Input:
Solve simultaneously:
10x + 6y = 57/2
9x + 7y = 101/4

Output:
10x + 6y = 57/2
9x + 7y = 101/4

Using elimination
9*(10x + 6y = 57/2)
10*(9x + 7y = 101/4)
90x + 54y = 513/2
90x + 70y = 505/2
Subtract equations
-16y = 4
y = 4/-16
y = -1/4

Substitute y
10x + 6(-1/4) = 57/2
10x = 30
x = 30/10
x = 3


Input: Solve quickly: x^3 + 723/70x^2 + 991/35x + 156/7 = 0

Output:
x^3 + 723/70x^2 + 991/35x + 156/7 = 0
(x - -12/5)(x - -13/2)(x - -10/7) = 0
x - -12/5 = 0
x - -13/2 = 0
x - -10/7 = 0
x = -12/5
x = -13/2
x = -10/7


Input: Determine x in 1x + 19/8 = 0

Output:
1x + 19/8 = 0
1x = -19/8
x = -19/8 / 1
x = -19/8


Input: Solve quickly: 6x - 27 = 0

Output:
6x - 27 = 0
6x = 27
x = 27 / 6
x = 9/2


Input: Determine x in x^2 + 37/10x + 8/5 = 0

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


Input: Find x for 7x - 21 = 0

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


Input:
Solve the equations:
2x + 5y = 49/45
3x + 1y = -154/45

Output:
2x + 5y = 49/45
3x + 1y = -154/45

Using elimination
3*(2x + 5y = 49/45)
2*(3x + 1y = -154/45)
6x + 15y = 49/15
6x + 2y = -308/45
Subtract equations
13y = 91/9
y = 91/9/13
y = 7/9

Substitute y
2x + 5(7/9) = 49/45
2x = -14/5
x = -14/5/2
x = -7/5


Input: Find x in 9x - 90 = 0

Output:
9x - 90 = 0
9x = 90
x = 90 / 9
x = 10


Input: Determine x in 3x - 57/7 = 0

Output:
3x - 57/7 = 0
3x = 57/7
x = 57/7 / 3
x = 19/7


Input: Find the solution to 1x + 1/8 = 0

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


Input: Compute the solution of x^2 - 17/63x - 10/63 = 0

Output:
x^2 - 17/63x - 10/63 = 0
(x - 5/9)(x - -2/7) = 0
x - 5/9 = 0  or  x - -2/7 = 0
x = 5/9
x = -2/7


Input: Solve 9x + 45/2 = 0

Output:
9x + 45/2 = 0
9x = -45/2
x = -45/2 / 9
x = -5/2


Input: Solve x^3 - 13/20x^2 - 221/40x + 9/4 = 0

Output:
x^3 - 13/20x^2 - 221/40x + 9/4 = 0
(x - 2/5)(x - 5/2)(x - -9/4) = 0
x - 2/5 = 0
x - 5/2 = 0
x - -9/4 = 0
x = 2/5
x = 5/2
x = -9/4


Input: Find the solution to x^3 + 89/18x^2 + 49/16x + 17/36 = 0

Output:
x^3 + 89/18x^2 + 49/16x + 17/36 = 0
(x - -1/4)(x - -4/9)(x - -17/4) = 0
x - -1/4 = 0
x - -4/9 = 0
x - -17/4 = 0
x = -1/4
x = -4/9
x = -17/4


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

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


Input:
Find x and y such that
3x + 9y = 33/2
7x + 9y = 22

Output:
3x + 9y = 33/2
7x + 9y = 22

Using elimination
7*(3x + 9y = 33/2)
3*(7x + 9y = 22)
21x + 63y = 231/2
21x + 27y = 66
Subtract equations
36y = 99/2
y = 99/2/36
y = 11/8

Substitute y
3x + 9(11/8) = 33/2
3x = 33/8
x = 33/8/3
x = 11/8


Input: Find x for x^2 - 2/3x - 8/9 = 0

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


Input: What value of x satisfies 4x + 17/2 = 0

Output:
4x + 17/2 = 0
4x = -17/2
x = -17/2 / 4
x = -17/8


Input: Solve the equation 7x + 14/5 = 0

Output:
7x + 14/5 = 0
7x = -14/5
x = -14/5 / 7
x = -2/5


Input: What value of x satisfies x^3 - 16/9x^2 - 1793/144x - 95/12 = 0

Output:
x^3 - 16/9x^2 - 1793/144x - 95/12 = 0
(x - 19/4)(x - -20/9)(x - -3/4) = 0
x - 19/4 = 0
x - -20/9 = 0
x - -3/4 = 0
x = 19/4
x = -20/9
x = -3/4


Input: Compute the solution of 9x + 27/8 = 0

Output:
9x + 27/8 = 0
9x = -27/8
x = -27/8 / 9
x = -3/8


Input: Solve the equation 4x + 68 = 0

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


Input: What value of x satisfies 7x - 133/10 = 0

Output:
7x - 133/10 = 0
7x = 133/10
x = 133/10 / 7
x = 19/10


Input: Solve quickly: x^2 - 14x - 15 = 0

Output:
x^2 - 14x - 15 = 0
(x - -1)(x - 15) = 0
x - -1 = 0  or  x - 15 = 0
x = -1
x = 15


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

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


Input: What value of x satisfies 1x - 5 = 0

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


Input: Compute the solution of x^2 - 3x - 40 = 0

Output:
x^2 - 3x - 40 = 0
(x - 8)(x - -5) = 0
x - 8 = 0  or  x - -5 = 0
x = 8
x = -5


Input: Find the solution to x^2 + 5/7x - 48/7 = 0

Output:
x^2 + 5/7x - 48/7 = 0
(x - -3)(x - 16/7) = 0
x - -3 = 0  or  x - 16/7 = 0
x = -3
x = 16/7


Input: What value of x satisfies 1x - 7/6 = 0

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


Input: Compute the solution of 8x + 4 = 0

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


Input: Solve x^2 + 25/4x + 57/8 = 0

Output:
x^2 + 25/4x + 57/8 = 0
(x - -3/2)(x - -19/4) = 0
x - -3/2 = 0  or  x - -19/4 = 0
x = -3/2
x = -19/4


Input: Solve x^2 + 109/9x + 190/9 = 0

Output:
x^2 + 109/9x + 190/9 = 0
(x - -19/9)(x - -10) = 0
x - -19/9 = 0  or  x - -10 = 0
x = -19/9
x = -10


Input: Solve the equation x^2 + 77/9x + 40/9 = 0

Output:
x^2 + 77/9x + 40/9 = 0
(x - -8)(x - -5/9) = 0
x - -8 = 0  or  x - -5/9 = 0
x = -8
x = -5/9


Input:
Solve simultaneously:
7x + 1y = -1192/45
2x + 10y = -292/45

Output:
7x + 1y = -1192/45
2x + 10y = -292/45

Using elimination
2*(7x + 1y = -1192/45)
7*(2x + 10y = -292/45)
14x + 2y = -2384/45
14x + 70y = -2044/45
Subtract equations
-68y = -68/9
y = -68/9/-68
y = 1/9

Substitute y
7x + 1(1/9) = -1192/45
7x = -133/5
x = -133/5/7
x = -19/5


Input: Find x for x^3 + 7/6x^2 - 66x - 459/2 = 0

Output:
x^3 + 7/6x^2 - 66x - 459/2 = 0
(x - -9/2)(x - 9)(x - -17/3) = 0
x - -9/2 = 0
x - 9 = 0
x - -17/3 = 0
x = -9/2
x = 9
x = -17/3


Input: Solve x^3 - 31/3x^2 + 415/12x - 75/2 = 0

Output:
x^3 - 31/3x^2 + 415/12x - 75/2 = 0
(x - 9/2)(x - 5/2)(x - 10/3) = 0
x - 9/2 = 0
x - 5/2 = 0
x - 10/3 = 0
x = 9/2
x = 5/2
x = 10/3


Input: Solve the equation x^3 - 529/30x^2 - 521/10x + 286/3 = 0

Output:
x^3 - 529/30x^2 - 521/10x + 286/3 = 0
(x - 13/10)(x - -11/3)(x - 20) = 0
x - 13/10 = 0
x - -11/3 = 0
x - 20 = 0
x = 13/10
x = -11/3
x = 20


Input: Solve x^2 + 1x - 28/9 = 0

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


Input:
Solve simultaneously:
6x + 8y = 137/6
4x + 1y = 11/3

Output:
6x + 8y = 137/6
4x + 1y = 11/3

Using elimination
4*(6x + 8y = 137/6)
6*(4x + 1y = 11/3)
24x + 32y = 274/3
24x + 6y = 22
Subtract equations
26y = 208/3
y = 208/3/26
y = 8/3

Substitute y
6x + 8(8/3) = 137/6
6x = 3/2
x = 3/2/6
x = 1/4


Input:
Find x and y such that
1x + 6y = 281/10
8x + 1y = 133/10

Output:
1x + 6y = 281/10
8x + 1y = 133/10

Using elimination
8*(1x + 6y = 281/10)
1*(8x + 1y = 133/10)
8x + 48y = 1124/5
8x + 1y = 133/10
Subtract equations
47y = 423/2
y = 423/2/47
y = 9/2

Substitute y
1x + 6(9/2) = 281/10
1x = 11/10
x = 11/10/1
x = 11/10


Input:
Solve the equations:
8x + 9y = 64
4x + 3y = 20

Output:
8x + 9y = 64
4x + 3y = 20

Using elimination
4*(8x + 9y = 64)
8*(4x + 3y = 20)
32x + 36y = 256
32x + 24y = 160
Subtract equations
12y = 96
y = 96/12
y = 8

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


Input:
Find x and y such that
8x + 10y = 110/3
7x + 4y = 44/3

Output:
8x + 10y = 110/3
7x + 4y = 44/3

Using elimination
7*(8x + 10y = 110/3)
8*(7x + 4y = 44/3)
56x + 70y = 770/3
56x + 32y = 352/3
Subtract equations
38y = 418/3
y = 418/3/38
y = 11/3

Substitute y
8x + 10(11/3) = 110/3
8x = 0
x = 0/8
x = 0


Input: Solve quickly: x^2 + 9/7x - 36/7 = 0

Output:
x^2 + 9/7x - 36/7 = 0
(x - 12/7)(x - -3) = 0
x - 12/7 = 0  or  x - -3 = 0
x = 12/7
x = -3


Input: Find x for x^3 + 89/30x^2 + 19/15x - 3/2 = 0

Output:
x^3 + 89/30x^2 + 19/15x - 3/2 = 0
(x - -9/5)(x - 1/2)(x - -5/3) = 0
x - -9/5 = 0
x - 1/2 = 0
x - -5/3 = 0
x = -9/5
x = 1/2
x = -5/3


Input: Find the solution to 4x + 34 = 0

Output:
4x + 34 = 0
4x = -34
x = -34 / 4
x = -17/2


Input:
Solve the system:
10x + 4y = 65/3
2x + 10y = 59/3

Output:
10x + 4y = 65/3
2x + 10y = 59/3

Using elimination
2*(10x + 4y = 65/3)
10*(2x + 10y = 59/3)
20x + 8y = 130/3
20x + 100y = 590/3
Subtract equations
-92y = -460/3
y = -460/3/-92
y = 5/3

Substitute y
10x + 4(5/3) = 65/3
10x = 15
x = 15/10
x = 3/2


Input: Find the solution to x^3 - 172/35x^2 + 179/35x + 66/35 = 0

Output:
x^3 - 172/35x^2 + 179/35x + 66/35 = 0
(x - 3)(x - -2/7)(x - 11/5) = 0
x - 3 = 0
x - -2/7 = 0
x - 11/5 = 0
x = 3
x = -2/7
x = 11/5


Input: Find x in x^3 + 221/15x^2 + 506/15x + 56/5 = 0

Output:
x^3 + 221/15x^2 + 506/15x + 56/5 = 0
(x - -12)(x - -2/5)(x - -7/3) = 0
x - -12 = 0
x - -2/5 = 0
x - -7/3 = 0
x = -12
x = -2/5
x = -7/3


Input:
Find x and y such that
8x + 1y = -50/3
3x + 1y = -35/6

Output:
8x + 1y = -50/3
3x + 1y = -35/6

Using elimination
3*(8x + 1y = -50/3)
8*(3x + 1y = -35/6)
24x + 3y = -50
24x + 8y = -140/3
Subtract equations
-5y = -10/3
y = -10/3/-5
y = 2/3

Substitute y
8x + 1(2/3) = -50/3
8x = -52/3
x = -52/3/8
x = -13/6


Input: Solve quickly: x^2 + 32/5x + 7 = 0

Output:
x^2 + 32/5x + 7 = 0
(x - -5)(x - -7/5) = 0
x - -5 = 0  or  x - -7/5 = 0
x = -5
x = -7/5


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

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


Input: Find the solution to x^3 - 29/70x^2 - 1346/245x - 208/49 = 0

Output:
x^3 - 29/70x^2 - 1346/245x - 208/49 = 0
(x - 20/7)(x - -13/10)(x - -8/7) = 0
x - 20/7 = 0
x - -13/10 = 0
x - -8/7 = 0
x = 20/7
x = -13/10
x = -8/7


Input: Find x in x^2 - 17/2x - 9/2 = 0

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


Input: Solve quickly: 1x - 10 = 0

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


Input: Solve x^3 + 5x^2 - 274x + 520 = 0

Output:
x^3 + 5x^2 - 274x + 520 = 0
(x - 2)(x - 13)(x - -20) = 0
x - 2 = 0
x - 13 = 0
x - -20 = 0
x = 2
x = 13
x = -20


Input: Solve x^3 - 169/105x^2 - 187/35x + 9 = 0

Output:
x^3 - 169/105x^2 - 187/35x + 9 = 0
(x - 9/5)(x - 15/7)(x - -7/3) = 0
x - 9/5 = 0
x - 15/7 = 0
x - -7/3 = 0
x = 9/5
x = 15/7
x = -7/3


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

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


Input:
Solve simultaneously:
3x + 8y = -22/5
2x + 10y = -52/5

Output:
3x + 8y = -22/5
2x + 10y = -52/5

Using elimination
2*(3x + 8y = -22/5)
3*(2x + 10y = -52/5)
6x + 16y = -44/5
6x + 30y = -156/5
Subtract equations
-14y = 112/5
y = 112/5/-14
y = -8/5

Substitute y
3x + 8(-8/5) = -22/5
3x = 42/5
x = 42/5/3
x = 14/5


Input: Determine x in x^2 - 93/10x - 19/10 = 0

Output:
x^2 - 93/10x - 19/10 = 0
(x - -1/5)(x - 19/2) = 0
x - -1/5 = 0  or  x - 19/2 = 0
x = -1/5
x = 19/2


Input: Solve 5x - 10 = 0

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


Input: Find x in x^3 + 1597/360x^2 + 1451/240x + 1729/720 = 0

Output:
x^3 + 1597/360x^2 + 1451/240x + 1729/720 = 0
(x - -19/9)(x - -13/8)(x - -7/10) = 0
x - -19/9 = 0
x - -13/8 = 0
x - -7/10 = 0
x = -19/9
x = -13/8
x = -7/10


Input: What value of x satisfies x^3 - 37/10x^2 + 11/20x + 21/40 = 0

Output:
x^3 - 37/10x^2 + 11/20x + 21/40 = 0
(x - 1/2)(x - -3/10)(x - 7/2) = 0
x - 1/2 = 0
x - -3/10 = 0
x - 7/2 = 0
x = 1/2
x = -3/10
x = 7/2


Input: Solve the equation x^2 - 11/3x - 26/9 = 0

Output:
x^2 - 11/3x - 26/9 = 0
(x - 13/3)(x - -2/3) = 0
x - 13/3 = 0  or  x - -2/3 = 0
x = 13/3
x = -2/3


Input:
Solve simultaneously:
10x + 9y = 307/5
6x + 5y = 37

Output:
10x + 9y = 307/5
6x + 5y = 37

Using elimination
6*(10x + 9y = 307/5)
10*(6x + 5y = 37)
60x + 54y = 1842/5
60x + 50y = 370
Subtract equations
4y = -8/5
y = -8/5/4
y = -2/5

Substitute y
10x + 9(-2/5) = 307/5
10x = 65
x = 65/10
x = 13/2


Input: Compute the solution of 7x + 21 = 0

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


Input: Solve x^2 - 17/3x - 76 = 0

Output:
x^2 - 17/3x - 76 = 0
(x - 12)(x - -19/3) = 0
x - 12 = 0  or  x - -19/3 = 0
x = 12
x = -19/3


Input: Solve quickly: x^2 + 259/72x + 209/72 = 0

Output:
x^2 + 259/72x + 209/72 = 0
(x - -19/8)(x - -11/9) = 0
x - -19/8 = 0  or  x - -11/9 = 0
x = -19/8
x = -11/9


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

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


Input: Solve the equation 9x + 135/7 = 0

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


Input:
Solve the equations:
10x + 10y = -100/3
1x + 8y = -52/3

Output:
10x + 10y = -100/3
1x + 8y = -52/3

Using elimination
1*(10x + 10y = -100/3)
10*(1x + 8y = -52/3)
10x + 10y = -100/3
10x + 80y = -520/3
Subtract equations
-70y = 140
y = 140/-70
y = -2

Substitute y
10x + 10(-2) = -100/3
10x = -40/3
x = -40/3/10
x = -4/3


Input: Find x for x^2 + 55/4x + 323/8 = 0

Output:
x^2 + 55/4x + 323/8 = 0
(x - -17/4)(x - -19/2) = 0
x - -17/4 = 0  or  x - -19/2 = 0
x = -17/4
x = -19/2


Input: Solve x^2 - 7/3x - 26/3 = 0

Output:
x^2 - 7/3x - 26/3 = 0
(x - -2)(x - 13/3) = 0
x - -2 = 0  or  x - 13/3 = 0
x = -2
x = 13/3


Input: Compute the solution of x^2 - 13/4x - 3 = 0

Output:
x^2 - 13/4x - 3 = 0
(x - 4)(x - -3/4) = 0
x - 4 = 0  or  x - -3/4 = 0
x = 4
x = -3/4


