Input: Compute the solution of x^3 - 43/2x^2 + 213/2x - 135 = 0

Output:
x^3 - 43/2x^2 + 213/2x - 135 = 0
(x - 2)(x - 9/2)(x - 15) = 0
x - 2 = 0
x - 9/2 = 0
x - 15 = 0
x = 2
x = 9/2
x = 15


Input:
Find x and y such that
8x + 4y = -688/5
8x + 5y = -134

Output:
8x + 4y = -688/5
8x + 5y = -134

Using elimination
8*(8x + 4y = -688/5)
8*(8x + 5y = -134)
64x + 32y = -5504/5
64x + 40y = -1072
Subtract equations
-8y = -144/5
y = -144/5/-8
y = 18/5

Substitute y
8x + 4(18/5) = -688/5
8x = -152
x = -152/8
x = -19


Input: Find x for x^3 - 3/2x^2 - 107/18x + 13/3 = 0

Output:
x^3 - 3/2x^2 - 107/18x + 13/3 = 0
(x - -13/6)(x - 3)(x - 2/3) = 0
x - -13/6 = 0
x - 3 = 0
x - 2/3 = 0
x = -13/6
x = 3
x = 2/3


Input: Find the solution to x^2 - 20/3x - 21 = 0

Output:
x^2 - 20/3x - 21 = 0
(x - -7/3)(x - 9) = 0
x - -7/3 = 0  or  x - 9 = 0
x = -7/3
x = 9


Input:
Solve the system:
7x + 1y = -223/10
5x + 2y = -88/5

Output:
7x + 1y = -223/10
5x + 2y = -88/5

Using elimination
5*(7x + 1y = -223/10)
7*(5x + 2y = -88/5)
35x + 5y = -223/2
35x + 14y = -616/5
Subtract equations
-9y = 117/10
y = 117/10/-9
y = -13/10

Substitute y
7x + 1(-13/10) = -223/10
7x = -21
x = -21/7
x = -3


Input: Solve the equation 10x - 45/4 = 0

Output:
10x - 45/4 = 0
10x = 45/4
x = 45/4 / 10
x = 9/8


Input:
Solve the system:
2x + 7y = -64/15
4x + 6y = -32/15

Output:
2x + 7y = -64/15
4x + 6y = -32/15

Using elimination
4*(2x + 7y = -64/15)
2*(4x + 6y = -32/15)
8x + 28y = -256/15
8x + 12y = -64/15
Subtract equations
16y = -64/5
y = -64/5/16
y = -4/5

Substitute y
2x + 7(-4/5) = -64/15
2x = 4/3
x = 4/3/2
x = 2/3


Input: Solve quickly: x^2 + 101/30x + 77/30 = 0

Output:
x^2 + 101/30x + 77/30 = 0
(x - -11/5)(x - -7/6) = 0
x - -11/5 = 0  or  x - -7/6 = 0
x = -11/5
x = -7/6


Input: Determine x in x^3 + 148/9x^2 + 1793/27x + 1936/27 = 0

Output:
x^3 + 148/9x^2 + 1793/27x + 1936/27 = 0
(x - -11/3)(x - -11)(x - -16/9) = 0
x - -11/3 = 0
x - -11 = 0
x - -16/9 = 0
x = -11/3
x = -11
x = -16/9


Input: Solve quickly: x^3 - 91/10x^2 + 67/5x + 91/10 = 0

Output:
x^3 - 91/10x^2 + 67/5x + 91/10 = 0
(x - 13/5)(x - 7)(x - -1/2) = 0
x - 13/5 = 0
x - 7 = 0
x - -1/2 = 0
x = 13/5
x = 7
x = -1/2


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

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


Input: Solve 8x + 88/5 = 0

Output:
8x + 88/5 = 0
8x = -88/5
x = -88/5 / 8
x = -11/5


Input: Determine x in x^3 - 3x^2 - 532/9x - 980/9 = 0

Output:
x^3 - 3x^2 - 532/9x - 980/9 = 0
(x - 10)(x - -14/3)(x - -7/3) = 0
x - 10 = 0
x - -14/3 = 0
x - -7/3 = 0
x = 10
x = -14/3
x = -7/3


