14/9 = 0  or  x - -7/3 = 0
x = 14/9
x = -7/3


Input: Solve quickly: x^2 + 1/4x - 55/8 = 0

Output:
x^2 + 1/4x - 55/8 = 0
(x - 5/2)(x - -11/4) = 0
x - 5/2 = 0  or  x - -11/4 = 0
x = 5/2
x = -11/4


Input: Solve 9x  = 0

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


Input:
Find x and y such that
8x + 6y = 134/5
5x + 4y = 19

Output:
8x + 6y = 134/5
5x + 4y = 19

Using elimination
5*(8x + 6y = 134/5)
8*(5x + 4y = 19)
40x + 30y = 134
40x + 32y = 152
Subtract equations
-2y = -18
y = -18/-2
y = 9

Substitute y
8x + 6(9) = 134/5
8x = -136/5
x = -136/5/8
x = -17/5


Input: Solve x^2 + 76/9x - 5 = 0

Output:
x^2 + 76/9x - 5 = 0
(x - 5/9)(x - -9) = 0
x - 5/9 = 0  or  x - -9 = 0
x = 5/9
x = -9


Input:
Find x and y such that
2x + 1y = -79/10
9x + 10y = -107/4

Output:
2x + 1y = -79/10
9x + 10y = -107/4

Using elimination
9*(2x + 1y = -79/10)
2*(9x + 10y = -107/4)
18x + 9y = -711/10
18x + 20y = -107/2
Subtract equations
-11y = -88/5
y = -88/5/-11
y = 8/5

Substitute y
2x + 1(8/5) = -79/10
2x = -19/2
x = -19/2/2
x = -19/4


Input: Solve x^3 + 257/15x^2 + 496/15x + 16 = 0

Output:
x^3 + 257/15x^2 + 496/15x + 16 = 0
(x - -4/5)(x - -4/3)(x - -15) = 0
x - -4/5 = 0
x - -4/3 = 0
x - -15 = 0
x = -4/5
x = -4/3
x = -15


Input: Find x for x^2 - 35/8x + 143/32 = 0

Output:
x^2 - 35/8x + 143/32 = 0
(x - 11/4)(x - 13/8) = 0
x - 11/4 = 0  or  x - 13/8 = 0
x = 11/4
x = 13/8


Input: Compute the solution of x^2 - 9/8x - 45/8 = 0

Output:
x^2 - 9/8x - 45/8 = 0
(x - -15/8)(x - 3) = 0
x - -15/8 = 0  or  x - 3 = 0
x = -15/8
x = 3


Input:
Find x and y such that
3x + 1y = 4
4x + 7y = 39/2

Output:
3x + 1y = 4
4x + 7y = 39/2

Using elimination
4*(3x + 1y = 4)
3*(4x + 7y = 39/2)
12x + 4y = 16
12x + 21y = 117/2
Subtract equations
-17y = -85/2
y = -85/2/-17
y = 5/2

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


Input:
Find x and y such that
1x + 2y = -13/6
7x + 6y = 7/2

Output:
1x + 2y = -13/6
7x + 6y = 7/2

Using elimination
7*(1x + 2y = -13/6)
1*(7x + 6y = 7/2)
7x + 14y = -91/6
7x + 6y = 7/2
Subtract equations
8y = -56/3
y = -56/3/8
y = -7/3

Substitute y
1x + 2(-7/3) = -13/6
1x = 5/2
x = 5/2/1
x = 5/2


Input: Compute the solution of x^3 + 41/15x^2 + 33/20x  = 0

Output:
x^3 + 41/15x^2 + 33/20x  = 0
(x - -11/6)(x - -9/10)(x - 0) = 0
x - -11/6 = 0
x - -9/10 = 0
x - 0 = 0
x = -11/6
x = -9/10
x = 0


Input: Solve the equation x^3 + 67/6x^2 - 227/6x + 77/3 = 0

Output:
x^3 + 67/6x^2 - 227/6x + 77/3 = 0
(x - 1)(x - 11/6)(x - -14) = 0
x - 1 = 0
x - 11/6 = 0
x - -14 = 0
x = 1
x = 11/6
x = -14


Input:
Find x and y such that
9x + 7y = -165/2
3x + 5y = -87/2

Output:
9x + 7y = -165/2
3x + 5y = -87/2

Using elimination
3*(9x + 7y = -165/2)
9*(3x + 5y = -87/2)
27x + 21y = -495/2
27x + 45y = -783/2
Subtract equations
-24y = 144
y = 144/-24
y = -6

Substitute y
9x + 7(-6) = -165/2
9x = -81/2
x = -81/2/9
x = -9/2


Input:
Solve simultaneously:
4x + 5y = 1/3
2x + 4y = 5/3

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

Using elimination
2*(4x + 5y = 1/3)
4*(2x + 4y = 5/3)
8x + 10y = 2/3
8x + 16y = 20/3
Subtract equations
-6y = -6
y = -6/-6
y = 1

Substitute y
4x + 5(1) = 1/3
4x = -14/3
x = -14/3/4
x = -7/6


Input:
Solve the equations:
10x + 3y = -9
7x + 1y = -19/10

Output:
10x + 3y = -9
7x + 1y = -19/10

Using elimination
7*(10x + 3y = -9)
10*(7x + 1y = -19/10)
70x + 21y = -63
70x + 10y = -19
Subtract equations
11y = -44
y = -44/11
y = -4

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


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

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


Input: Solve 2x - 8/5 = 0

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


Input:
Find x and y such that
8x + 9y = 177
7x + 1y = 38

Output:
8x + 9y = 177
7x + 1y = 38

Using elimination
7*(8x + 9y = 177)
8*(7x + 1y = 38)
56x + 63y = 1239
56x + 8y = 304
Subtract equations
55y = 935
y = 935/55
y = 17

Substitute y
8x + 9(17) = 177
8x = 24
x = 24/8
x = 3


Input: Find x in 7x + 49/9 = 0

Output:
7x + 49/9 = 0
7x = -49/9
x = -49/9 / 7
x = -7/9


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

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


Input: Solve the equation 6x + 15 = 0

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


Input: Solve 4x - 16/5 = 0

Output:
4x - 16/5 = 0
4x = 16/5
x = 16/5 / 4
x = 4/5


Input: What value of x satisfies 10x + 35/2 = 0

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


Input: Compute the solution of 1x + 5/4 = 0

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


Input: Solve the equation x^3 + 10x^2 + 11/9x - 70 = 0

Output:
x^3 + 10x^2 + 11/9x - 70 = 0
(x - -10/3)(x - 7/3)(x - -9) = 0
x - -10/3 = 0
x - 7/3 = 0
x - -9 = 0
x = -10/3
x = 7/3
x = -9


Input: Compute the solution of x^2 - 54/7x - 160/7 = 0

Output:
x^2 - 54/7x - 160/7 = 0
(x - 10)(x - -16/7) = 0
x - 10 = 0  or  x - -16/7 = 0
x = 10
x = -16/7