Input:
Solve the system:
6x + 3y = 446/21
7x + 3y = 1471/63

Output:
6x + 3y = 446/21
7x + 3y = 1471/63

Using elimination
7*(6x + 3y = 446/21)
6*(7x + 3y = 1471/63)
42x + 21y = 446/3
42x + 18y = 2942/21
Subtract equations
3y = 60/7
y = 60/7/3
y = 20/7

Substitute y
6x + 3(20/7) = 446/21
6x = 38/3
x = 38/3/6
x = 19/9


Input: Find x for 8x + 136/9 = 0

Output:
8x + 136/9 = 0
8x = -136/9
x = -136/9 / 8
x = -17/9


Input: Solve the equation x^2 - 39/40x - 1 = 0

Output:
x^2 - 39/40x - 1 = 0
(x - 8/5)(x - -5/8) = 0
x - 8/5 = 0  or  x - -5/8 = 0
x = 8/5
x = -5/8


Input: Solve the equation 7x + 119/4 = 0

Output:
7x + 119/4 = 0
7x = -119/4
x = -119/4 / 7
x = -17/4


Input: Determine x in x^2 - 71/8x - 45/4 = 0

Output:
x^2 - 71/8x - 45/4 = 0
(x - 10)(x - -9/8) = 0
x - 10 = 0  or  x - -9/8 = 0
x = 10
x = -9/8


Input: Solve quickly: 1x + 3/4 = 0

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


Input: Determine x in x^2 + 3/8x - 13/4 = 0

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


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

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


Input:
Find x and y such that
9x + 4y = -98/5
1x + 10y = -6

Output:
9x + 4y = -98/5
1x + 10y = -6

Using elimination
1*(9x + 4y = -98/5)
9*(1x + 10y = -6)
9x + 4y = -98/5
9x + 90y = -54
Subtract equations
-86y = 172/5
y = 172/5/-86
y = -2/5

Substitute y
9x + 4(-2/5) = -98/5
9x = -18
x = -18/9
x = -2


Input: Determine x in x^3 + 21x^2 + 104x  = 0

Output:
x^3 + 21x^2 + 104x  = 0
(x - 0)(x - -8)(x - -13) = 0
x - 0 = 0
x - -8 = 0
x - -13 = 0
x = 0
x = -8
x = -13


Input: Determine x in x^2 + 3/2x + 11/25 = 0

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


Input:
Find x and y such that
3x + 2y = 19/2
9x + 10y = 71/2

Output:
3x + 2y = 19/2
9x + 10y = 71/2

Using elimination
9*(3x + 2y = 19/2)
3*(9x + 10y = 71/2)
27x + 18y = 171/2
27x + 30y = 213/2
Subtract equations
-12y = -21
y = -21/-12
y = 7/4

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


Input: Find x in 3x + 18 = 0

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


Input: Determine x in 8x - 40/3 = 0

Output:
8x - 40/3 = 0
8x = 40/3
x = 40/3 / 8
x = 5/3


Input: Find x in x^2 + 11/8x - 5/4 = 0

Output:
x^2 + 11/8x - 5/4 = 0
(x - -2)(x - 5/8) = 0
x - -2 = 0  or  x - 5/8 = 0
x = -2
x = 5/8


Input:
Solve simultaneously:
9x + 5y = -91/2
9x + 3y = -93/2

Output:
9x + 5y = -91/2
9x + 3y = -93/2

Using elimination
9*(9x + 5y = -91/2)
9*(9x + 3y = -93/2)
81x + 45y = -819/2
81x + 27y = -837/2
Subtract equations
18y = 9
y = 9/18
y = 1/2

Substitute y
9x + 5(1/2) = -91/2
9x = -48
x = -48/9
x = -16/3


Input:
Solve simultaneously:
1x + 10y = -9/4
8x + 1y = -18

Output:
1x + 10y = -9/4
8x + 1y = -18

Using elimination
8*(1x + 10y = -9/4)
1*(8x + 1y = -18)
8x + 80y = -18
8x + 1y = -18
Subtract equations
79y = 0
y = 0/79
y = 0

Substitute y
1x + 10(0) = -9/4
1x = -9/4
x = -9/4/1
x = -9/4


Input: Solve 10x + 15/2 = 0

Output:
10x + 15/2 = 0
10x = -15/2
x = -15/2 / 10
x = -3/4


Input: Find x for 4x - 38 = 0

Output:
4x - 38 = 0
4x = 38
x = 38 / 4
x = 19/2


Input: Solve quickly: x^2 + 13/4x - 3 = 0

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


Input: What value of x satisfies 4x + 11/2 = 0

Output:
4x + 11/2 = 0
4x = -11/2
x = -11/2 / 4
x = -11/8


Input: Solve 1x - 1/3 = 0

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


Input: What value of x satisfies x^3 + 23/3x^2 + 2x - 56/3 = 0

Output:
x^3 + 23/3x^2 + 2x - 56/3 = 0
(x - -7)(x - -2)(x - 4/3) = 0
x - -7 = 0
x - -2 = 0
x - 4/3 = 0
x = -7
x = -2
x = 4/3


Input: Solve quickly: 5x - 13 = 0

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


Input: Solve x^3 - 29/36x^2 - 161/54x - 49/36 = 0

Output:
x^3 - 29/36x^2 - 161/54x - 49/36 = 0
(x - -3/4)(x - -7/9)(x - 7/3) = 0
x - -3/4 = 0
x - -7/9 = 0
x - 7/3 = 0
x = -3/4
x = -7/9
x = 7/3


Input: Determine x in x^3 - 31/40x^2 - 361/160x + 77/80 = 0

Output:
x^3 - 31/40x^2 - 361/160x + 77/80 = 0
(x - 7/4)(x - 2/5)(x - -11/8) = 0
x - 7/4 = 0
x - 2/5 = 0
x - -11/8 = 0
x = 7/4
x = 2/5
x = -11/8


Input:
Solve simultaneously:
4x + 4y = 58/9
4x + 7y = 143/18

Output:
4x + 4y = 58/9
4x + 7y = 143/18

Using elimination
4*(4x + 4y = 58/9)
4*(4x + 7y = 143/18)
16x + 16y = 232/9
16x + 28y = 286/9
Subtract equations
-12y = -6
y = -6/-12
y = 1/2

Substitute y
4x + 4(1/2) = 58/9
4x = 40/9
x = 40/9/4
x = 10/9


Input:
Solve the system:
10x + 6y = 79/7
6x + 4y = 46/7

Output:
10x + 6y = 79/7
6x + 4y = 46/7

Using elimination
6*(10x + 6y = 79/7)
10*(6x + 4y = 46/7)
60x + 36y = 474/7
60x + 40y = 460/7
Subtract equations
-4y = 2
y = 2/-4
y = -1/2

Substitute y
10x + 6(-1/2) = 79/7
10x = 100/7
x = 100/7/10
x = 10/7


Input: Determine x in x^3 + 53/12x^2 - 52/3x + 21/4 = 0

Output:
x^3 + 53/12x^2 - 52/3x + 21/4 = 0
(x - 9/4)(x - 1/3)(x - -7) = 0
x - 9/4 = 0
x - 1/3 = 0
x - -7 = 0
x = 9/4
x = 1/3
x = -7


Input: Find x for x^2 - 87/8x - 27/2 = 0

Output:
x^2 - 87/8x - 27/2 = 0
(x - -9/8)(x - 12) = 0
x - -9/8 = 0  or  x - 12 = 0
x = -9/8
x = 12


Input: Solve quickly: x^3 - 43/70x^2 - 5/14x - 1/35 = 0

Output:
x^3 - 43/70x^2 - 5/14x - 1/35 = 0
(x - -1/10)(x - 1)(x - -2/7) = 0
x - -1/10 = 0
x - 1 = 0
x - -2/7 = 0
x = -1/10
x = 1
x = -2/7


Input: Find x in 8x + 40/3 = 0

Output:
8x + 40/3 = 0
8x = -40/3
x = -40/3 / 8
x = -5/3


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

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


Input:
Solve simultaneously:
10x + 1y = -493/42
3x + 5y = -773/42

Output:
10x + 1y = -493/42
3x + 5y = -773/42

Using elimination
3*(10x + 1y = -493/42)
10*(3x + 5y = -773/42)
30x + 3y = -493/14
30x + 50y = -3865/21
Subtract equations
-47y = 893/6
y = 893/6/-47
y = -19/6

Substitute y
10x + 1(-19/6) = -493/42
10x = -60/7
x = -60/7/10
x = -6/7


Input: Solve the equation 10x + 160 = 0

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


Input: Solve the equation x^2 - 19/3x - 68 = 0

Output:
x^2 - 19/3x - 68 = 0
(x - -17/3)(x - 12) = 0
x - -17/3 = 0  or  x - 12 = 0
x = -17/3
x = 12


Input: Find x in x^3 + 10x^2 - 1349/25x + 714/25 = 0

Output:
x^3 + 10x^2 - 1349/25x + 714/25 = 0
(x - 17/5)(x - -14)(x - 3/5) = 0
x - 17/5 = 0
x - -14 = 0
x - 3/5 = 0
x = 17/5
x = -14
x = 3/5


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

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


Input:
Find x and y such that
7x + 4y = 4/3
2x + 1y = 2/3

Output:
7x + 4y = 4/3
2x + 1y = 2/3

Using elimination
2*(7x + 4y = 4/3)
7*(2x + 1y = 2/3)
14x + 8y = 8/3
14x + 7y = 14/3
Subtract equations
1y = -2
y = -2/1
y = -2

Substitute y
7x + 4(-2) = 4/3
7x = 28/3
x = 28/3/7
x = 4/3


Input: Solve the equation x^3 - 49/4x^2 + 329/8x - 165/4 = 0

Output:
x^3 - 49/4x^2 + 329/8x - 165/4 = 0
(x - 11/4)(x - 2)(x - 15/2) = 0
x - 11/4 = 0
x - 2 = 0
x - 15/2 = 0
x = 11/4
x = 2
x = 15/2


Input:
Find x and y such that
3x + 9y = -933/56
10x + 9y = -1493/56

Output:
3x + 9y = -933/56
10x + 9y = -1493/56

Using elimination
10*(3x + 9y = -933/56)
3*(10x + 9y = -1493/56)
30x + 90y = -4665/28
30x + 27y = -4479/56
Subtract equations
63y = -693/8
y = -693/8/63
y = -11/8

Substitute y
3x + 9(-11/8) = -933/56
3x = -30/7
x = -30/7/3
x = -10/7


Input: Solve x^2 - 5x - 6 = 0

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


Input: Solve quickly: x^2 + 25/3x + 38/3 = 0

Output:
x^2 + 25/3x + 38/3 = 0
(x - -2)(x - -19/3) = 0
x - -2 = 0  or  x - -19/3 = 0
x = -2
x = -19/3


Input: Solve x^3 + 454/45x^2 - 169/45x - 418/9 = 0

Output:
x^3 + 454/45x^2 - 169/45x - 418/9 = 0
(x - -11/5)(x - 19/9)(x - -10) = 0
x - -11/5 = 0
x - 19/9 = 0
x - -10 = 0
x = -11/5
x = 19/9
x = -10


Input: Find x in x^2 + 23/6x - 2/3 = 0

Output:
x^2 + 23/6x - 2/3 = 0
(x - 1/6)(x - -4) = 0
x - 1/6 = 0  or  x - -4 = 0
x = 1/6
x = -4


Input: What value of x satisfies x^3 - 11/18x^2 - 13/9x + 1/6 = 0

Output:
x^3 - 11/18x^2 - 13/9x + 1/6 = 0
(x - 3/2)(x - -1)(x - 1/9) = 0
x - 3/2 = 0
x - -1 = 0
x - 1/9 = 0
x = 3/2
x = -1
x = 1/9


Input:
Solve the system:
9x + 3y = 67/5
8x + 3y = 64/5

Output:
9x + 3y = 67/5
8x + 3y = 64/5

Using elimination
8*(9x + 3y = 67/5)
9*(8x + 3y = 64/5)
72x + 24y = 536/5
72x + 27y = 576/5
Subtract equations
-3y = -8
y = -8/-3
y = 8/3

Substitute y
9x + 3(8/3) = 67/5
9x = 27/5
x = 27/5/9
x = 3/5


Input: What value of x satisfies 8x - 40 = 0

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


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

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


Input: Find the solution to 10x + 26 = 0

Output:
10x + 26 = 0
10x = -26
x = -26 / 10
x = -13/5


Input: Find x in x^3 + 941/56x^2 - 177/8x - 297/28 = 0

Output:
x^3 + 941/56x^2 - 177/8x - 297/28 = 0
(x - -18)(x - -3/8)(x - 11/7) = 0
x - -18 = 0
x - -3/8 = 0
x - 11/7 = 0
x = -18
x = -3/8
x = 11/7


Input: Find the solution to x^2 - 22/5x + 17/5 = 0

Output:
x^2 - 22/5x + 17/5 = 0
(x - 17/5)(x - 1) = 0
x - 17/5 = 0  or  x - 1 = 0
x = 17/5
x = 1


Input: What value of x satisfies x^3 - 9/35x^2 - 34/7x - 24/35 = 0

Output:
x^3 - 9/35x^2 - 34/7x - 24/35 = 0
(x - -2)(x - -1/7)(x - 12/5) = 0
x - -2 = 0
x - -1/7 = 0
x - 12/5 = 0
x = -2
x = -1/7
x = 12/5


Input:
Solve the equations:
9x + 7y = 729/70
8x + 2y = 457/35

Output:
9x + 7y = 729/70
8x + 2y = 457/35

Using elimination
8*(9x + 7y = 729/70)
9*(8x + 2y = 457/35)
72x + 56y = 2916/35
72x + 18y = 4113/35
Subtract equations
38y = -171/5
y = -171/5/38
y = -9/10

Substitute y
9x + 7(-9/10) = 729/70
9x = 117/7
x = 117/7/9
x = 13/7


Input: Solve the equation x^3 + 138/35x^2 + 113/25x + 264/175 = 0

Output:
x^3 + 138/35x^2 + 113/25x + 264/175 = 0
(x - -11/5)(x - -8/7)(x - -3/5) = 0
x - -11/5 = 0
x - -8/7 = 0
x - -3/5 = 0
x = -11/5
x = -8/7
x = -3/5


Input:
Find x and y such that
6x + 6y = 300/7
7x + 9y = 60

Output:
6x + 6y = 300/7
7x + 9y = 60

Using elimination
7*(6x + 6y = 300/7)
6*(7x + 9y = 60)
42x + 42y = 300
42x + 54y = 360
Subtract equations
-12y = -60
y = -60/-12
y = 5

Substitute y
6x + 6(5) = 300/7
6x = 90/7
x = 90/7/6
x = 15/7


Input:
Solve the equations:
8x + 2y = -10/21
6x + 10y = 766/21

Output:
8x + 2y = -10/21
6x + 10y = 766/21

Using elimination
6*(8x + 2y = -10/21)
8*(6x + 10y = 766/21)
48x + 12y = -20/7
48x + 80y = 6128/21
Subtract equations
-68y = -884/3
y = -884/3/-68
y = 13/3

Substitute y
8x + 2(13/3) = -10/21
8x = -64/7
x = -64/7/8
x = -8/7


Input: Find x in x^3 - 58/21x^2 - 19/21x + 4/7 = 0

Output:
x^3 - 58/21x^2 - 19/21x + 4/7 = 0
(x - 1/3)(x - -4/7)(x - 3) = 0
x - 1/3 = 0
x - -4/7 = 0
x - 3 = 0
x = 1/3
x = -4/7
x = 3


Input: Find x for x^2 - 37/10x + 21/10 = 0

Output:
x^2 - 37/10x + 21/10 = 0
(x - 7/10)(x - 3) = 0
x - 7/10 = 0  or  x - 3 = 0
x = 7/10
x = 3


Input:
Solve the equations:
10x + 2y = -826/9
1x + 10y = -161/9

Output:
10x + 2y = -826/9
1x + 10y = -161/9

Using elimination
1*(10x + 2y = -826/9)
10*(1x + 10y = -161/9)
10x + 2y = -826/9
10x + 100y = -1610/9
Subtract equations
-98y = 784/9
y = 784/9/-98
y = -8/9

Substitute y
10x + 2(-8/9) = -826/9
10x = -90
x = -90/10
x = -9


Input:
Solve the equations:
4x + 10y = 472/9
3x + 5y = 73/3

Output:
4x + 10y = 472/9
3x + 5y = 73/3

Using elimination
3*(4x + 10y = 472/9)
4*(3x + 5y = 73/3)
12x + 30y = 472/3
12x + 20y = 292/3
Subtract equations
10y = 60
y = 60/10
y = 6

Substitute y
4x + 10(6) = 472/9
4x = -68/9
x = -68/9/4
x = -17/9


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

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


Input: Solve quickly: x^2 - 13/8x + 21/32 = 0

Output:
x^2 - 13/8x + 21/32 = 0
(x - 7/8)(x - 3/4) = 0
x - 7/8 = 0  or  x - 3/4 = 0
x = 7/8
x = 3/4


Input: Compute the solution of x^2 + 93/20x + 17/10 = 0

Output:
x^2 + 93/20x + 17/10 = 0
(x - -17/4)(x - -2/5) = 0
x - -17/4 = 0  or  x - -2/5 = 0
x = -17/4
x = -2/5


Input: Determine x in 8x + 64/5 = 0

Output:
8x + 64/5 = 0
8x = -64/5
x = -64/5 / 8
x = -8/5


Input:
Solve simultaneously:
1x + 5y = 155/12
1x + 7y = 211/12

Output:
1x + 5y = 155/12
1x + 7y = 211/12

Using elimination
1*(1x + 5y = 155/12)
1*(1x + 7y = 211/12)
1x + 5y = 155/12
1x + 7y = 211/12
Subtract equations
-2y = -14/3
y = -14/3/-2
y = 7/3

Substitute y
1x + 5(7/3) = 155/12
1x = 5/4
x = 5/4/1
x = 5/4


Input: Find x for 10x - 70/3 = 0

Output:
10x - 70/3 = 0
10x = 70/3
x = 70/3 / 10
x = 7/3


Input: Find the solution to 7x - 112/3 = 0

Output:
7x - 112/3 = 0
7x = 112/3
x = 112/3 / 7
x = 16/3


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

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


Input: Solve the equation 4x - 4 = 0

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


Input: Solve quickly: 5x - 65 = 0

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


Input: Find x in x^3 - 11/6x^2 + 61/162x + 5/27 = 0

Output:
x^3 - 11/6x^2 + 61/162x + 5/27 = 0
(x - 3/2)(x - -2/9)(x - 5/9) = 0
x - 3/2 = 0
x - -2/9 = 0
x - 5/9 = 0
x = 3/2
x = -2/9
x = 5/9