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

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


Input: Determine x in 2x - 2 = 0

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


Input: Find x for x^3 - 37/10x^2 + 7/10x  = 0

Output:
x^3 - 37/10x^2 + 7/10x  = 0
(x - 0)(x - 1/5)(x - 7/2) = 0
x - 0 = 0
x - 1/5 = 0
x - 7/2 = 0
x = 0
x = 1/5
x = 7/2


Input: Find x in x^3 - 53/30x^2 - 21x - 132/5 = 0

Output:
x^3 - 53/30x^2 - 21x - 132/5 = 0
(x - -12/5)(x - -11/6)(x - 6) = 0
x - -12/5 = 0
x - -11/6 = 0
x - 6 = 0
x = -12/5
x = -11/6
x = 6


Input:
Solve simultaneously:
1x + 10y = -1772/63
7x + 6y = -884/63

Output:
1x + 10y = -1772/63
7x + 6y = -884/63

Using elimination
7*(1x + 10y = -1772/63)
1*(7x + 6y = -884/63)
7x + 70y = -1772/9
7x + 6y = -884/63
Subtract equations
64y = -1280/7
y = -1280/7/64
y = -20/7

Substitute y
1x + 10(-20/7) = -1772/63
1x = 4/9
x = 4/9/1
x = 4/9


Input:
Solve simultaneously:
7x + 1y = 166/3
9x + 9y = 210

Output:
7x + 1y = 166/3
9x + 9y = 210

Using elimination
9*(7x + 1y = 166/3)
7*(9x + 9y = 210)
63x + 9y = 498
63x + 63y = 1470
Subtract equations
-54y = -972
y = -972/-54
y = 18

Substitute y
7x + 1(18) = 166/3
7x = 112/3
x = 112/3/7
x = 16/3


Input: Solve x^2 + 38/15x + 77/60 = 0

Output:
x^2 + 38/15x + 77/60 = 0
(x - -11/6)(x - -7/10) = 0
x - -11/6 = 0  or  x - -7/10 = 0
x = -11/6
x = -7/10


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

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


Input: Determine x in 6x - 8/3 = 0

Output:
6x - 8/3 = 0
6x = 8/3
x = 8/3 / 6
x = 4/9


Input: Solve the equation x^3 + 401/315x^2 - 24/7x - 68/45 = 0

Output:
x^3 + 401/315x^2 - 24/7x - 68/45 = 0
(x - -17/7)(x - 14/9)(x - -2/5) = 0
x - -17/7 = 0
x - 14/9 = 0
x - -2/5 = 0
x = -17/7
x = 14/9
x = -2/5


Input:
Find x and y such that
8x + 3y = 406/15
7x + 8y = 581/15

Output:
8x + 3y = 406/15
7x + 8y = 581/15

Using elimination
7*(8x + 3y = 406/15)
8*(7x + 8y = 581/15)
56x + 21y = 2842/15
56x + 64y = 4648/15
Subtract equations
-43y = -602/5
y = -602/5/-43
y = 14/5

Substitute y
8x + 3(14/5) = 406/15
8x = 56/3
x = 56/3/8
x = 7/3


Input: Solve quickly: 3x - 3 = 0

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


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

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


Input: What value of x satisfies x^3 - 49/2x^2 + 114x + 459/2 = 0

Output:
x^3 - 49/2x^2 + 114x + 459/2 = 0
(x - 17)(x - -3/2)(x - 9) = 0
x - 17 = 0
x - -3/2 = 0
x - 9 = 0
x = 17
x = -3/2
x = 9


Input: Find x for x^2 - 86/35x + 48/35 = 0

Output:
x^2 - 86/35x + 48/35 = 0
(x - 6/7)(x - 8/5) = 0
x - 6/7 = 0  or  x - 8/5 = 0
x = 6/7
x = 8/5


Input: Solve the equation x^3 - 295/18x^2 + 509/9x + 760/9 = 0

Output:
x^3 - 295/18x^2 + 509/9x + 760/9 = 0
(x - 8)(x - -10/9)(x - 19/2) = 0
x - 8 = 0
x - -10/9 = 0
x - 19/2 = 0
x = 8
x = -10/9
x = 19/2