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

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


Input: Find the solution to 2x + 7/5 = 0

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


Input: Solve x^2 - 27/4x + 81/8 = 0

Output:
x^2 - 27/4x + 81/8 = 0
(x - 9/2)(x - 9/4) = 0
x - 9/2 = 0  or  x - 9/4 = 0
x = 9/2
x = 9/4


Input: Solve the equation 9x - 12 = 0

Output:
9x - 12 = 0
9x = 12
x = 12 / 9
x = 4/3


Input: Solve the equation 7x - 14 = 0

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


Input: What value of x satisfies x^2 - 2/3x + 5/81 = 0

Output:
x^2 - 2/3x + 5/81 = 0
(x - 1/9)(x - 5/9) = 0
x - 1/9 = 0  or  x - 5/9 = 0
x = 1/9
x = 5/9


Input: Find x in x^3 - 97/40x^2 + 191/160x + 11/32 = 0

Output:
x^3 - 97/40x^2 + 191/160x + 11/32 = 0
(x - 11/8)(x - 5/4)(x - -1/5) = 0
x - 11/8 = 0
x - 5/4 = 0
x - -1/5 = 0
x = 11/8
x = 5/4
x = -1/5


Input:
Solve simultaneously:
5x + 8y = 53/5
1x + 10y = -13

Output:
5x + 8y = 53/5
1x + 10y = -13

Using elimination
1*(5x + 8y = 53/5)
5*(1x + 10y = -13)
5x + 8y = 53/5
5x + 50y = -65
Subtract equations
-42y = 378/5
y = 378/5/-42
y = -9/5

Substitute y
5x + 8(-9/5) = 53/5
5x = 25
x = 25/5
x = 5


Input:
Solve the equations:
9x + 3y = 33/2
5x + 4y = 129/10

Output:
9x + 3y = 33/2
5x + 4y = 129/10

Using elimination
5*(9x + 3y = 33/2)
9*(5x + 4y = 129/10)
45x + 15y = 165/2
45x + 36y = 1161/10
Subtract equations
-21y = -168/5
y = -168/5/-21
y = 8/5

Substitute y
9x + 3(8/5) = 33/2
9x = 117/10
x = 117/10/9
x = 13/10


Input: Determine x in x^3 - 16x^2 - 76x - 80 = 0

Output:
x^3 - 16x^2 - 76x - 80 = 0
(x - -2)(x - -2)(x - 20) = 0
x - -2 = 0
x - -2 = 0
x - 20 = 0
x = -2
x = -2
x = 20


Input:
Solve the system:
4x + 4y = 8
1x + 5y = 22/3

Output:
4x + 4y = 8
1x + 5y = 22/3

Using elimination
1*(4x + 4y = 8)
4*(1x + 5y = 22/3)
4x + 4y = 8
4x + 20y = 88/3
Subtract equations
-16y = -64/3
y = -64/3/-16
y = 4/3

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


Input:
Solve simultaneously:
4x + 5y = 61/5
2x + 3y = 33/5

Output:
4x + 5y = 61/5
2x + 3y = 33/5

Using elimination
2*(4x + 5y = 61/5)
4*(2x + 3y = 33/5)
8x + 10y = 122/5
8x + 12y = 132/5
Subtract equations
-2y = -2
y = -2/-2
y = 1

Substitute y
4x + 5(1) = 61/5
4x = 36/5
x = 36/5/4
x = 9/5


Input: Find x in x^3 + 152/63x^2 - 281/189x - 884/189 = 0

Output:
x^3 + 152/63x^2 - 281/189x - 884/189 = 0
(x - -13/7)(x - -17/9)(x - 4/3) = 0
x - -13/7 = 0
x - -17/9 = 0
x - 4/3 = 0
x = -13/7
x = -17/9
x = 4/3


Input: Solve the equation x^2 - 19/8x  = 0

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


Input: Find x in x^2 - 13/18x - 10/3 = 0

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


Input: Solve x^3 - 1/15x^2 - 16/3x - 64/15 = 0

Output:
x^3 - 1/15x^2 - 16/3x - 64/15 = 0
(x - -8/5)(x - 8/3)(x - -1) = 0
x - -8/5 = 0
x - 8/3 = 0
x - -1 = 0
x = -8/5
x = 8/3
x = -1


Input:
Solve the system:
9x + 6y = -37
3x + 4y = -77/3

Output:
9x + 6y = -37
3x + 4y = -77/3

Using elimination
3*(9x + 6y = -37)
9*(3x + 4y = -77/3)
27x + 18y = -111
27x + 36y = -231
Subtract equations
-18y = 120
y = 120/-18
y = -20/3

Substitute y
9x + 6(-20/3) = -37
9x = 3
x = 3/9
x = 1/3


Input:
Solve simultaneously:
3x + 5y = -10
6x + 5y = -10

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

Using elimination
6*(3x + 5y = -10)
3*(6x + 5y = -10)
18x + 30y = -60
18x + 15y = -30
Subtract equations
15y = -30
y = -30/15
y = -2

Substitute y
3x + 5(-2) = -10
3x = 0
x = 0/3
x = 0


Input: Find the solution to x^2 - 2x + 19/100 = 0

Output:
x^2 - 2x + 19/100 = 0
(x - 19/10)(x - 1/10) = 0
x - 19/10 = 0  or  x - 1/10 = 0
x = 19/10
x = 1/10


Input: Solve quickly: 5x + 10/3 = 0

Output:
5x + 10/3 = 0
5x = -10/3
x = -10/3 / 5
x = -2/3


Input: What value of x satisfies x^2 + 7x + 110/9 = 0

Output:
x^2 + 7x + 110/9 = 0
(x - -11/3)(x - -10/3) = 0
x - -11/3 = 0  or  x - -10/3 = 0
x = -11/3
x = -10/3


Input:
Solve the equations:
4x + 4y = 16/9
3x + 10y = -86/9

Output:
4x + 4y = 16/9
3x + 10y = -86/9

Using elimination
3*(4x + 4y = 16/9)
4*(3x + 10y = -86/9)
12x + 12y = 16/3
12x + 40y = -344/9
Subtract equations
-28y = 392/9
y = 392/9/-28
y = -14/9

Substitute y
4x + 4(-14/9) = 16/9
4x = 8
x = 8/4
x = 2


Input: Find x in x^2 - 1/10x - 9/10 = 0

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


Input: Determine x in x^2 - 28/15x - 32/15 = 0

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


Input: Find x in 1x + 3/8 = 0

Output:
1x + 3/8 = 0
1x = -3/8
x = -3/8 / 1
x = -3/8


Input: Solve quickly: x^2 + 73/10x + 26/5 = 0

Output:
x^2 + 73/10x + 26/5 = 0
(x - -13/2)(x - -4/5) = 0
x - -13/2 = 0  or  x - -4/5 = 0
x = -13/2
x = -4/5


Input: What value of x satisfies x^2 - 107/12x + 15 = 0

Output:
x^2 - 107/12x + 15 = 0
(x - 9/4)(x - 20/3) = 0
x - 9/4 = 0  or  x - 20/3 = 0
x = 9/4
x = 20/3


Input: Find x in x^2 - 37/90x - 7/9 = 0

Output:
x^2 - 37/90x - 7/9 = 0
(x - 10/9)(x - -7/10) = 0
x - 10/9 = 0  or  x - -7/10 = 0
x = 10/9
x = -7/10


Input: What value of x satisfies x^3 + 49/60x^2 - 41/5x + 119/60 = 0

Output:
x^3 + 49/60x^2 - 41/5x + 119/60 = 0
(x - 1/4)(x - -17/5)(x - 7/3) = 0
x - 1/4 = 0
x - -17/5 = 0
x - 7/3 = 0
x = 1/4
x = -17/5
x = 7/3


Input:
Find x and y such that
3x + 3y = -69/2
9x + 10y = -211/2

Output:
3x + 3y = -69/2
9x + 10y = -211/2

Using elimination
9*(3x + 3y = -69/2)
3*(9x + 10y = -211/2)
27x + 27y = -621/2
27x + 30y = -633/2
Subtract equations
-3y = 6
y = 6/-3
y = -2

Substitute y
3x + 3(-2) = -69/2
3x = -57/2
x = -57/2/3
x = -19/2


Input:
Solve simultaneously:
7x + 8y = -547/7
8x + 10y = -626/7

Output:
7x + 8y = -547/7
8x + 10y = -626/7

Using elimination
8*(7x + 8y = -547/7)
7*(8x + 10y = -626/7)
56x + 64y = -4376/7
56x + 70y = -626
Subtract equations
-6y = 6/7
y = 6/7/-6
y = -1/7

Substitute y
7x + 8(-1/7) = -547/7
7x = -77
x = -77/7
x = -11


Input: Find the solution to x^2 + 19/5x + 18/5 = 0

Output:
x^2 + 19/5x + 18/5 = 0
(x - -9/5)(x - -2) = 0
x - -9/5 = 0  or  x - -2 = 0
x = -9/5
x = -2


Input: Determine x in 1x - 17 = 0

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


Input: Solve quickly: x^3 - 151/6x^2 + 625/6x - 50/3 = 0

Output:
x^3 - 151/6x^2 + 625/6x - 50/3 = 0
(x - 5)(x - 20)(x - 1/6) = 0
x - 5 = 0
x - 20 = 0
x - 1/6 = 0
x = 5
x = 20
x = 1/6


Input: Find the solution to x^2 + 37/24x + 11/48 = 0

Output:
x^2 + 37/24x + 11/48 = 0
(x - -11/8)(x - -1/6) = 0
x - -11/8 = 0  or  x - -1/6 = 0
x = -11/8
x = -1/6


Input:
Solve the system:
3x + 7y = 437/4
3x + 2y = 157/4

Output:
3x + 7y = 437/4
3x + 2y = 157/4

Using elimination
3*(3x + 7y = 437/4)
3*(3x + 2y = 157/4)
9x + 21y = 1311/4
9x + 6y = 471/4
Subtract equations
15y = 210
y = 210/15
y = 14

Substitute y
3x + 7(14) = 437/4
3x = 45/4
x = 45/4/3
x = 15/4


Input:
Find x and y such that
3x + 9y = 69/5
1x + 9y = 74/5

Output:
3x + 9y = 69/5
1x + 9y = 74/5

Using elimination
1*(3x + 9y = 69/5)
3*(1x + 9y = 74/5)
3x + 9y = 69/5
3x + 27y = 222/5
Subtract equations
-18y = -153/5
y = -153/5/-18
y = 17/10

Substitute y
3x + 9(17/10) = 69/5
3x = -3/2
x = -3/2/3
x = -1/2


Input: Solve 6x + 108/5 = 0

Output:
6x + 108/5 = 0
6x = -108/5
x = -108/5 / 6
x = -18/5


Input: Find the solution to 2x + 26/5 = 0

Output:
2x + 26/5 = 0
2x = -26/5
x = -26/5 / 2
x = -13/5


Input: Determine x in 4x + 8 = 0

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


Input: Compute the solution of x^2 + 4/7x - 20/7 = 0

Output:
x^2 + 4/7x - 20/7 = 0
(x - 10/7)(x - -2) = 0
x - 10/7 = 0  or  x - -2 = 0
x = 10/7
x = -2


Input:
Solve the equations:
4x + 8y = -64/3
9x + 3y = 12

Output:
4x + 8y = -64/3
9x + 3y = 12

Using elimination
9*(4x + 8y = -64/3)
4*(9x + 3y = 12)
36x + 72y = -192
36x + 12y = 48
Subtract equations
60y = -240
y = -240/60
y = -4

Substitute y
4x + 8(-4) = -64/3
4x = 32/3
x = 32/3/4
x = 8/3


Input: Find the solution to x^3 + 103/45x^2 - 110/27x - 136/135 = 0

Output:
x^3 + 103/45x^2 - 110/27x - 136/135 = 0
(x - -17/5)(x - 4/3)(x - -2/9) = 0
x - -17/5 = 0
x - 4/3 = 0
x - -2/9 = 0
x = -17/5
x = 4/3
x = -2/9


Input: Find x in 2x + 1 = 0

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


Input: Find x for x^3 - 137/24x^2 + 175/24x - 11/6 = 0

Output:
x^3 - 137/24x^2 + 175/24x - 11/6 = 0
(x - 4)(x - 1/3)(x - 11/8) = 0
x - 4 = 0
x - 1/3 = 0
x - 11/8 = 0
x = 4
x = 1/3
x = 11/8


Input: Find x for x^3 + 47/10x^2 - 46/5x - 42/5 = 0

Output:
x^3 + 47/10x^2 - 46/5x - 42/5 = 0
(x - 2)(x - -7/10)(x - -6) = 0
x - 2 = 0
x - -7/10 = 0
x - -6 = 0
x = 2
x = -7/10
x = -6


Input: What value of x satisfies x^3 - 103/42x^2 - 2/21x + 65/42 = 0

Output:
x^3 - 103/42x^2 - 2/21x + 65/42 = 0
(x - 1)(x - 13/6)(x - -5/7) = 0
x - 1 = 0
x - 13/6 = 0
x - -5/7 = 0
x = 1
x = 13/6
x = -5/7


Input: Solve x^3 + 103/18x^2 + 22/9x - 35/6 = 0

Output:
x^3 + 103/18x^2 + 22/9x - 35/6 = 0
(x - 7/9)(x - -3/2)(x - -5) = 0
x - 7/9 = 0
x - -3/2 = 0
x - -5 = 0
x = 7/9
x = -3/2
x = -5


Input: Solve x^2 + 13/63x - 2/21 = 0

Output:
x^2 + 13/63x - 2/21 = 0
(x - 2/9)(x - -3/7) = 0
x - 2/9 = 0  or  x - -3/7 = 0
x = 2/9
x = -3/7


Input:
Solve simultaneously:
4x + 7y = 74/9
5x + 8y = 91/9

Output:
4x + 7y = 74/9
5x + 8y = 91/9

Using elimination
5*(4x + 7y = 74/9)
4*(5x + 8y = 91/9)
20x + 35y = 370/9
20x + 32y = 364/9
Subtract equations
3y = 2/3
y = 2/3/3
y = 2/9

Substitute y
4x + 7(2/9) = 74/9
4x = 20/3
x = 20/3/4
x = 5/3


Input: Find the solution to x^2 - 269/90x + 187/90 = 0

Output:
x^2 - 269/90x + 187/90 = 0
(x - 11/10)(x - 17/9) = 0
x - 11/10 = 0  or  x - 17/9 = 0
x = 11/10
x = 17/9


Input: Find x for x^3 + 58/5x^2 - 63/5x - 468/5 = 0

Output:
x^3 + 58/5x^2 - 63/5x - 468/5 = 0
(x - -13/5)(x - 3)(x - -12) = 0
x - -13/5 = 0
x - 3 = 0
x - -12 = 0
x = -13/5
x = 3
x = -12


Input: Find x for x^3 - 39/10x^2 + 1699/405x - 304/405 = 0

Output:
x^3 - 39/10x^2 + 1699/405x - 304/405 = 0
(x - 19/10)(x - 16/9)(x - 2/9) = 0
x - 19/10 = 0
x - 16/9 = 0
x - 2/9 = 0
x = 19/10
x = 16/9
x = 2/9


Input:
Solve simultaneously:
2x + 1y = -38/21
5x + 7y = -536/21

Output:
2x + 1y = -38/21
5x + 7y = -536/21

Using elimination
5*(2x + 1y = -38/21)
2*(5x + 7y = -536/21)
10x + 5y = -190/21
10x + 14y = -1072/21
Subtract equations
-9y = 42
y = 42/-9
y = -14/3

Substitute y
2x + 1(-14/3) = -38/21
2x = 20/7
x = 20/7/2
x = 10/7


Input: Solve the equation 4x - 24 = 0

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


Input: Find x in 1x - 9 = 0

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


Input: What value of x satisfies x^3 - 11/2x^2 + 10x - 6 = 0

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


Input: Determine x in x^3 + 1/9x^2 - 20/27x + 4/27 = 0

Output:
x^3 + 1/9x^2 - 20/27x + 4/27 = 0
(x - 2/9)(x - 2/3)(x - -1) = 0
x - 2/9 = 0
x - 2/3 = 0
x - -1 = 0
x = 2/9
x = 2/3
x = -1


Input: Solve x^2 + 65/28x + 33/28 = 0

Output:
x^2 + 65/28x + 33/28 = 0
(x - -3/4)(x - -11/7) = 0
x - -3/4 = 0  or  x - -11/7 = 0
x = -3/4
x = -11/7


Input: What value of x satisfies 8x - 11 = 0

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


Input: Compute the solution of 7x + 49/2 = 0

Output:
7x + 49/2 = 0
7x = -49/2
x = -49/2 / 7
x = -7/2


Input: Solve 1x - 17 = 0

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


Input: What value of x satisfies 4x - 68/9 = 0

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


Input:
Solve the equations:
2x + 2y = -105/4
1x + 10y = 15/4

Output:
2x + 2y = -105/4
1x + 10y = 15/4

Using elimination
1*(2x + 2y = -105/4)
2*(1x + 10y = 15/4)
2x + 2y = -105/4
2x + 20y = 15/2
Subtract equations
-18y = -135/4
y = -135/4/-18
y = 15/8

Substitute y
2x + 2(15/8) = -105/4
2x = -30
x = -30/2
x = -15


Input:
Find x and y such that
1x + 10y = -38/3
3x + 6y = -10

Output:
1x + 10y = -38/3
3x + 6y = -10

Using elimination
3*(1x + 10y = -38/3)
1*(3x + 6y = -10)
3x + 30y = -38
3x + 6y = -10
Subtract equations
24y = -28
y = -28/24
y = -7/6

Substitute y
1x + 10(-7/6) = -38/3
1x = -1
x = -1/1
x = -1


Input: Solve 10x - 6 = 0

Output:
10x - 6 = 0
10x = 6
x = 6 / 10
x = 3/5


Input: Determine x in x^2 + 53/21x - 8/21 = 0

Output:
x^2 + 53/21x - 8/21 = 0
(x - -8/3)(x - 1/7) = 0
x - -8/3 = 0  or  x - 1/7 = 0
x = -8/3
x = 1/7