Input: Solve quickly: 7x - 91/5 = 0

Output:
7x - 91/5 = 0
7x = 91/5
x = 91/5 / 7
x = 13/5


Input: Find x for x^3 + 197/90x^2 - 268/45x + 19/30 = 0

Output:
x^3 + 197/90x^2 - 268/45x + 19/30 = 0
(x - 3/2)(x - 1/9)(x - -19/5) = 0
x - 3/2 = 0
x - 1/9 = 0
x - -19/5 = 0
x = 3/2
x = 1/9
x = -19/5


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

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


Input: Solve x^2 - 49/9x + 130/27 = 0

Output:
x^2 - 49/9x + 130/27 = 0
(x - 10/9)(x - 13/3) = 0
x - 10/9 = 0  or  x - 13/3 = 0
x = 10/9
x = 13/3


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

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


Input:
Solve the system:
5x + 3y = 48/7
8x + 7y = 123/7

Output:
5x + 3y = 48/7
8x + 7y = 123/7

Using elimination
8*(5x + 3y = 48/7)
5*(8x + 7y = 123/7)
40x + 24y = 384/7
40x + 35y = 615/7
Subtract equations
-11y = -33
y = -33/-11
y = 3

Substitute y
5x + 3(3) = 48/7
5x = -15/7
x = -15/7/5
x = -3/7


Input:
Find x and y such that
6x + 6y = 267/20
1x + 9y = 289/40

Output:
6x + 6y = 267/20
1x + 9y = 289/40

Using elimination
1*(6x + 6y = 267/20)
6*(1x + 9y = 289/40)
6x + 6y = 267/20
6x + 54y = 867/20
Subtract equations
-48y = -30
y = -30/-48
y = 5/8

Substitute y
6x + 6(5/8) = 267/20
6x = 48/5
x = 48/5/6
x = 8/5


Input: Solve quickly: x^3 - 1/8x^2 - 145/16x - 77/8 = 0

Output:
x^3 - 1/8x^2 - 145/16x - 77/8 = 0
(x - 7/2)(x - -11/8)(x - -2) = 0
x - 7/2 = 0
x - -11/8 = 0
x - -2 = 0
x = 7/2
x = -11/8
x = -2


Input: Find the solution to x^3 + 337/70x^2 + 13/2x + 76/35 = 0

Output:
x^3 + 337/70x^2 + 13/2x + 76/35 = 0
(x - -8/5)(x - -1/2)(x - -19/7) = 0
x - -8/5 = 0
x - -1/2 = 0
x - -19/7 = 0
x = -8/5
x = -1/2
x = -19/7


Input: Solve quickly: x^2 + 11x + 10 = 0

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


Input: Find the solution to x^2 + 23/24x - 95/12 = 0

Output:
x^2 + 23/24x - 95/12 = 0
(x - 19/8)(x - -10/3) = 0
x - 19/8 = 0  or  x - -10/3 = 0
x = 19/8
x = -10/3


Input:
Find x and y such that
8x + 4y = -6/5
3x + 1y = -7/10

Output:
8x + 4y = -6/5
3x + 1y = -7/10

Using elimination
3*(8x + 4y = -6/5)
8*(3x + 1y = -7/10)
24x + 12y = -18/5
24x + 8y = -28/5
Subtract equations
4y = 2
y = 2/4
y = 1/2

Substitute y
8x + 4(1/2) = -6/5
8x = -16/5
x = -16/5/8
x = -2/5


Input: Find the solution to x^2 - 64/5x + 48/5 = 0

Output:
x^2 - 64/5x + 48/5 = 0
(x - 12)(x - 4/5) = 0
x - 12 = 0  or  x - 4/5 = 0
x = 12
x = 4/5


Input: Determine x in x^2 + 166/35x + 144/35 = 0

Output:
x^2 + 166/35x + 144/35 = 0
(x - -18/5)(x - -8/7) = 0
x - -18/5 = 0  or  x - -8/7 = 0
x = -18/5
x = -8/7


Input: Find x for 2x + 34/7 = 0

Output:
2x + 34/7 = 0
2x = -34/7
x = -34/7 / 2
x = -17/7


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

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


Input:
Solve the system:
1x + 3y = 3/2
4x + 6y = -6

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

Using elimination
4*(1x + 3y = 3/2)
1*(4x + 6y = -6)
4x + 12y = 6
4x + 6y = -6
Subtract equations
6y = 12
y = 12/6
y = 2