Input: Solve x^2 - 5x - 6 = 0

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


Input: Compute the solution of x^3 - 62/15x^2 + 73/15x - 6/5 = 0

Output:
x^3 - 62/15x^2 + 73/15x - 6/5 = 0
(x - 2)(x - 1/3)(x - 9/5) = 0
x - 2 = 0
x - 1/3 = 0
x - 9/5 = 0
x = 2
x = 1/3
x = 9/5


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

Output:
2x - 7/3 = 0
2x = 7/3
x = 7/3 / 2
x = 7/6


Input: Solve x^2 - 17/5x + 14/5 = 0

Output:
x^2 - 17/5x + 14/5 = 0
(x - 7/5)(x - 2) = 0
x - 7/5 = 0  or  x - 2 = 0
x = 7/5
x = 2


Input:
Solve simultaneously:
6x + 4y = 21/5
1x + 7y = -587/30

Output:
6x + 4y = 21/5
1x + 7y = -587/30

Using elimination
1*(6x + 4y = 21/5)
6*(1x + 7y = -587/30)
6x + 4y = 21/5
6x + 42y = -587/5
Subtract equations
-38y = 608/5
y = 608/5/-38
y = -16/5

Substitute y
6x + 4(-16/5) = 21/5
6x = 17
x = 17/6
x = 17/6


Input: Find the solution to x^2 + 38/5x + 48/5 = 0

Output:
x^2 + 38/5x + 48/5 = 0
(x - -8/5)(x - -6) = 0
x - -8/5 = 0  or  x - -6 = 0
x = -8/5
x = -6


Input: Solve the equation x^3 + 37/10x^2 + 3/25x - 297/50 = 0

Output:
x^3 + 37/10x^2 + 3/25x - 297/50 = 0
(x - -3)(x - 11/10)(x - -9/5) = 0
x - -3 = 0
x - 11/10 = 0
x - -9/5 = 0
x = -3
x = 11/10
x = -9/5


Input: Solve quickly: 1x  = 0

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


Input: Find x in 5x - 85/7 = 0

Output:
5x - 85/7 = 0
5x = 85/7
x = 85/7 / 5
x = 17/7


Input: Find the solution to x^3 + 13/18x^2 - 190/27x + 50/9 = 0

Output:
x^3 + 13/18x^2 - 190/27x + 50/9 = 0
(x - -10/3)(x - 10/9)(x - 3/2) = 0
x - -10/3 = 0
x - 10/9 = 0
x - 3/2 = 0
x = -10/3
x = 10/9
x = 3/2


Input: Solve x^3 + 14x^2 + 23x - 110 = 0

Output:
x^3 + 14x^2 + 23x - 110 = 0
(x - 2)(x - -11)(x - -5) = 0
x - 2 = 0
x - -11 = 0
x - -5 = 0
x = 2
x = -11
x = -5


Input: Find x in x^3 + 9/2x^2 - 16x - 39/2 = 0

Output:
x^3 + 9/2x^2 - 16x - 39/2 = 0
(x - -1)(x - 3)(x - -13/2) = 0
x - -1 = 0
x - 3 = 0
x - -13/2 = 0
x = -1
x = 3
x = -13/2


Input: Find the solution to x^3 + 14x^2 + 151/4x - 45/2 = 0

Output:
x^3 + 14x^2 + 151/4x - 45/2 = 0
(x - 1/2)(x - -9/2)(x - -10) = 0
x - 1/2 = 0
x - -9/2 = 0
x - -10 = 0
x = 1/2
x = -9/2
x = -10


Input: Find the solution to x^2 + 9/4x - 45/8 = 0

Output:
x^2 + 9/4x - 45/8 = 0
(x - -15/4)(x - 3/2) = 0
x - -15/4 = 0  or  x - 3/2 = 0
x = -15/4
x = 3/2


Input:
Solve the equations:
6x + 8y = 413/5
2x + 4y = 211/5

Output:
6x + 8y = 413/5
2x + 4y = 211/5

Using elimination
2*(6x + 8y = 413/5)
6*(2x + 4y = 211/5)
12x + 16y = 826/5
12x + 24y = 1266/5
Subtract equations
-8y = -88
y = -88/-8
y = 11

Substitute y
6x + 8(11) = 413/5
6x = -27/5
x = -27/5/6
x = -9/10


Input: What value of x satisfies x^3 - 15/4x^2 + 783/200x - 19/25 = 0

Output:
x^3 - 15/4x^2 + 783/200x - 19/25 = 0
(x - 1/4)(x - 8/5)(x - 19/10) = 0
x - 1/4 = 0
x - 8/5 = 0
x - 19/10 = 0
x = 1/4
x = 8/5
x = 19/10


Input: Find x for x^2 + 19x + 34 = 0

Output:
x^2 + 19x + 34 = 0
(x - -17)(x - -2) = 0
x - -17 = 0  or  x - -2 = 0
x = -17
x = -2


Input: Find the solution to x^3 + 13/6x^2 - 83/6x - 15 = 0

Output:
x^3 + 13/6x^2 - 83/6x - 15 = 0
(x - -1)(x - 10/3)(x - -9/2) = 0
x - -1 = 0
x - 10/3 = 0
x - -9/2 = 0
x = -1
x = 10/3
x = -9/2


Input: Find x in x^2 + 161/36x + 143/36 = 0

Output:
x^2 + 161/36x + 143/36 = 0
(x - -13/4)(x - -11/9) = 0
x - -13/4 = 0  or  x - -11/9 = 0
x = -13/4
x = -11/9


Input: Determine x in x^2 - 19/5x + 78/25 = 0

Output:
x^2 - 19/5x + 78/25 = 0
(x - 6/5)(x - 13/5) = 0
x - 6/5 = 0  or  x - 13/5 = 0
x = 6/5
x = 13/5


Input:
Find x and y such that
3x + 1y = -13/4
8x + 10y = -217/6

Output:
3x + 1y = -13/4
8x + 10y = -217/6

Using elimination
8*(3x + 1y = -13/4)
3*(8x + 10y = -217/6)
24x + 8y = -26
24x + 30y = -217/2
Subtract equations
-22y = 165/2
y = 165/2/-22
y = -15/4

Substitute y
3x + 1(-15/4) = -13/4
3x = 1/2
x = 1/2/3
x = 1/6


Input:
Find x and y such that
9x + 7y = -91/8
10x + 10y = -265/28

Output:
9x + 7y = -91/8
10x + 10y = -265/28

Using elimination
10*(9x + 7y = -91/8)
9*(10x + 10y = -265/28)
90x + 70y = -455/4
90x + 90y = -2385/28
Subtract equations
-20y = -200/7
y = -200/7/-20
y = 10/7

Substitute y
9x + 7(10/7) = -91/8
9x = -171/8
x = -171/8/9
x = -19/8


Input:
Solve simultaneously:
6x + 2y = 98/15
10x + 8y = 70/3

Output:
6x + 2y = 98/15
10x + 8y = 70/3

Using elimination
10*(6x + 2y = 98/15)
6*(10x + 8y = 70/3)
60x + 20y = 196/3
60x + 48y = 140
Subtract equations
-28y = -224/3
y = -224/3/-28
y = 8/3

Substitute y
6x + 2(8/3) = 98/15
6x = 6/5
x = 6/5/6
x = 1/5


Input: Find the solution to 2x + 20/3 = 0

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


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

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


Input: Compute the solution of x^3 - 11/3x^2 - 577/12x - 209/3 = 0

Output:
x^3 - 11/3x^2 - 577/12x - 209/3 = 0
(x - 19/2)(x - -11/6)(x - -4) = 0
x - 19/2 = 0
x - -11/6 = 0
x - -4 = 0
x = 19/2
x = -11/6
x = -4


Input: Solve x^2 + 7/3x - 10/3 = 0

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


Input: Find x for x^3 - 43/10x^2 + 211/45x - 68/45 = 0

Output:
x^3 - 43/10x^2 + 211/45x - 68/45 = 0
(x - 4/5)(x - 2/3)(x - 17/6) = 0
x - 4/5 = 0
x - 2/3 = 0
x - 17/6 = 0
x = 4/5
x = 2/3
x = 17/6


Input:
Solve simultaneously:
1x + 1y = -65/9
10x + 7y = -515/9

Output:
1x + 1y = -65/9
10x + 7y = -515/9

Using elimination
10*(1x + 1y = -65/9)
1*(10x + 7y = -515/9)
10x + 10y = -650/9
10x + 7y = -515/9
Subtract equations
3y = -15
y = -15/3
y = -5

Substitute y
1x + 1(-5) = -65/9
1x = -20/9
x = -20/9/1
x = -20/9


Input: Solve 9x + 9 = 0

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


Input: Find the solution to x^3 - 6/5x^2 - 549/20x - 81/10 = 0

Output:
x^3 - 6/5x^2 - 549/20x - 81/10 = 0
(x - 6)(x - -9/2)(x - -3/10) = 0
x - 6 = 0
x - -9/2 = 0
x - -3/10 = 0
x = 6
x = -9/2
x = -3/10


Input: Find x in x^2 - 146/9x - 119/9 = 0

Output:
x^2 - 146/9x - 119/9 = 0
(x - 17)(x - -7/9) = 0
x - 17 = 0  or  x - -7/9 = 0
x = 17
x = -7/9


Input:
Find x and y such that
4x + 7y = -79/10
2x + 7y = -99/10

Output:
4x + 7y = -79/10
2x + 7y = -99/10

Using elimination
2*(4x + 7y = -79/10)
4*(2x + 7y = -99/10)
8x + 14y = -79/5
8x + 28y = -198/5
Subtract equations
-14y = 119/5
y = 119/5/-14
y = -17/10

Substitute y
4x + 7(-17/10) = -79/10
4x = 4
x = 4/4
x = 1


Input:
Solve simultaneously:
3x + 8y = 59/3
4x + 5y = 134/9

Output:
3x + 8y = 59/3
4x + 5y = 134/9

Using elimination
4*(3x + 8y = 59/3)
3*(4x + 5y = 134/9)
12x + 32y = 236/3
12x + 15y = 134/3
Subtract equations
17y = 34
y = 34/17
y = 2

Substitute y
3x + 8(2) = 59/3
3x = 11/3
x = 11/3/3
x = 11/9


Input: What value of x satisfies x^2 - 25/4x - 21/4 = 0

Output:
x^2 - 25/4x - 21/4 = 0
(x - -3/4)(x - 7) = 0
x - -3/4 = 0  or  x - 7 = 0
x = -3/4
x = 7


Input: Solve the equation 6x - 15 = 0

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


Input: Find x in x^2 + 13/12x - 15/2 = 0

Output:
x^2 + 13/12x - 15/2 = 0
(x - -10/3)(x - 9/4) = 0
x - -10/3 = 0  or  x - 9/4 = 0
x = -10/3
x = 9/4


Input: Compute the solution of x^3 - 43/40x^2 - 29/160x + 3/80 = 0

Output:
x^3 - 43/40x^2 - 29/160x + 3/80 = 0
(x - 1/8)(x - 6/5)(x - -1/4) = 0
x - 1/8 = 0
x - 6/5 = 0
x - -1/4 = 0
x = 1/8
x = 6/5
x = -1/4


Input: Find x in 8x - 160/3 = 0

Output:
8x - 160/3 = 0
8x = 160/3
x = 160/3 / 8
x = 20/3


Input:
Find x and y such that
4x + 5y = -67/9
4x + 3y = -11/3

Output:
4x + 5y = -67/9
4x + 3y = -11/3

Using elimination
4*(4x + 5y = -67/9)
4*(4x + 3y = -11/3)
16x + 20y = -268/9
16x + 12y = -44/3
Subtract equations
8y = -136/9
y = -136/9/8
y = -17/9

Substitute y
4x + 5(-17/9) = -67/9
4x = 2
x = 2/4
x = 1/2


Input: Solve the equation x^2 - 6x - 133/4 = 0

Output:
x^2 - 6x - 133/4 = 0
(x - -7/2)(x - 19/2) = 0
x - -7/2 = 0  or  x - 19/2 = 0
x = -7/2
x = 19/2


Input: Solve 2x - 2 = 0

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


Input: Find x for x^2 + 21x + 20 = 0

Output:
x^2 + 21x + 20 = 0
(x - -20)(x - -1) = 0
x - -20 = 0  or  x - -1 = 0
x = -20
x = -1


Input: Solve quickly: x^3 + 194/35x^2 + 353/35x + 6 = 0

Output:
x^3 + 194/35x^2 + 353/35x + 6 = 0
(x - -7/5)(x - -2)(x - -15/7) = 0
x - -7/5 = 0
x - -2 = 0
x - -15/7 = 0
x = -7/5
x = -2
x = -15/7


Input:
Find x and y such that
3x + 2y = 18/5
4x + 6y = -26/5

Output:
3x + 2y = 18/5
4x + 6y = -26/5

Using elimination
4*(3x + 2y = 18/5)
3*(4x + 6y = -26/5)
12x + 8y = 72/5
12x + 18y = -78/5
Subtract equations
-10y = 30
y = 30/-10
y = -3

Substitute y
3x + 2(-3) = 18/5
3x = 48/5
x = 48/5/3
x = 16/5


Input:
Solve the equations:
5x + 8y = 121/6
7x + 9y = 55/2

Output:
5x + 8y = 121/6
7x + 9y = 55/2

Using elimination
7*(5x + 8y = 121/6)
5*(7x + 9y = 55/2)
35x + 56y = 847/6
35x + 45y = 275/2
Subtract equations
11y = 11/3
y = 11/3/11
y = 1/3

Substitute y
5x + 8(1/3) = 121/6
5x = 35/2
x = 35/2/5
x = 7/2


Input: Determine x in x^2 - 43/18x - 19/2 = 0

Output:
x^2 - 43/18x - 19/2 = 0
(x - 9/2)(x - -19/9) = 0
x - 9/2 = 0  or  x - -19/9 = 0
x = 9/2
x = -19/9


Input:
Solve simultaneously:
7x + 3y = -206/63
3x + 8y = -110/21

Output:
7x + 3y = -206/63
3x + 8y = -110/21

Using elimination
3*(7x + 3y = -206/63)
7*(3x + 8y = -110/21)
21x + 9y = -206/21
21x + 56y = -110/3
Subtract equations
-47y = 188/7
y = 188/7/-47
y = -4/7

Substitute y
7x + 3(-4/7) = -206/63
7x = -14/9
x = -14/9/7
x = -2/9


Input: Compute the solution of x^3 - 17/12x^2 - 247/18x + 169/36 = 0

Output:
x^3 - 17/12x^2 - 247/18x + 169/36 = 0
(x - 13/3)(x - 1/3)(x - -13/4) = 0
x - 13/3 = 0
x - 1/3 = 0
x - -13/4 = 0
x = 13/3
x = 1/3
x = -13/4


Input:
Find x and y such that
7x + 3y = -361/63
2x + 4y = -584/63

Output:
7x + 3y = -361/63
2x + 4y = -584/63

Using elimination
2*(7x + 3y = -361/63)
7*(2x + 4y = -584/63)
14x + 6y = -722/63
14x + 28y = -584/9
Subtract equations
-22y = 374/7
y = 374/7/-22
y = -17/7

Substitute y
7x + 3(-17/7) = -361/63
7x = 14/9
x = 14/9/7
x = 2/9


Input: What value of x satisfies x^2 + 157/8x - 15/2 = 0

Output:
x^2 + 157/8x - 15/2 = 0
(x - 3/8)(x - -20) = 0
x - 3/8 = 0  or  x - -20 = 0
x = 3/8
x = -20


Input: Find the solution to 7x - 56/5 = 0

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


Input:
Solve the system:
3x + 6y = -173/21
6x + 1y = -730/63

Output:
3x + 6y = -173/21
6x + 1y = -730/63

Using elimination
6*(3x + 6y = -173/21)
3*(6x + 1y = -730/63)
18x + 36y = -346/7
18x + 3y = -730/21
Subtract equations
33y = -44/3
y = -44/3/33
y = -4/9

Substitute y
3x + 6(-4/9) = -173/21
3x = -39/7
x = -39/7/3
x = -13/7


Input:
Solve simultaneously:
10x + 6y = 130/9
1x + 1y = 25/9

Output:
10x + 6y = 130/9
1x + 1y = 25/9

Using elimination
1*(10x + 6y = 130/9)
10*(1x + 1y = 25/9)
10x + 6y = 130/9
10x + 10y = 250/9
Subtract equations
-4y = -40/3
y = -40/3/-4
y = 10/3

Substitute y
10x + 6(10/3) = 130/9
10x = -50/9
x = -50/9/10
x = -5/9


Input:
Solve the equations:
8x + 2y = 38
1x + 9y = 719/4

Output:
8x + 2y = 38
1x + 9y = 719/4

Using elimination
1*(8x + 2y = 38)
8*(1x + 9y = 719/4)
8x + 2y = 38
8x + 72y = 1438
Subtract equations
-70y = -1400
y = -1400/-70
y = 20

Substitute y
8x + 2(20) = 38
8x = -2
x = -2/8
x = -1/4


Input: Find x for 10x + 20/3 = 0

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


Input: Find x for 6x - 51/2 = 0

Output:
6x - 51/2 = 0
6x = 51/2
x = 51/2 / 6
x = 17/4


Input:
Solve the equations:
6x + 9y = -48/5
5x + 5y = -11/2

Output:
6x + 9y = -48/5
5x + 5y = -11/2

Using elimination
5*(6x + 9y = -48/5)
6*(5x + 5y = -11/2)
30x + 45y = -48
30x + 30y = -33
Subtract equations
15y = -15
y = -15/15
y = -1

Substitute y
6x + 9(-1) = -48/5
6x = -3/5
x = -3/5/6
x = -1/10


Input: Solve 1x + 5/9 = 0

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


Input: Find the solution to x^3 + 11/12x^2 - 19/8x - 15/8 = 0

Output:
x^3 + 11/12x^2 - 19/8x - 15/8 = 0
(x - -3/4)(x - 3/2)(x - -5/3) = 0
x - -3/4 = 0
x - 3/2 = 0
x - -5/3 = 0
x = -3/4
x = 3/2
x = -5/3


Input: Solve quickly: x^3 + 159/8x^2 + 285/32x - 4693/32 = 0

Output:
x^3 + 159/8x^2 + 285/32x - 4693/32 = 0
(x - -13/4)(x - -19)(x - 19/8) = 0
x - -13/4 = 0
x - -19 = 0
x - 19/8 = 0
x = -13/4
x = -19
x = 19/8


Input:
Find x and y such that
10x + 10y = -75/2
10x + 7y = -33

Output:
10x + 10y = -75/2
10x + 7y = -33

Using elimination
10*(10x + 10y = -75/2)
10*(10x + 7y = -33)
100x + 100y = -375
100x + 70y = -330
Subtract equations
30y = -45
y = -45/30
y = -3/2

Substitute y
10x + 10(-3/2) = -75/2
10x = -45/2
x = -45/2/10
x = -9/4


Input: Determine x in 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: What value of x satisfies x^3 - 49/10x^2  + 72/5 = 0

Output:
x^3 - 49/10x^2  + 72/5 = 0
(x - -3/2)(x - 4)(x - 12/5) = 0
x - -3/2 = 0
x - 4 = 0
x - 12/5 = 0
x = -3/2
x = 4
x = 12/5


Input:
Solve the system:
9x + 10y = -109/4
1x + 8y = -53/3

Output:
9x + 10y = -109/4
1x + 8y = -53/3

Using elimination
1*(9x + 10y = -109/4)
9*(1x + 8y = -53/3)
9x + 10y = -109/4
9x + 72y = -159
Subtract equations
-62y = 527/4
y = 527/4/-62
y = -17/8

Substitute y
9x + 10(-17/8) = -109/4
9x = -6
x = -6/9
x = -2/3


Input: What value of x satisfies x^3 - 24/5x^2 + 3x + 4/5 = 0

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


Input:
Solve the system:
10x + 9y = -30
5x + 9y = -20

Output:
10x + 9y = -30
5x + 9y = -20

Using elimination
5*(10x + 9y = -30)
10*(5x + 9y = -20)
50x + 45y = -150
50x + 90y = -200
Subtract equations
-45y = 50
y = 50/-45
y = -10/9

Substitute y
10x + 9(-10/9) = -30
10x = -20
x = -20/10
x = -2


Input: Compute the solution of 4x - 20/3 = 0

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


Input: Solve the equation x^2 + 19/8x + 21/16 = 0

Output:
x^2 + 19/8x + 21/16 = 0
(x - -7/8)(x - -3/2) = 0
x - -7/8 = 0  or  x - -3/2 = 0
x = -7/8
x = -3/2


Input:
Solve simultaneously:
2x + 3y = 7/2
5x + 3y = 71/4

Output:
2x + 3y = 7/2
5x + 3y = 71/4

Using elimination
5*(2x + 3y = 7/2)
2*(5x + 3y = 71/4)
10x + 15y = 35/2
10x + 6y = 71/2
Subtract equations
9y = -18
y = -18/9
y = -2

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


Input: Solve quickly: 3x + 42 = 0

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


Input: Solve quickly: 3x + 7 = 0

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


Input:
Solve the equations:
10x + 1y = -335/9
6x + 2y = -956/45

Output:
10x + 1y = -335/9
6x + 2y = -956/45

Using elimination
6*(10x + 1y = -335/9)
10*(6x + 2y = -956/45)
60x + 6y = -670/3
60x + 20y = -1912/9
Subtract equations
-14y = -98/9
y = -98/9/-14
y = 7/9

Substitute y
10x + 1(7/9) = -335/9
10x = -38
x = -38/10
x = -19/5


Input: Determine x in 9x + 81/10 = 0

Output:
9x + 81/10 = 0
9x = -81/10
x = -81/10 / 9
x = -9/10


Input:
Find x and y such that
10x + 7y = 76
3x + 1y = 64/3

Output:
10x + 7y = 76
3x + 1y = 64/3

Using elimination
3*(10x + 7y = 76)
10*(3x + 1y = 64/3)
30x + 21y = 228
30x + 10y = 640/3
Subtract equations
11y = 44/3
y = 44/3/11
y = 4/3

Substitute y
10x + 7(4/3) = 76
10x = 200/3
x = 200/3/10
x = 20/3


Input:
Solve the equations:
3x + 4y = 45/2
1x + 1y = 13/2

Output:
3x + 4y = 45/2
1x + 1y = 13/2

Using elimination
1*(3x + 4y = 45/2)
3*(1x + 1y = 13/2)
3x + 4y = 45/2
3x + 3y = 39/2
Subtract equations
1y = 3
y = 3/1
y = 3

Substitute y
3x + 4(3) = 45/2
3x = 21/2
x = 21/2/3
x = 7/2


Input: Solve x^2 - 9x - 90 = 0

Output:
x^2 - 9x - 90 = 0
(x - -6)(x - 15) = 0
x - -6 = 0  or  x - 15 = 0
x = -6
x = 15


Input: Find x for x^3 + 173/18x^2 - 371/9x + 221/6 = 0

Output:
x^3 + 173/18x^2 - 371/9x + 221/6 = 0
(x - -13)(x - 3/2)(x - 17/9) = 0
x - -13 = 0
x - 3/2 = 0
x - 17/9 = 0
x = -13
x = 3/2
x = 17/9


Input:
Solve the equations:
2x + 3y = -31/7
7x + 5y = -81/7

Output:
2x + 3y = -31/7
7x + 5y = -81/7

Using elimination
7*(2x + 3y = -31/7)
2*(7x + 5y = -81/7)
14x + 21y = -31
14x + 10y = -162/7
Subtract equations
11y = -55/7
y = -55/7/11
y = -5/7

Substitute y
2x + 3(-5/7) = -31/7
2x = -16/7
x = -16/7/2
x = -8/7


Input: Find x in 6x + 90/7 = 0

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


Input: Find x in x^3 - 82/7x^2 - 1205/7x + 900/7 = 0

Output:
x^3 - 82/7x^2 - 1205/7x + 900/7 = 0
(x - 20)(x - -9)(x - 5/7) = 0
x - 20 = 0
x - -9 = 0
x - 5/7 = 0
x = 20
x = -9
x = 5/7


Input: Find the solution to 5x - 95/4 = 0

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


Input:
Solve the equations:
2x + 9y = -67/4
7x + 3y = -343/24

Output:
2x + 9y = -67/4
7x + 3y = -343/24

Using elimination
7*(2x + 9y = -67/4)
2*(7x + 3y = -343/24)
14x + 63y = -469/4
14x + 6y = -343/12
Subtract equations
57y = -266/3
y = -266/3/57
y = -14/9

Substitute y
2x + 9(-14/9) = -67/4
2x = -11/4
x = -11/4/2
x = -11/8


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

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


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

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


Input: Solve quickly: x^2 + 89/40x + 99/80 = 0

Output:
x^2 + 89/40x + 99/80 = 0
(x - -9/8)(x - -11/10) = 0
x - -9/8 = 0  or  x - -11/10 = 0
x = -9/8
x = -11/10


Input: Find the solution to 7x + 119/8 = 0

Output:
7x + 119/8 = 0
7x = -119/8
x = -119/8 / 7
x = -17/8


Input: Solve the equation x^3 + 108/35x^2 + 387/140x + 81/140 = 0

Output:
x^3 + 108/35x^2 + 387/140x + 81/140 = 0
(x - -9/7)(x - -3/2)(x - -3/10) = 0
x - -9/7 = 0
x - -3/2 = 0
x - -3/10 = 0
x = -9/7
x = -3/2
x = -3/10


Input:
Solve the system:
10x + 3y = 146
8x + 9y = 130

Output:
10x + 3y = 146
8x + 9y = 130

Using elimination
8*(10x + 3y = 146)
10*(8x + 9y = 130)
80x + 24y = 1168
80x + 90y = 1300
Subtract equations
-66y = -132
y = -132/-66
y = 2

Substitute y
10x + 3(2) = 146
10x = 140
x = 140/10
x = 14


Input: Solve x^3 + 29/45x^2 - 1564/405x - 64/81 = 0

Output:
x^3 + 29/45x^2 - 1564/405x - 64/81 = 0
(x - 16/9)(x - -1/5)(x - -20/9) = 0
x - 16/9 = 0
x - -1/5 = 0
x - -20/9 = 0
x = 16/9
x = -1/5
x = -20/9


Input:
Find x and y such that
2x + 6y = 29/4
5x + 10y = 95/8

Output:
2x + 6y = 29/4
5x + 10y = 95/8

Using elimination
5*(2x + 6y = 29/4)
2*(5x + 10y = 95/8)
10x + 30y = 145/4
10x + 20y = 95/4
Subtract equations
10y = 25/2
y = 25/2/10
y = 5/4

Substitute y
2x + 6(5/4) = 29/4
2x = -1/4
x = -1/4/2
x = -1/8


Input: Compute the solution of 8x - 24 = 0

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


Input: Find x for x^3 - 163/24x^2 + 233/24x - 15/4 = 0

Output:
x^3 - 163/24x^2 + 233/24x - 15/4 = 0
(x - 5)(x - 9/8)(x - 2/3) = 0
x - 5 = 0
x - 9/8 = 0
x - 2/3 = 0
x = 5
x = 9/8
x = 2/3


Input: Determine x in x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0

Output:
x^3 - 274/9x^2 + 2087/9x - 2470/9 = 0
(x - 10)(x - 13/9)(x - 19) = 0
x - 10 = 0
x - 13/9 = 0
x - 19 = 0
x = 10
x = 13/9
x = 19


Input: Solve quickly: 8x  = 0

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


Input:
Solve simultaneously:
9x + 9y = 9/5
3x + 1y = -17/5

Output:
9x + 9y = 9/5
3x + 1y = -17/5

Using elimination
3*(9x + 9y = 9/5)
9*(3x + 1y = -17/5)
27x + 27y = 27/5
27x + 9y = -153/5
Subtract equations
18y = 36
y = 36/18
y = 2

Substitute y
9x + 9(2) = 9/5
9x = -81/5
x = -81/5/9
x = -9/5


Input:
Solve the equations:
6x + 7y = -25/3
5x + 2y = -28/9

Output:
6x + 7y = -25/3
5x + 2y = -28/9

Using elimination
5*(6x + 7y = -25/3)
6*(5x + 2y = -28/9)
30x + 35y = -125/3
30x + 12y = -56/3
Subtract equations
23y = -23
y = -23/23
y = -1

Substitute y
6x + 7(-1) = -25/3
6x = -4/3
x = -4/3/6
x = -2/9


Input: Find x in x^3 + 81/20x^2 + 141/40x - 7/8 = 0

Output:
x^3 + 81/20x^2 + 141/40x - 7/8 = 0
(x - 1/5)(x - -5/2)(x - -7/4) = 0
x - 1/5 = 0
x - -5/2 = 0
x - -7/4 = 0
x = 1/5
x = -5/2
x = -7/4


Input: Find the solution to x^3 - 3/2x^2 - 35/2x + 18 = 0

Output:
x^3 - 3/2x^2 - 35/2x + 18 = 0
(x - 9/2)(x - -4)(x - 1) = 0
x - 9/2 = 0
x - -4 = 0
x - 1 = 0
x = 9/2
x = -4
x = 1


Input: Find the solution to x^3 + 125/18x^2 - 175/6x + 125/9 = 0

Output:
x^3 + 125/18x^2 - 175/6x + 125/9 = 0
(x - 5/2)(x - -10)(x - 5/9) = 0
x - 5/2 = 0
x - -10 = 0
x - 5/9 = 0
x = 5/2
x = -10
x = 5/9


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

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


Input: Solve the equation x^3 + 5/2x^2 - 57/4x + 99/8 = 0

Output:
x^3 + 5/2x^2 - 57/4x + 99/8 = 0
(x - 3/2)(x - -11/2)(x - 3/2) = 0
x - 3/2 = 0
x - -11/2 = 0
x - 3/2 = 0
x = 3/2
x = -11/2
x = 3/2


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

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


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

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


Input: Find x in x^2 + 1/42x - 1/42 = 0

Output:
x^2 + 1/42x - 1/42 = 0
(x - -1/6)(x - 1/7) = 0
x - -1/6 = 0  or  x - 1/7 = 0
x = -1/6
x = 1/7


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

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


Input: Determine x in 2x - 7 = 0

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


Input:
Find x and y such that
5x + 7y = -11/2
7x + 2y = 59/5

Output:
5x + 7y = -11/2
7x + 2y = 59/5

Using elimination
7*(5x + 7y = -11/2)
5*(7x + 2y = 59/5)
35x + 49y = -77/2
35x + 10y = 59
Subtract equations
39y = -195/2
y = -195/2/39
y = -5/2

Substitute y
5x + 7(-5/2) = -11/2
5x = 12
x = 12/5
x = 12/5


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

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


Input: Find the solution to 1x - 4/9 = 0

Output:
1x - 4/9 = 0
1x = 4/9
x = 4/9 / 1
x = 4/9


Input: Solve the equation x^2 + 26/5x + 1 = 0

Output:
x^2 + 26/5x + 1 = 0
(x - -1/5)(x - -5) = 0
x - -1/5 = 0  or  x - -5 = 0
x = -1/5
x = -5


Input: Solve quickly: 1x + 10 = 0

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


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

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

Using elimination
7*(10x + 3y = 12)
10*(7x + 7y = 7/2)
70x + 21y = 84
70x + 70y = 35
Subtract equations
-49y = 49
y = 49/-49
y = -1

Substitute y
10x + 3(-1) = 12
10x = 15
x = 15/10
x = 3/2


Input: Solve 10x - 75 = 0

Output:
10x - 75 = 0
10x = 75
x = 75 / 10
x = 15/2


Input: Compute the solution of x^2 + 37/10x - 6/5 = 0

Output:
x^2 + 37/10x - 6/5 = 0
(x - -4)(x - 3/10) = 0
x - -4 = 0  or  x - 3/10 = 0
x = -4
x = 3/10


Input: Compute the solution of x^3 - 19/42x^2 - 193/21x + 80/7 = 0

Output:
x^3 - 19/42x^2 - 193/21x + 80/7 = 0
(x - 16/7)(x - -10/3)(x - 3/2) = 0
x - 16/7 = 0
x - -10/3 = 0
x - 3/2 = 0
x = 16/7
x = -10/3
x = 3/2


Input: Find x in x^3 + 29/24x^2 - 221/48x  = 0

Output:
x^3 + 29/24x^2 - 221/48x  = 0
(x - 0)(x - -17/6)(x - 13/8) = 0
x - 0 = 0
x - -17/6 = 0
x - 13/8 = 0
x = 0
x = -17/6
x = 13/8


Input: Solve the equation x^2 - 49/6x - 17/6 = 0

Output:
x^2 - 49/6x - 17/6 = 0
(x - 17/2)(x - -1/3) = 0
x - 17/2 = 0  or  x - -1/3 = 0
x = 17/2
x = -1/3


Input: Solve x^3 - 77/12x^2 + 4x + 17/12 = 0

Output:
x^3 - 77/12x^2 + 4x + 17/12 = 0
(x - 1)(x - -1/4)(x - 17/3) = 0
x - 1 = 0
x - -1/4 = 0
x - 17/3 = 0
x = 1
x = -1/4
x = 17/3


Input:
Solve simultaneously:
3x + 6y = -5
10x + 4y = -10/3

Output:
3x + 6y = -5
10x + 4y = -10/3

Using elimination
10*(3x + 6y = -5)
3*(10x + 4y = -10/3)
30x + 60y = -50
30x + 12y = -10
Subtract equations
48y = -40
y = -40/48
y = -5/6

Substitute y
3x + 6(-5/6) = -5
3x = 0
x = 0/3
x = 0


Input: Compute the solution of x^3 - 4x^2 - 52x - 80 = 0

Output:
x^3 - 4x^2 - 52x - 80 = 0
(x - -2)(x - -4)(x - 10) = 0
x - -2 = 0
x - -4 = 0
x - 10 = 0
x = -2
x = -4
x = 10


Input: Find x in 9x + 13 = 0

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


Input: Determine x in x^3 + 53/9x^2 + 862/81x + 160/27 = 0

Output:
x^3 + 53/9x^2 + 862/81x + 160/27 = 0
(x - -3)(x - -16/9)(x - -10/9) = 0
x - -3 = 0
x - -16/9 = 0
x - -10/9 = 0
x = -3
x = -16/9
x = -10/9


Input:
Find x and y such that
2x + 4y = -46/9
7x + 5y = -233/9

Output:
2x + 4y = -46/9
7x + 5y = -233/9

Using elimination
7*(2x + 4y = -46/9)
2*(7x + 5y = -233/9)
14x + 28y = -322/9
14x + 10y = -466/9
Subtract equations
18y = 16
y = 16/18
y = 8/9

Substitute y
2x + 4(8/9) = -46/9
2x = -26/3
x = -26/3/2
x = -13/3


Input: Find x in 10x - 180/7 = 0

Output:
10x - 180/7 = 0
10x = 180/7
x = 180/7 / 10
x = 18/7


Input: Solve quickly: x^2 + 1/10x  = 0

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


Input:
Find x and y such that
5x + 1y = -13/6
5x + 9y = -23/2

Output:
5x + 1y = -13/6
5x + 9y = -23/2

Using elimination
5*(5x + 1y = -13/6)
5*(5x + 9y = -23/2)
25x + 5y = -65/6
25x + 45y = -115/2
Subtract equations
-40y = 140/3
y = 140/3/-40
y = -7/6

Substitute y
5x + 1(-7/6) = -13/6
5x = -1
x = -1/5
x = -1/5


Input: Determine x in x^2 - 115/6x + 221/6 = 0

Output:
x^2 - 115/6x + 221/6 = 0
(x - 17)(x - 13/6) = 0
x - 17 = 0  or  x - 13/6 = 0
x = 17
x = 13/6


Input: Find the solution to x^3 - 31/20x^2 - 6/5x + 27/20 = 0

Output:
x^3 - 31/20x^2 - 6/5x + 27/20 = 0
(x - 3/4)(x - 9/5)(x - -1) = 0
x - 3/4 = 0
x - 9/5 = 0
x - -1 = 0
x = 3/4
x = 9/5
x = -1