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


Input: Find x in x^2 + 157/9x - 266/9 = 0

Output:
x^2 + 157/9x - 266/9 = 0
(x - -19)(x - 14/9) = 0
x - -19 = 0  or  x - 14/9 = 0
x = -19
x = 14/9


Input: Determine x in x^2 - 56/9x + 221/27 = 0

Output:
x^2 - 56/9x + 221/27 = 0
(x - 13/3)(x - 17/9) = 0
x - 13/3 = 0  or  x - 17/9 = 0
x = 13/3
x = 17/9


Input: Find x for x^2 - 45/28x - 13/28 = 0

Output:
x^2 - 45/28x - 13/28 = 0
(x - 13/7)(x - -1/4) = 0
x - 13/7 = 0  or  x - -1/4 = 0
x = 13/7
x = -1/4


Input: Find x for x^3 + 22x^2 + 83/4x - 385 = 0

Output:
x^3 + 22x^2 + 83/4x - 385 = 0
(x - 7/2)(x - -20)(x - -11/2) = 0
x - 7/2 = 0
x - -20 = 0
x - -11/2 = 0
x = 7/2
x = -20
x = -11/2


Input:
Solve simultaneously:
10x + 4y = 122/5
4x + 3y = 113/10

Output:
10x + 4y = 122/5
4x + 3y = 113/10

Using elimination
4*(10x + 4y = 122/5)
10*(4x + 3y = 113/10)
40x + 16y = 488/5
40x + 30y = 113
Subtract equations
-14y = -77/5
y = -77/5/-14
y = 11/10

Substitute y
10x + 4(11/10) = 122/5
10x = 20
x = 20/10
x = 2


Input: Compute the solution of x^3 + 121/45x^2 - 37/9x + 19/45 = 0

Output:
x^3 + 121/45x^2 - 37/9x + 19/45 = 0
(x - 1/9)(x - 1)(x - -19/5) = 0
x - 1/9 = 0
x - 1 = 0
x - -19/5 = 0
x = 1/9
x = 1
x = -19/5


Input:
Solve simultaneously:
1x + 7y = -8/3
10x + 2y = 460/21

Output:
1x + 7y = -8/3
10x + 2y = 460/21

Using elimination
10*(1x + 7y = -8/3)
1*(10x + 2y = 460/21)
10x + 70y = -80/3
10x + 2y = 460/21
Subtract equations
68y = -340/7
y = -340/7/68
y = -5/7

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


Input: Determine x in x^2 - 1/6x - 17/2 = 0

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


Input: Determine x in x^2 - 4/3x - 160/81 = 0

Output:
x^2 - 4/3x - 160/81 = 0
(x - 20/9)(x - -8/9) = 0
x - 20/9 = 0  or  x - -8/9 = 0
x = 20/9
x = -8/9


Input: Solve quickly: x^3 + 97/6x^2 + 319/6x + 38 = 0

Output:
x^3 + 97/6x^2 + 319/6x + 38 = 0
(x - -19/6)(x - -12)(x - -1) = 0
x - -19/6 = 0
x - -12 = 0
x - -1 = 0
x = -19/6
x = -12
x = -1


Input:
Solve simultaneously:
7x + 5y = 32
9x + 3y = 48

Output:
7x + 5y = 32
9x + 3y = 48

Using elimination
9*(7x + 5y = 32)
7*(9x + 3y = 48)
63x + 45y = 288
63x + 21y = 336
Subtract equations
24y = -48
y = -48/24
y = -2

Substitute y
7x + 5(-2) = 32
7x = 42
x = 42/7
x = 6


Input: Find x for 10x - 50/9 = 0

Output:
10x - 50/9 = 0
10x = 50/9
x = 50/9 / 10
x = 5/9


Input: Solve 10x + 30 = 0

Output:
10x + 30 = 0
10x = -30
x = -30 / 10
x = -3


Input:
Find x and y such that
7x + 8y = -102/5
8x + 9y = -116/5

Output:
7x + 8y = -102/5
8x + 9y = -116/5

Using elimination
8*(7x + 8y = -102/5)
7*(8x + 9y = -116/5)
56x + 64y = -816/5
56x + 63y = -812/5
Subtract equations
1y = -4/5
y = -4/5/1
y = -4/5