Input: Solve x^2 + 22/5x + 63/20 = 0

Output:
x^2 + 22/5x + 63/20 = 0
(x - -9/10)(x - -7/2) = 0
x - -9/10 = 0  or  x - -7/2 = 0
x = -9/10
x = -7/2


Input: Find x in x^2 + 3x + 182/81 = 0

Output:
x^2 + 3x + 182/81 = 0
(x - -13/9)(x - -14/9) = 0
x - -13/9 = 0  or  x - -14/9 = 0
x = -13/9
x = -14/9


Input: Solve quickly: x^3 - 287/60x^2 + 97/24x - 5/8 = 0

Output:
x^3 - 287/60x^2 + 97/24x - 5/8 = 0
(x - 15/4)(x - 5/6)(x - 1/5) = 0
x - 15/4 = 0
x - 5/6 = 0
x - 1/5 = 0
x = 15/4
x = 5/6
x = 1/5


Input: Find the solution to x^3 - 115/36x^2 + 73/36x + 13/18 = 0

Output:
x^3 - 115/36x^2 + 73/36x + 13/18 = 0
(x - 13/9)(x - 2)(x - -1/4) = 0
x - 13/9 = 0
x - 2 = 0
x - -1/4 = 0
x = 13/9
x = 2
x = -1/4


Input: Compute the solution of x^3 + 51/4x^2 + 159/8x + 55/8 = 0

Output:
x^3 + 51/4x^2 + 159/8x + 55/8 = 0
(x - -1/2)(x - -5/4)(x - -11) = 0
x - -1/2 = 0
x - -5/4 = 0
x - -11 = 0
x = -1/2
x = -5/4
x = -11


Input: Solve quickly: 10x - 20 = 0

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


Input:
Solve the equations:
8x + 10y = 662/9
1x + 7y = 445/9

Output:
8x + 10y = 662/9
1x + 7y = 445/9

Using elimination
1*(8x + 10y = 662/9)
8*(1x + 7y = 445/9)
8x + 10y = 662/9
8x + 56y = 3560/9
Subtract equations
-46y = -322
y = -322/-46
y = 7

Substitute y
8x + 10(7) = 662/9
8x = 32/9
x = 32/9/8
x = 4/9


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

Output:
2x - 10/3 = 0
2x = 10/3
x = 10/3 / 2
x = 5/3


Input: Find x in x^3 - 53/6x^2 - 109/3x - 20 = 0

Output:
x^3 - 53/6x^2 - 109/3x - 20 = 0
(x - 12)(x - -2/3)(x - -5/2) = 0
x - 12 = 0
x - -2/3 = 0
x - -5/2 = 0
x = 12
x = -2/3
x = -5/2


Input:
Solve the equations:
2x + 8y = 482/63
1x + 8y = 349/63

Output:
2x + 8y = 482/63
1x + 8y = 349/63

Using elimination
1*(2x + 8y = 482/63)
2*(1x + 8y = 349/63)
2x + 8y = 482/63
2x + 16y = 698/63
Subtract equations
-8y = -24/7
y = -24/7/-8
y = 3/7

Substitute y
2x + 8(3/7) = 482/63
2x = 38/9
x = 38/9/2
x = 19/9


Input:
Solve the equations:
3x + 6y = 156/5
3x + 5y = 131/5

Output:
3x + 6y = 156/5
3x + 5y = 131/5

Using elimination
3*(3x + 6y = 156/5)
3*(3x + 5y = 131/5)
9x + 18y = 468/5
9x + 15y = 393/5
Subtract equations
3y = 15
y = 15/3
y = 5

Substitute y
3x + 6(5) = 156/5
3x = 6/5
x = 6/5/3
x = 2/5


Input: Determine x in x^2 + 45/7x + 68/7 = 0

Output:
x^2 + 45/7x + 68/7 = 0
(x - -4)(x - -17/7) = 0
x - -4 = 0  or  x - -17/7 = 0
x = -4
x = -17/7


Input: What value of x satisfies 9x + 117/8 = 0

Output:
9x + 117/8 = 0
9x = -117/8
x = -117/8 / 9
x = -13/8


Input: Determine x in x^3 - 97/15x^2 + 56/5x - 16/3 = 0

Output:
x^3 - 97/15x^2 + 56/5x - 16/3 = 0
(x - 5/3)(x - 4/5)(x - 4) = 0
x - 5/3 = 0
x - 4/5 = 0
x - 4 = 0
x = 5/3
x = 4/5
x = 4


Input: Solve quickly: x^3 + 61/45x^2 - 61/45x - 1 = 0

Output:
x^3 + 61/45x^2 - 61/45x - 1 = 0
(x - -5/9)(x - -9/5)(x - 1) = 0
x - -5/9 = 0
x - -9/5 = 0
x - 1 = 0
x = -5/9
x = -9/5
x = 1


Input:
Solve simultaneously:
4x + 1y = 67/9
5x + 10y = 1265/9

Output:
4x + 1y = 67/9
5x + 10y = 1265/9

Using elimination
5*(4x + 1y = 67/9)
4*(5x + 10y = 1265/9)
20x + 5y = 335/9
20x + 40y = 5060/9
Subtract equations
-35y = -525
y = -525/-35
y = 15

Substitute y
4x + 1(15) = 67/9
4x = -68/9
x = -68/9/4
x = -17/9


Input: Solve the equation x^2 + 3/2x - 27 = 0

Output:
x^2 + 3/2x - 27 = 0
(x - 9/2)(x - -6) = 0
x - 9/2 = 0  or  x - -6 = 0
x = 9/2
x = -6


Input: Compute the solution of x^2 + 17/2x - 15 = 0

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


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

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


Input:
Solve the equations:
8x + 10y = 34
4x + 2y = 67/5

Output:
8x + 10y = 34
4x + 2y = 67/5

Using elimination
4*(8x + 10y = 34)
8*(4x + 2y = 67/5)
32x + 40y = 136
32x + 16y = 536/5
Subtract equations
24y = 144/5
y = 144/5/24
y = 6/5

Substitute y
8x + 10(6/5) = 34
8x = 22
x = 22/8
x = 11/4


Input: Determine x in x^2 + 4x - 77 = 0

Output:
x^2 + 4x - 77 = 0
(x - 7)(x - -11) = 0
x - 7 = 0  or  x - -11 = 0
x = 7
x = -11


Input: What value of x satisfies x^3 - 101/45x^2 + 52/45x  = 0

Output:
x^3 - 101/45x^2 + 52/45x  = 0
(x - 13/9)(x - 0)(x - 4/5) = 0
x - 13/9 = 0
x - 0 = 0
x - 4/5 = 0
x = 13/9
x = 0
x = 4/5


Input: Find x for x^3 - 32/63x^2 - 43/7x - 4 = 0

Output:
x^3 - 32/63x^2 - 43/7x - 4 = 0
(x - 3)(x - -7/9)(x - -12/7) = 0
x - 3 = 0
x - -7/9 = 0
x - -12/7 = 0
x = 3
x = -7/9
x = -12/7


Input: What value of x satisfies x^3 + 4x^2 - 243/4x - 765/4 = 0

Output:
x^3 + 4x^2 - 243/4x - 765/4 = 0
(x - -3)(x - -17/2)(x - 15/2) = 0
x - -3 = 0
x - -17/2 = 0
x - 15/2 = 0
x = -3
x = -17/2
x = 15/2


Input: Compute the solution of x^3 + 13/7x^2 - 2/7x  = 0

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


Input: Solve 2x - 32/5 = 0

Output:
2x - 32/5 = 0
2x = 32/5
x = 32/5 / 2
x = 16/5


Input:
Find x and y such that
5x + 4y = 42/5
1x + 8y = -78/5

Output:
5x + 4y = 42/5
1x + 8y = -78/5

Using elimination
1*(5x + 4y = 42/5)
5*(1x + 8y = -78/5)
5x + 4y = 42/5
5x + 40y = -78
Subtract equations
-36y = 432/5
y = 432/5/-36
y = -12/5

Substitute y
5x + 4(-12/5) = 42/5
5x = 18
x = 18/5
x = 18/5


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

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


Input: Solve x^3 + 49/5x^2 + 72/5x  = 0

Output:
x^3 + 49/5x^2 + 72/5x  = 0
(x - -9/5)(x - 0)(x - -8) = 0
x - -9/5 = 0
x - 0 = 0
x - -8 = 0
x = -9/5
x = 0
x = -8


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

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


Input: Solve the equation x^2 + 31/2x + 55 = 0

Output:
x^2 + 31/2x + 55 = 0
(x - -11/2)(x - -10) = 0
x - -11/2 = 0  or  x - -10 = 0
x = -11/2
x = -10


Input: Find the solution to x^3 - 47/42x^2 - 16/21x + 2/7 = 0

Output:
x^3 - 47/42x^2 - 16/21x + 2/7 = 0
(x - 2/7)(x - -2/3)(x - 3/2) = 0
x - 2/7 = 0
x - -2/3 = 0
x - 3/2 = 0
x = 2/7
x = -2/3
x = 3/2


Input:
Solve the system:
9x + 2y = -1441/72
5x + 1y = -797/72

Output:
9x + 2y = -1441/72
5x + 1y = -797/72

Using elimination
5*(9x + 2y = -1441/72)
9*(5x + 1y = -797/72)
45x + 10y = -7205/72
45x + 9y = -797/8
Subtract equations
1y = -4/9
y = -4/9/1
y = -4/9

Substitute y
9x + 2(-4/9) = -1441/72
9x = -153/8
x = -153/8/9
x = -17/8


Input: Find x in 8x - 10 = 0

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


Input:
Solve the system:
10x + 10y = 1/3
4x + 6y = 4/5

Output:
10x + 10y = 1/3
4x + 6y = 4/5

Using elimination
4*(10x + 10y = 1/3)
10*(4x + 6y = 4/5)
40x + 40y = 4/3
40x + 60y = 8
Subtract equations
-20y = -20/3
y = -20/3/-20
y = 1/3

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


Input: Find the solution to x^2 + 101/7x - 60/7 = 0

Output:
x^2 + 101/7x - 60/7 = 0
(x - 4/7)(x - -15) = 0
x - 4/7 = 0  or  x - -15 = 0
x = 4/7
x = -15


Input: Find the solution to 8x - 36 = 0

Output:
8x - 36 = 0
8x = 36
x = 36 / 8
x = 9/2


Input:
Solve simultaneously:
1x + 8y = 43/3
5x + 7y = 17/3

Output:
1x + 8y = 43/3
5x + 7y = 17/3

Using elimination
5*(1x + 8y = 43/3)
1*(5x + 7y = 17/3)
5x + 40y = 215/3
5x + 7y = 17/3
Subtract equations
33y = 66
y = 66/33
y = 2

Substitute y
1x + 8(2) = 43/3
1x = -5/3
x = -5/3/1
x = -5/3


Input:
Solve the equations:
1x + 1y = -13/2
6x + 10y = -73

Output:
1x + 1y = -13/2
6x + 10y = -73

Using elimination
6*(1x + 1y = -13/2)
1*(6x + 10y = -73)
6x + 6y = -39
6x + 10y = -73
Subtract equations
-4y = 34
y = 34/-4
y = -17/2

Substitute y
1x + 1(-17/2) = -13/2
1x = 2
x = 2/1
x = 2


Input: Compute the solution of 1x - 7/2 = 0

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


Input: Compute the solution of x^2 + 8x + 12 = 0

Output:
x^2 + 8x + 12 = 0
(x - -6)(x - -2) = 0
x - -6 = 0  or  x - -2 = 0
x = -6
x = -2


Input:
Solve simultaneously:
9x + 4y = 133
10x + 1y = 165

Output:
9x + 4y = 133
10x + 1y = 165

Using elimination
10*(9x + 4y = 133)
9*(10x + 1y = 165)
90x + 40y = 1330
90x + 9y = 1485
Subtract equations
31y = -155
y = -155/31
y = -5

Substitute y
9x + 4(-5) = 133
9x = 153
x = 153/9
x = 17


Input:
Solve the equations:
7x + 10y = 80/9
7x + 6y = 16/3

Output:
7x + 10y = 80/9
7x + 6y = 16/3

Using elimination
7*(7x + 10y = 80/9)
7*(7x + 6y = 16/3)
49x + 70y = 560/9
49x + 42y = 112/3
Subtract equations
28y = 224/9
y = 224/9/28
y = 8/9

Substitute y
7x + 10(8/9) = 80/9
7x = 0
x = 0/7
x = 0


Input:
Solve the equations:
1x + 2y = -4
4x + 4y = -14

Output:
1x + 2y = -4
4x + 4y = -14

Using elimination
4*(1x + 2y = -4)
1*(4x + 4y = -14)
4x + 8y = -16
4x + 4y = -14
Subtract equations
4y = -2
y = -2/4
y = -1/2

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


Input:
Solve the system:
2x + 6y = 97/6
5x + 8y = 1091/36

Output:
2x + 6y = 97/6
5x + 8y = 1091/36

Using elimination
5*(2x + 6y = 97/6)
2*(5x + 8y = 1091/36)
10x + 30y = 485/6
10x + 16y = 1091/18
Subtract equations
14y = 182/9
y = 182/9/14
y = 13/9

Substitute y
2x + 6(13/9) = 97/6
2x = 15/2
x = 15/2/2
x = 15/4


Input:
Solve the system:
10x + 4y = 73/3
4x + 6y = 20

Output:
10x + 4y = 73/3
4x + 6y = 20

Using elimination
4*(10x + 4y = 73/3)
10*(4x + 6y = 20)
40x + 16y = 292/3
40x + 60y = 200
Subtract equations
-44y = -308/3
y = -308/3/-44
y = 7/3

Substitute y
10x + 4(7/3) = 73/3
10x = 15
x = 15/10
x = 3/2


Input: Solve quickly: x^2 - 35/9x - 4/9 = 0

Output:
x^2 - 35/9x - 4/9 = 0
(x - -1/9)(x - 4) = 0
x - -1/9 = 0  or  x - 4 = 0
x = -1/9
x = 4


Input: Find the solution to 1x - 1/5 = 0

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


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

Output:
x^2 - 5/2x - 6 = 0
(x - -3/2)(x - 4) = 0
x - -3/2 = 0  or  x - 4 = 0
x = -3/2
x = 4


Input: Find x in x^2 - 3/8x - 11/8 = 0

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


Input:
Solve the equations:
9x + 10y = -34
8x + 6y = -23

Output:
9x + 10y = -34
8x + 6y = -23

Using elimination
8*(9x + 10y = -34)
9*(8x + 6y = -23)
72x + 80y = -272
72x + 54y = -207
Subtract equations
26y = -65
y = -65/26
y = -5/2

Substitute y
9x + 10(-5/2) = -34
9x = -9
x = -9/9
x = -1


Input:
Find x and y such that
8x + 6y = 24
8x + 3y = 17

Output:
8x + 6y = 24
8x + 3y = 17

Using elimination
8*(8x + 6y = 24)
8*(8x + 3y = 17)
64x + 48y = 192
64x + 24y = 136
Subtract equations
24y = 56
y = 56/24
y = 7/3

Substitute y
8x + 6(7/3) = 24
8x = 10
x = 10/8
x = 5/4


Input: Solve x^2 + 13/9x - 16/27 = 0

Output:
x^2 + 13/9x - 16/27 = 0
(x - 1/3)(x - -16/9) = 0
x - 1/3 = 0  or  x - -16/9 = 0
x = 1/3
x = -16/9


Input: Determine x in x^3 + 8/5x^2 - 447/5x - 54 = 0

Output:
x^3 + 8/5x^2 - 447/5x - 54 = 0
(x - -10)(x - -3/5)(x - 9) = 0
x - -10 = 0
x - -3/5 = 0
x - 9 = 0
x = -10
x = -3/5
x = 9


Input: Determine x in 3x - 6 = 0

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


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

Output:
2x - 10/9 = 0
2x = 10/9
x = 10/9 / 2
x = 5/9


Input: Find x for 2x - 19 = 0

Output:
2x - 19 = 0
2x = 19
x = 19 / 2
x = 19/2


Input: What value of x satisfies 4x - 32/5 = 0

Output:
4x - 32/5 = 0
4x = 32/5
x = 32/5 / 4
x = 8/5


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

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


Input: Find x in x^2 - 13/5x - 48/25 = 0

Output:
x^2 - 13/5x - 48/25 = 0
(x - -3/5)(x - 16/5) = 0
x - -3/5 = 0  or  x - 16/5 = 0
x = -3/5
x = 16/5


Input:
Solve simultaneously:
5x + 10y = -120
4x + 9y = -109

Output:
5x + 10y = -120
4x + 9y = -109

Using elimination
4*(5x + 10y = -120)
5*(4x + 9y = -109)
20x + 40y = -480
20x + 45y = -545
Subtract equations
-5y = 65
y = 65/-5
y = -13

Substitute y
5x + 10(-13) = -120
5x = 10
x = 10/5
x = 2


Input: What value of x satisfies x^2 + 5/3x - 50/3 = 0

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


Input: Solve quickly: x^3 - 22x^2 + 67x + 90 = 0

Output:
x^3 - 22x^2 + 67x + 90 = 0
(x - 18)(x - 5)(x - -1) = 0
x - 18 = 0
x - 5 = 0
x - -1 = 0
x = 18
x = 5
x = -1


Input:
Solve simultaneously:
2x + 7y = 43/5
8x + 7y = 5

Output:
2x + 7y = 43/5
8x + 7y = 5

Using elimination
8*(2x + 7y = 43/5)
2*(8x + 7y = 5)
16x + 56y = 344/5
16x + 14y = 10
Subtract equations
42y = 294/5
y = 294/5/42
y = 7/5

Substitute y
2x + 7(7/5) = 43/5
2x = -6/5
x = -6/5/2
x = -3/5


Input:
Solve the system:
3x + 8y = 91/5
2x + 10y = 119/5

Output:
3x + 8y = 91/5
2x + 10y = 119/5

Using elimination
2*(3x + 8y = 91/5)
3*(2x + 10y = 119/5)
6x + 16y = 182/5
6x + 30y = 357/5
Subtract equations
-14y = -35
y = -35/-14
y = 5/2

Substitute y
3x + 8(5/2) = 91/5
3x = -9/5
x = -9/5/3
x = -3/5


Input: Solve x^3 - 19/4x^2 + 57/8x - 27/8 = 0

Output:
x^3 - 19/4x^2 + 57/8x - 27/8 = 0
(x - 9/4)(x - 1)(x - 3/2) = 0
x - 9/4 = 0
x - 1 = 0
x - 3/2 = 0
x = 9/4
x = 1
x = 3/2


Input: Solve the equation x^3 - 121/20x^2 + 57/5x - 27/4 = 0

Output:
x^3 - 121/20x^2 + 57/5x - 27/4 = 0
(x - 3)(x - 9/5)(x - 5/4) = 0
x - 3 = 0
x - 9/5 = 0
x - 5/4 = 0
x = 3
x = 9/5
x = 5/4


Input: Find x in x^2 + 104/15x + 169/15 = 0

Output:
x^2 + 104/15x + 169/15 = 0
(x - -13/3)(x - -13/5) = 0
x - -13/3 = 0  or  x - -13/5 = 0
x = -13/3
x = -13/5


Input: Determine x in 9x + 16 = 0

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


Input:
Solve the equations:
9x + 9y = 99/35
9x + 6y = 24/35

Output:
9x + 9y = 99/35
9x + 6y = 24/35

Using elimination
9*(9x + 9y = 99/35)
9*(9x + 6y = 24/35)
81x + 81y = 891/35
81x + 54y = 216/35
Subtract equations
27y = 135/7
y = 135/7/27
y = 5/7

Substitute y
9x + 9(5/7) = 99/35
9x = -18/5
x = -18/5/9
x = -2/5


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

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


Input: Find x for x^2 - 109/10x + 51/2 = 0

Output:
x^2 - 109/10x + 51/2 = 0
(x - 15/2)(x - 17/5) = 0
x - 15/2 = 0  or  x - 17/5 = 0
x = 15/2
x = 17/5


Input: What value of x satisfies x^3 + 5/42x^2 - 253/42x - 95/21 = 0

Output:
x^3 + 5/42x^2 - 253/42x - 95/21 = 0
(x - 19/7)(x - -2)(x - -5/6) = 0
x - 19/7 = 0
x - -2 = 0
x - -5/6 = 0
x = 19/7
x = -2
x = -5/6


Input:
Solve the system:
8x + 4y = 272/7
2x + 3y = 64/7

Output:
8x + 4y = 272/7
2x + 3y = 64/7

Using elimination
2*(8x + 4y = 272/7)
8*(2x + 3y = 64/7)
16x + 8y = 544/7
16x + 24y = 512/7
Subtract equations
-16y = 32/7
y = 32/7/-16
y = -2/7

Substitute y
8x + 4(-2/7) = 272/7
8x = 40
x = 40/8
x = 5


Input: Solve quickly: x^3 + 1273/252x^2 + 601/84x + 143/63 = 0

Output:
x^3 + 1273/252x^2 + 601/84x + 143/63 = 0
(x - -13/7)(x - -11/4)(x - -4/9) = 0
x - -13/7 = 0
x - -11/4 = 0
x - -4/9 = 0
x = -13/7
x = -11/4
x = -4/9


Input: Compute the solution of x^3 + 157/20x^2 - 59/4x - 198/5 = 0

Output:
x^3 + 157/20x^2 - 59/4x - 198/5 = 0
(x - 11/4)(x - -8/5)(x - -9) = 0
x - 11/4 = 0
x - -8/5 = 0
x - -9 = 0
x = 11/4
x = -8/5
x = -9


Input:
Solve simultaneously:
10x + 4y = 289/6
2x + 3y = 10

Output:
10x + 4y = 289/6
2x + 3y = 10

Using elimination
2*(10x + 4y = 289/6)
10*(2x + 3y = 10)
20x + 8y = 289/3
20x + 30y = 100
Subtract equations
-22y = -11/3
y = -11/3/-22
y = 1/6

Substitute y
10x + 4(1/6) = 289/6
10x = 95/2
x = 95/2/10
x = 19/4


Input: Solve quickly: x^3 - 51/10x^2 - 733/10x - 114 = 0

Output:
x^3 - 51/10x^2 - 733/10x - 114 = 0
(x - -5)(x - 12)(x - -19/10) = 0
x - -5 = 0
x - 12 = 0
x - -19/10 = 0
x = -5
x = 12
x = -19/10


Input: What value of x satisfies x^3 - 337/126x^2 - 505/63x + 323/18 = 0

Output:
x^3 - 337/126x^2 - 505/63x + 323/18 = 0
(x - 17/9)(x - 7/2)(x - -19/7) = 0
x - 17/9 = 0
x - 7/2 = 0
x - -19/7 = 0
x = 17/9
x = 7/2
x = -19/7


Input: Determine x in x^3 - 1/3x^2 - 10/3x  = 0

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


Input:
Solve the equations:
1x + 7y = 142/9
9x + 2y = -43/7

Output:
1x + 7y = 142/9
9x + 2y = -43/7

Using elimination
9*(1x + 7y = 142/9)
1*(9x + 2y = -43/7)
9x + 63y = 142
9x + 2y = -43/7
Subtract equations
61y = 1037/7
y = 1037/7/61
y = 17/7

Substitute y
1x + 7(17/7) = 142/9
1x = -11/9
x = -11/9/1
x = -11/9


Input: Find x for x^2 - 79/8x + 285/16 = 0

Output:
x^2 - 79/8x + 285/16 = 0
(x - 19/8)(x - 15/2) = 0
x - 19/8 = 0  or  x - 15/2 = 0
x = 19/8
x = 15/2


Input: Find x for x^3 + 25/8x^2 + 1/8x - 17/4 = 0

Output:
x^3 + 25/8x^2 + 1/8x - 17/4 = 0
(x - -2)(x - 1)(x - -17/8) = 0
x - -2 = 0
x - 1 = 0
x - -17/8 = 0
x = -2
x = 1
x = -17/8


Input: Find x for x^3 - 161/20x^2 + 2097/100x - 891/50 = 0

Output:
x^3 - 161/20x^2 + 2097/100x - 891/50 = 0
(x - 11/5)(x - 18/5)(x - 9/4) = 0
x - 11/5 = 0
x - 18/5 = 0
x - 9/4 = 0
x = 11/5
x = 18/5
x = 9/4


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

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


Input: Find x in x^2 - 49/12x - 57/4 = 0

Output:
x^2 - 49/12x - 57/4 = 0
(x - 19/3)(x - -9/4) = 0
x - 19/3 = 0  or  x - -9/4 = 0
x = 19/3
x = -9/4


Input: Find the solution to 7x - 70 = 0

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


Input: Find x in x^2 - 28/15x - 323/15 = 0

Output:
x^2 - 28/15x - 323/15 = 0
(x - -19/5)(x - 17/3) = 0
x - -19/5 = 0  or  x - 17/3 = 0
x = -19/5
x = 17/3


Input: What value of x satisfies x^2 - 9/7x - 36/7 = 0

Output:
x^2 - 9/7x - 36/7 = 0
(x - 3)(x - -12/7) = 0
x - 3 = 0  or  x - -12/7 = 0
x = 3
x = -12/7


Input: Solve x^2 - 23/3x - 12 = 0

Output:
x^2 - 23/3x - 12 = 0
(x - -4/3)(x - 9) = 0
x - -4/3 = 0  or  x - 9 = 0
x = -4/3
x = 9


Input:
Solve simultaneously:
5x + 7y = -141/2
1x + 4y = -18

Output:
5x + 7y = -141/2
1x + 4y = -18

Using elimination
1*(5x + 7y = -141/2)
5*(1x + 4y = -18)
5x + 7y = -141/2
5x + 20y = -90
Subtract equations
-13y = 39/2
y = 39/2/-13
y = -3/2

Substitute y
5x + 7(-3/2) = -141/2
5x = -60
x = -60/5
x = -12


Input: Find the solution to x^3 + 41/12x^2 + 667/192x + 35/32 = 0

Output:
x^3 + 41/12x^2 + 667/192x + 35/32 = 0
(x - -2/3)(x - -15/8)(x - -7/8) = 0
x - -2/3 = 0
x - -15/8 = 0
x - -7/8 = 0
x = -2/3
x = -15/8
x = -7/8


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

Output:
x^2 - 7/2x - 15 = 0
(x - 6)(x - -5/2) = 0
x - 6 = 0  or  x - -5/2 = 0
x = 6
x = -5/2


Input:
Solve the equations:
8x + 2y = 196/15
3x + 6y = 7/5

Output:
8x + 2y = 196/15
3x + 6y = 7/5

Using elimination
3*(8x + 2y = 196/15)
8*(3x + 6y = 7/5)
24x + 6y = 196/5
24x + 48y = 56/5
Subtract equations
-42y = 28
y = 28/-42
y = -2/3

Substitute y
8x + 2(-2/3) = 196/15
8x = 72/5
x = 72/5/8
x = 9/5


Input:
Solve simultaneously:
5x + 7y = -573/35
3x + 1y = -299/35

Output:
5x + 7y = -573/35
3x + 1y = -299/35

Using elimination
3*(5x + 7y = -573/35)
5*(3x + 1y = -299/35)
15x + 21y = -1719/35
15x + 5y = -299/7
Subtract equations
16y = -32/5
y = -32/5/16
y = -2/5

Substitute y
5x + 7(-2/5) = -573/35
5x = -95/7
x = -95/7/5
x = -19/7


Input: Solve the equation x^2 + 31/3x + 238/9 = 0

Output:
x^2 + 31/3x + 238/9 = 0
(x - -14/3)(x - -17/3) = 0
x - -14/3 = 0  or  x - -17/3 = 0
x = -14/3
x = -17/3


Input: Find the solution to 2x - 7/5 = 0

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


Input: Solve the equation x^2 - 43/15x - 16/15 = 0

Output:
x^2 - 43/15x - 16/15 = 0
(x - 16/5)(x - -1/3) = 0
x - 16/5 = 0  or  x - -1/3 = 0
x = 16/5
x = -1/3


Input: Find x in x^3 + 1157/56x^2 + 523/8x + 374/7 = 0

Output:
x^3 + 1157/56x^2 + 523/8x + 374/7 = 0
(x - -11/8)(x - -17)(x - -16/7) = 0
x - -11/8 = 0
x - -17 = 0
x - -16/7 = 0
x = -11/8
x = -17
x = -16/7


Input: Find x for x^3 - 73/5x^2 + 427/20x - 143/20 = 0

Output:
x^3 - 73/5x^2 + 427/20x - 143/20 = 0
(x - 11/10)(x - 13)(x - 1/2) = 0
x - 11/10 = 0
x - 13 = 0
x - 1/2 = 0
x = 11/10
x = 13
x = 1/2


Input: Find x for x^3 + 35/6x^2 + 1/2x - 22/3 = 0

Output:
x^3 + 35/6x^2 + 1/2x - 22/3 = 0
(x - -11/2)(x - 1)(x - -4/3) = 0
x - -11/2 = 0
x - 1 = 0
x - -4/3 = 0
x = -11/2
x = 1
x = -4/3


Input: Find the solution to x^3 - 10/7x^2 - 277/49x + 442/49 = 0

Output:
x^3 - 10/7x^2 - 277/49x + 442/49 = 0
(x - 13/7)(x - 2)(x - -17/7) = 0
x - 13/7 = 0
x - 2 = 0
x - -17/7 = 0
x = 13/7
x = 2
x = -17/7


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

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


Input: What value of x satisfies x^2 + 17/7x - 12/7 = 0

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


Input: Determine x in x^2 - 1/9x - 34/9 = 0

Output:
x^2 - 1/9x - 34/9 = 0
(x - -17/9)(x - 2) = 0
x - -17/9 = 0  or  x - 2 = 0
x = -17/9
x = 2


Input:
Find x and y such that
3x + 5y = 221/4
3x + 7y = 301/4

Output:
3x + 5y = 221/4
3x + 7y = 301/4

Using elimination
3*(3x + 5y = 221/4)
3*(3x + 7y = 301/4)
9x + 15y = 663/4
9x + 21y = 903/4
Subtract equations
-6y = -60
y = -60/-6
y = 10

Substitute y
3x + 5(10) = 221/4
3x = 21/4
x = 21/4/3
x = 7/4


Input: Determine x in 4x + 32/3 = 0

Output:
4x + 32/3 = 0
4x = -32/3
x = -32/3 / 4
x = -8/3


Input: Find x for x^2 + 39/7x + 44/7 = 0

Output:
x^2 + 39/7x + 44/7 = 0
(x - -11/7)(x - -4) = 0
x - -11/7 = 0  or  x - -4 = 0
x = -11/7
x = -4


Input: Compute the solution of 7x - 56 = 0

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


Input: Solve quickly: x^3 + 3x^2 - 64x + 60 = 0

Output:
x^3 + 3x^2 - 64x + 60 = 0
(x - -10)(x - 1)(x - 6) = 0
x - -10 = 0
x - 1 = 0
x - 6 = 0
x = -10
x = 1
x = 6


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

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


Input: Determine x in x^2 + 43/2x + 30 = 0

Output:
x^2 + 43/2x + 30 = 0
(x - -3/2)(x - -20) = 0
x - -3/2 = 0  or  x - -20 = 0
x = -3/2
x = -20


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

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


Input: Find x for x^2 - 59/18x + 8/3 = 0

Output:
x^2 - 59/18x + 8/3 = 0
(x - 16/9)(x - 3/2) = 0
x - 16/9 = 0  or  x - 3/2 = 0
x = 16/9
x = 3/2


Input: Solve x^3 - 46/3x^2 + 113/3x + 110 = 0

Output:
x^3 - 46/3x^2 + 113/3x + 110 = 0
(x - 6)(x - 11)(x - -5/3) = 0
x - 6 = 0
x - 11 = 0
x - -5/3 = 0
x = 6
x = 11
x = -5/3


Input:
Find x and y such that
5x + 4y = -184/15
5x + 6y = -226/15

Output:
5x + 4y = -184/15
5x + 6y = -226/15

Using elimination
5*(5x + 4y = -184/15)
5*(5x + 6y = -226/15)
25x + 20y = -184/3
25x + 30y = -226/3
Subtract equations
-10y = 14
y = 14/-10
y = -7/5

Substitute y
5x + 4(-7/5) = -184/15
5x = -20/3
x = -20/3/5
x = -4/3


Input: Find the solution to x^2 + 13/8x  = 0

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


Input: Solve the equation x^2 + 3/4x - 135/8 = 0

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


Input: Solve quickly: x^3 + 469/45x^2 + 196/15x + 12/5 = 0

Output:
x^3 + 469/45x^2 + 196/15x + 12/5 = 0
(x - -9)(x - -2/9)(x - -6/5) = 0
x - -9 = 0
x - -2/9 = 0
x - -6/5 = 0
x = -9
x = -2/9
x = -6/5


Input: Solve x^3 + 13/18x^2 - 19/9x - 11/6 = 0

Output:
x^3 + 13/18x^2 - 19/9x - 11/6 = 0
(x - 3/2)(x - -1)(x - -11/9) = 0
x - 3/2 = 0
x - -1 = 0
x - -11/9 = 0
x = 3/2
x = -1
x = -11/9


Input: What value of x satisfies 4x - 20 = 0

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


Input:
Find x and y such that
7x + 3y = -24
6x + 10y = -188/3

Output:
7x + 3y = -24
6x + 10y = -188/3

Using elimination
6*(7x + 3y = -24)
7*(6x + 10y = -188/3)
42x + 18y = -144
42x + 70y = -1316/3
Subtract equations
-52y = 884/3
y = 884/3/-52
y = -17/3

Substitute y
7x + 3(-17/3) = -24
7x = -7
x = -7/7
x = -1


Input:
Solve the equations:
4x + 4y = -32/7
7x + 4y = 1/7

Output:
4x + 4y = -32/7
7x + 4y = 1/7

Using elimination
7*(4x + 4y = -32/7)
4*(7x + 4y = 1/7)
28x + 28y = -32
28x + 16y = 4/7
Subtract equations
12y = -228/7
y = -228/7/12
y = -19/7

Substitute y
4x + 4(-19/7) = -32/7
4x = 44/7
x = 44/7/4
x = 11/7


Input: Solve 4x + 64/5 = 0

Output:
4x + 64/5 = 0
4x = -64/5
x = -64/5 / 4
x = -16/5


Input: Solve the equation 1x - 3 = 0

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


Input: What value of x satisfies 3x - 15 = 0

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


Input: Determine x in x^2 + 23x + 120 = 0

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


Input: Compute the solution of 6x - 114 = 0

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


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

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


Input:
Solve the system:
8x + 7y = -29
8x + 9y = -35

Output:
8x + 7y = -29
8x + 9y = -35

Using elimination
8*(8x + 7y = -29)
8*(8x + 9y = -35)
64x + 56y = -232
64x + 72y = -280
Subtract equations
-16y = 48
y = 48/-16
y = -3

Substitute y
8x + 7(-3) = -29
8x = -8
x = -8/8
x = -1


Input: Find x in x^3 - 241/180x^2 + 9/20x - 2/45 = 0

Output:
x^3 - 241/180x^2 + 9/20x - 2/45 = 0
(x - 8/9)(x - 1/4)(x - 1/5) = 0
x - 8/9 = 0
x - 1/4 = 0
x - 1/5 = 0
x = 8/9
x = 1/4
x = 1/5


Input: Solve the equation 8x - 128/5 = 0

Output:
8x - 128/5 = 0
8x = 128/5
x = 128/5 / 8
x = 16/5


Input: Solve the equation 5x + 55/9 = 0

Output:
5x + 55/9 = 0
5x = -55/9
x = -55/9 / 5
x = -11/9


Input: Determine x in x^3 + 93/56x^2 - 85/112x - 75/112 = 0

Output:
x^3 + 93/56x^2 - 85/112x - 75/112 = 0
(x - -15/8)(x - 5/7)(x - -1/2) = 0
x - -15/8 = 0
x - 5/7 = 0
x - -1/2 = 0
x = -15/8
x = 5/7
x = -1/2


Input: Find x for x^3 - 296/35x^2 + 111/7x - 234/35 = 0

Output:
x^3 - 296/35x^2 + 111/7x - 234/35 = 0
(x - 6)(x - 13/7)(x - 3/5) = 0
x - 6 = 0
x - 13/7 = 0
x - 3/5 = 0
x = 6
x = 13/7
x = 3/5


Input: Find x in 7x + 56/5 = 0

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


Input: What value of x satisfies 9x + 90 = 0

Output:
9x + 90 = 0
9x = -90
x = -90 / 9
x = -10


Input: Find x for 3x + 15/7 = 0

Output:
3x + 15/7 = 0
3x = -15/7
x = -15/7 / 3
x = -5/7


Input:
Find x and y such that
1x + 9y = 13
7x + 8y = -281/9

Output:
1x + 9y = 13
7x + 8y = -281/9

Using elimination
7*(1x + 9y = 13)
1*(7x + 8y = -281/9)
7x + 63y = 91
7x + 8y = -281/9
Subtract equations
55y = 1100/9
y = 1100/9/55
y = 20/9

Substitute y
1x + 9(20/9) = 13
1x = -7
x = -7/1
x = -7


Input:
Solve the equations:
7x + 1y = 113/4
2x + 9y = 41/4

Output:
7x + 1y = 113/4
2x + 9y = 41/4

Using elimination
2*(7x + 1y = 113/4)
7*(2x + 9y = 41/4)
14x + 2y = 113/2
14x + 63y = 287/4
Subtract equations
-61y = -61/4
y = -61/4/-61
y = 1/4

Substitute y
7x + 1(1/4) = 113/4
7x = 28
x = 28/7
x = 4


Input: Find x in x^3 + 153/20x^2 + 107/10x - 51/4 = 0

Output:
x^3 + 153/20x^2 + 107/10x - 51/4 = 0
(x - 3/4)(x - -5)(x - -17/5) = 0
x - 3/4 = 0
x - -5 = 0
x - -17/5 = 0
x = 3/4
x = -5
x = -17/5


Input: Compute the solution of x^2 + 17/9x - 10/3 = 0

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


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

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


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

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


Input: Determine x in x^3 - 301/90x^2 - 493/135x + 3179/270 = 0

Output:
x^3 - 301/90x^2 - 493/135x + 3179/270 = 0
(x - -17/9)(x - 17/5)(x - 11/6) = 0
x - -17/9 = 0
x - 17/5 = 0
x - 11/6 = 0
x = -17/9
x = 17/5
x = 11/6


Input: Solve x^3 - 47/10x^2 + 397/80x - 13/16 = 0

Output:
x^3 - 47/10x^2 + 397/80x - 13/16 = 0
(x - 1/5)(x - 5/4)(x - 13/4) = 0
x - 1/5 = 0
x - 5/4 = 0
x - 13/4 = 0
x = 1/5
x = 5/4
x = 13/4


Input: Compute the solution of x^2 - 37/4x + 51/8 = 0

Output:
x^2 - 37/4x + 51/8 = 0
(x - 17/2)(x - 3/4) = 0
x - 17/2 = 0  or  x - 3/4 = 0
x = 17/2
x = 3/4


Input: Solve the equation x^3 - 29/2x^2 - 47/2x - 8 = 0

Output:
x^3 - 29/2x^2 - 47/2x - 8 = 0
(x - 16)(x - -1)(x - -1/2) = 0
x - 16 = 0
x - -1 = 0
x - -1/2 = 0
x = 16
x = -1
x = -1/2


Input:
Solve the equations:
4x + 9y = -28/3
7x + 6y = 1

Output:
4x + 9y = -28/3
7x + 6y = 1

Using elimination
7*(4x + 9y = -28/3)
4*(7x + 6y = 1)
28x + 63y = -196/3
28x + 24y = 4
Subtract equations
39y = -208/3
y = -208/3/39
y = -16/9

Substitute y
4x + 9(-16/9) = -28/3
4x = 20/3
x = 20/3/4
x = 5/3


Input:
Solve the system:
4x + 2y = -75
3x + 6y = -63

Output:
4x + 2y = -75
3x + 6y = -63

Using elimination
3*(4x + 2y = -75)
4*(3x + 6y = -63)
12x + 6y = -225
12x + 24y = -252
Subtract equations
-18y = 27
y = 27/-18
y = -3/2

Substitute y
4x + 2(-3/2) = -75
4x = -72
x = -72/4
x = -18


Input: Solve quickly: x^2 + 11/3x - 4/3 = 0

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


Input: Find x in x^3 - 719/35x^2 + 981/35x + 171/7 = 0

Output:
x^3 - 719/35x^2 + 981/35x + 171/7 = 0
(x - -3/5)(x - 19)(x - 15/7) = 0
x - -3/5 = 0
x - 19 = 0
x - 15/7 = 0
x = -3/5
x = 19
x = 15/7


Input: Find x for x^3 - 601/40x^2 + 221/20x + 231/5 = 0

Output:
x^3 - 601/40x^2 + 221/20x + 231/5 = 0
(x - -11/8)(x - 12/5)(x - 14) = 0
x - -11/8 = 0
x - 12/5 = 0
x - 14 = 0
x = -11/8
x = 12/5
x = 14


Input:
Solve the system:
8x + 4y = 140/3
3x + 7y = 45

Output:
8x + 4y = 140/3
3x + 7y = 45

Using elimination
3*(8x + 4y = 140/3)
8*(3x + 7y = 45)
24x + 12y = 140
24x + 56y = 360
Subtract equations
-44y = -220
y = -220/-44
y = 5

Substitute y
8x + 4(5) = 140/3
8x = 80/3
x = 80/3/8
x = 10/3


Input:
Solve the system:
4x + 5y = -43/2
8x + 9y = -71/2

Output:
4x + 5y = -43/2
8x + 9y = -71/2

Using elimination
8*(4x + 5y = -43/2)
4*(8x + 9y = -71/2)
32x + 40y = -172
32x + 36y = -142
Subtract equations
4y = -30
y = -30/4
y = -15/2

Substitute y
4x + 5(-15/2) = -43/2
4x = 16
x = 16/4
x = 4


Input: Find the solution to 2x - 6 = 0

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


Input: Solve quickly: x^2 + 87/10x - 13 = 0

Output:
x^2 + 87/10x - 13 = 0
(x - -10)(x - 13/10) = 0
x - -10 = 0  or  x - 13/10 = 0
x = -10
x = 13/10


Input: Find the solution to 3x - 27/10 = 0

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


Input: Find x for x^2 - 67/18x + 187/54 = 0

Output:
x^2 - 67/18x + 187/54 = 0
(x - 11/6)(x - 17/9) = 0
x - 11/6 = 0  or  x - 17/9 = 0
x = 11/6
x = 17/9


Input: Solve x^2 - 35/9x + 98/27 = 0

Output:
x^2 - 35/9x + 98/27 = 0
(x - 7/3)(x - 14/9) = 0
x - 7/3 = 0  or  x - 14/9 = 0
x = 7/3
x = 14/9


Input: Find x for 9x - 54 = 0

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


Input: Solve x^3 + 67/20x^2 + 9/40x - 99/40 = 0

Output:
x^3 + 67/20x^2 + 9/40x - 99/40 = 0
(x - 3/4)(x - -3)(x - -11/10) = 0
x - 3/4 = 0
x - -3 = 0
x - -11/10 = 0
x = 3/4
x = -3
x = -11/10


Input:
Solve the system:
5x + 3y = 217/6
4x + 5y = 197/6

Output:
5x + 3y = 217/6
4x + 5y = 197/6

Using elimination
4*(5x + 3y = 217/6)
5*(4x + 5y = 197/6)
20x + 12y = 434/3
20x + 25y = 985/6
Subtract equations
-13y = -39/2
y = -39/2/-13
y = 3/2

Substitute y
5x + 3(3/2) = 217/6
5x = 95/3
x = 95/3/5
x = 19/3


Input: Solve the equation 10x + 10 = 0

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


Input: Solve quickly: x^3 - 89/36x^2 - 1121/54x - 2527/108 = 0

Output:
x^3 - 89/36x^2 - 1121/54x - 2527/108 = 0
(x - 19/3)(x - -7/4)(x - -19/9) = 0
x - 19/3 = 0
x - -7/4 = 0
x - -19/9 = 0
x = 19/3
x = -7/4
x = -19/9


Input: Compute the solution of x^3 - 29/30x^2 - 57/25x - 52/75 = 0

Output:
x^3 - 29/30x^2 - 57/25x - 52/75 = 0
(x - -2/5)(x - -4/5)(x - 13/6) = 0
x - -2/5 = 0
x - -4/5 = 0
x - 13/6 = 0
x = -2/5
x = -4/5
x = 13/6


Input: Determine x in x^3 - 29/12x^2 - 215/24x + 119/24 = 0

Output:
x^3 - 29/12x^2 - 215/24x + 119/24 = 0
(x - 1/2)(x - -7/3)(x - 17/4) = 0
x - 1/2 = 0
x - -7/3 = 0
x - 17/4 = 0
x = 1/2
x = -7/3
x = 17/4


Input: Find the solution to x^3 + 24/7x^2 - 127/63x - 680/63 = 0

Output:
x^3 + 24/7x^2 - 127/63x - 680/63 = 0
(x - -17/7)(x - 5/3)(x - -8/3) = 0
x - -17/7 = 0
x - 5/3 = 0
x - -8/3 = 0
x = -17/7
x = 5/3
x = -8/3


Input:
Solve the equations:
5x + 6y = -325/28
7x + 6y = -311/28

Output:
5x + 6y = -325/28
7x + 6y = -311/28

Using elimination
7*(5x + 6y = -325/28)
5*(7x + 6y = -311/28)
35x + 42y = -325/4
35x + 30y = -1555/28
Subtract equations
12y = -180/7
y = -180/7/12
y = -15/7

Substitute y
5x + 6(-15/7) = -325/28
5x = 5/4
x = 5/4/5
x = 1/4


Input:
Solve the equations:
8x + 1y = -95/7
5x + 7y = -461/7

Output:
8x + 1y = -95/7
5x + 7y = -461/7

Using elimination
5*(8x + 1y = -95/7)
8*(5x + 7y = -461/7)
40x + 5y = -475/7
40x + 56y = -3688/7
Subtract equations
-51y = 459
y = 459/-51
y = -9

Substitute y
8x + 1(-9) = -95/7
8x = -32/7
x = -32/7/8
x = -4/7


Input:
Solve the system:
6x + 5y = 96/5
4x + 10y = 64/5

Output:
6x + 5y = 96/5
4x + 10y = 64/5

Using elimination
4*(6x + 5y = 96/5)
6*(4x + 10y = 64/5)
24x + 20y = 384/5
24x + 60y = 384/5
Subtract equations
-40y = 0
y = 0/-40
y = 0

Substitute y
6x + 5(0) = 96/5
6x = 96/5
x = 96/5/6
x = 16/5


Input: Determine x in x^3 - 19/8x^2 - 289/100x + 5491/800 = 0

Output:
x^3 - 19/8x^2 - 289/100x + 5491/800 = 0
(x - 17/10)(x - -17/10)(x - 19/8) = 0
x - 17/10 = 0
x - -17/10 = 0
x - 19/8 = 0
x = 17/10
x = -17/10
x = 19/8


Input: Find the solution to 4x - 6 = 0

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


Input: Solve quickly: x^3 + 2/5x^2 - 49/20x - 6/5 = 0

Output:
x^3 + 2/5x^2 - 49/20x - 6/5 = 0
(x - -3/2)(x - -1/2)(x - 8/5) = 0
x - -3/2 = 0
x - -1/2 = 0
x - 8/5 = 0
x = -3/2
x = -1/2
x = 8/5


Input: Compute the solution of x^2 - 53/14x + 24/7 = 0

Output:
x^2 - 53/14x + 24/7 = 0
(x - 3/2)(x - 16/7) = 0
x - 3/2 = 0  or  x - 16/7 = 0
x = 3/2
x = 16/7


Input: Solve quickly: x^2 - 61/9x + 20/27 = 0

Output:
x^2 - 61/9x + 20/27 = 0
(x - 1/9)(x - 20/3) = 0
x - 1/9 = 0  or  x - 20/3 = 0
x = 1/9
x = 20/3


Input: Find x in x^2 - 24/7x + 17/7 = 0

Output:
x^2 - 24/7x + 17/7 = 0
(x - 1)(x - 17/7) = 0
x - 1 = 0  or  x - 17/7 = 0
x = 1
x = 17/7


Input:
Solve the equations:
4x + 1y = 0
5x + 3y = -63/8

Output:
4x + 1y = 0
5x + 3y = -63/8

Using elimination
5*(4x + 1y = 0)
4*(5x + 3y = -63/8)
20x + 5y = 0
20x + 12y = -63/2
Subtract equations
-7y = 63/2
y = 63/2/-7
y = -9/2

Substitute y
4x + 1(-9/2) = 0
4x = 9/2
x = 9/2/4
x = 9/8


Input: Solve 8x - 28/3 = 0

Output:
8x - 28/3 = 0
8x = 28/3
x = 28/3 / 8
x = 7/6


Input: Find x in 9x - 108/7 = 0

Output:
9x - 108/7 = 0
9x = 108/7
x = 108/7 / 9
x = 12/7


Input: Find x for x^3 + 1x^2 - 40/81x - 16/243 = 0

Output:
x^3 + 1x^2 - 40/81x - 16/243 = 0
(x - -4/3)(x - 4/9)(x - -1/9) = 0
x - -4/3 = 0
x - 4/9 = 0
x - -1/9 = 0
x = -4/3
x = 4/9
x = -1/9


Input:
Solve the equations:
2x + 3y = 9/2
3x + 4y = 31/5

Output:
2x + 3y = 9/2
3x + 4y = 31/5

Using elimination
3*(2x + 3y = 9/2)
2*(3x + 4y = 31/5)
6x + 9y = 27/2
6x + 8y = 62/5
Subtract equations
1y = 11/10
y = 11/10/1
y = 11/10

Substitute y
2x + 3(11/10) = 9/2
2x = 6/5
x = 6/5/2
x = 3/5


Input:
Solve simultaneously:
7x + 5y = -7
7x + 9y = -7

Output:
7x + 5y = -7
7x + 9y = -7

Using elimination
7*(7x + 5y = -7)
7*(7x + 9y = -7)
49x + 35y = -49
49x + 63y = -49
Subtract equations
-28y = 0
y = 0/-28
y = 0

Substitute y
7x + 5(0) = -7
7x = -7
x = -7/7
x = -1


Input: Find x in 6x - 45 = 0

Output:
6x - 45 = 0
6x = 45
x = 45 / 6
x = 15/2


Input:
Find x and y such that
5x + 2y = -179/6
7x + 6y = -107/2

Output:
5x + 2y = -179/6
7x + 6y = -107/2

Using elimination
7*(5x + 2y = -179/6)
5*(7x + 6y = -107/2)
35x + 14y = -1253/6
35x + 30y = -535/2
Subtract equations
-16y = 176/3
y = 176/3/-16
y = -11/3

Substitute y
5x + 2(-11/3) = -179/6
5x = -45/2
x = -45/2/5
x = -9/2


Input:
Solve the equations:
1x + 8y = 61/3
9x + 3y = -1

Output:
1x + 8y = 61/3
9x + 3y = -1

Using elimination
9*(1x + 8y = 61/3)
1*(9x + 3y = -1)
9x + 72y = 183
9x + 3y = -1
Subtract equations
69y = 184
y = 184/69
y = 8/3

Substitute y
1x + 8(8/3) = 61/3
1x = -1
x = -1/1
x = -1


Input: Solve x^2 + 31/5x + 77/20 = 0

Output:
x^2 + 31/5x + 77/20 = 0
(x - -7/10)(x - -11/2) = 0
x - -7/10 = 0  or  x - -11/2 = 0
x = -7/10
x = -11/2


Input:
Find x and y such that
6x + 5y = -16/5
8x + 10y = -48/5

Output:
6x + 5y = -16/5
8x + 10y = -48/5

Using elimination
8*(6x + 5y = -16/5)
6*(8x + 10y = -48/5)
48x + 40y = -128/5
48x + 60y = -288/5
Subtract equations
-20y = 32
y = 32/-20
y = -8/5

Substitute y
6x + 5(-8/5) = -16/5
6x = 24/5
x = 24/5/6
x = 4/5


Input: Solve the equation 9x - 99/8 = 0

Output:
9x - 99/8 = 0
9x = 99/8
x = 99/8 / 9
x = 11/8


Input: Find x for x^2 + 15/8x + 13/32 = 0

Output:
x^2 + 15/8x + 13/32 = 0
(x - -13/8)(x - -1/4) = 0
x - -13/8 = 0  or  x - -1/4 = 0
x = -13/8
x = -1/4


Input: Determine x in x^2 - 22/15x - 56/15 = 0

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


Input:
Solve the equations:
8x + 2y = -206/9
7x + 9y = -898/9

Output:
8x + 2y = -206/9
7x + 9y = -898/9

Using elimination
7*(8x + 2y = -206/9)
8*(7x + 9y = -898/9)
56x + 14y = -1442/9
56x + 72y = -7184/9
Subtract equations
-58y = 638
y = 638/-58
y = -11

Substitute y
8x + 2(-11) = -206/9
8x = -8/9
x = -8/9/8
x = -1/9


Input: Compute the solution of x^3 - 17/5x^2 - 33/20x + 171/20 = 0

Output:
x^3 - 17/5x^2 - 33/20x + 171/20 = 0
(x - 19/10)(x - -3/2)(x - 3) = 0
x - 19/10 = 0
x - -3/2 = 0
x - 3 = 0
x = 19/10
x = -3/2
x = 3


Input: Solve the equation x^2 + 4/5x  = 0

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


Input: Solve the equation 1x - 4/7 = 0

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


Input:
Solve simultaneously:
10x + 8y = -134/9
1x + 6y = -109/15

Output:
10x + 8y = -134/9
1x + 6y = -109/15

Using elimination
1*(10x + 8y = -134/9)
10*(1x + 6y = -109/15)
10x + 8y = -134/9
10x + 60y = -218/3
Subtract equations
-52y = 520/9
y = 520/9/-52
y = -10/9

Substitute y
10x + 8(-10/9) = -134/9
10x = -6
x = -6/10
x = -3/5


Input: Find the solution to 1x + 3/5 = 0

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


Input: What value of x satisfies x^3 - 291/40x^2 + 97/8x - 15/4 = 0

Output:
x^3 - 291/40x^2 + 97/8x - 15/4 = 0
(x - 2/5)(x - 15/8)(x - 5) = 0
x - 2/5 = 0
x - 15/8 = 0
x - 5 = 0
x = 2/5
x = 15/8
x = 5