Substitute y
7x + 8(-4/5) = -102/5
7x = -14
x = -14/7
x = -2


Input:
Solve the equations:
10x + 9y = 47
6x + 1y = 67/3

Output:
10x + 9y = 47
6x + 1y = 67/3

Using elimination
6*(10x + 9y = 47)
10*(6x + 1y = 67/3)
60x + 54y = 282
60x + 10y = 670/3
Subtract equations
44y = 176/3
y = 176/3/44
y = 4/3

Substitute y
10x + 9(4/3) = 47
10x = 35
x = 35/10
x = 7/2


Input: Solve x^3 - 91/40x^2 + 1/160x + 273/160 = 0

Output:
x^3 - 91/40x^2 + 1/160x + 273/160 = 0
(x - -3/4)(x - 13/8)(x - 7/5) = 0
x - -3/4 = 0
x - 13/8 = 0
x - 7/5 = 0
x = -3/4
x = 13/8
x = 7/5


Input: Solve quickly: x^2 - 35/4x - 39 = 0

Output:
x^2 - 35/4x - 39 = 0
(x - -13/4)(x - 12) = 0
x - -13/4 = 0  or  x - 12 = 0
x = -13/4
x = 12


Input: Determine x in x^3 + 19/15x^2 - 178/25x - 224/75 = 0

Output:
x^3 + 19/15x^2 - 178/25x - 224/75 = 0
(x - -2/5)(x - -16/5)(x - 7/3) = 0
x - -2/5 = 0
x - -16/5 = 0
x - 7/3 = 0
x = -2/5
x = -16/5
x = 7/3


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

Output:
1x - 20/3 = 0
1x = 20/3
x = 20/3 / 1
x = 20/3


Input: Solve 6x - 18 = 0

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


Input: Find x in x^2 - 17/6x - 1/2 = 0

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


Input: Compute the solution of x^3 - 75/4x^2 + 883/8x - 195 = 0

Output:
x^3 - 75/4x^2 + 883/8x - 195 = 0
(x - 15/2)(x - 13/4)(x - 8) = 0
x - 15/2 = 0
x - 13/4 = 0
x - 8 = 0
x = 15/2
x = 13/4
x = 8


Input: Solve quickly: x^3 + 135/56x^2 - 13/7x - 15/56 = 0

Output:
x^3 + 135/56x^2 - 13/7x - 15/56 = 0
(x - 5/7)(x - -3)(x - -1/8) = 0
x - 5/7 = 0
x - -3 = 0
x - -1/8 = 0
x = 5/7
x = -3
x = -1/8


Input:
Solve the system:
9x + 9y = 72
10x + 5y = 90

Output:
9x + 9y = 72
10x + 5y = 90

Using elimination
10*(9x + 9y = 72)
9*(10x + 5y = 90)
90x + 90y = 720
90x + 45y = 810
Subtract equations
45y = -90
y = -90/45
y = -2

Substitute y
9x + 9(-2) = 72
9x = 90
x = 90/9
x = 10


Input: Determine x in 10x - 25/2 = 0

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


Input: What value of x satisfies x^3 - 23/4x^2 + 811/196x + 285/98 = 0

Output:
x^3 - 23/4x^2 + 811/196x + 285/98 = 0
(x - -3/7)(x - 19/4)(x - 10/7) = 0
x - -3/7 = 0
x - 19/4 = 0
x - 10/7 = 0
x = -3/7
x = 19/4
x = 10/7


Input: Determine x in x^3 + 4x^2 + 3x  = 0

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


Input:
Solve simultaneously:
8x + 9y = 9
7x + 5y = 17/8

Output:
8x + 9y = 9
7x + 5y = 17/8

Using elimination
7*(8x + 9y = 9)
8*(7x + 5y = 17/8)
56x + 63y = 63
56x + 40y = 17
Subtract equations
23y = 46
y = 46/23
y = 2

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


Input: Find x for x^2 + 33/10x + 2 = 0

Output:
x^2 + 33/10x + 2 = 0
(x - -4/5)(x - -5/2) = 0
x - -4/5 = 0  or  x - -5/2 = 0
x = -4/5
x = -5/2


Input:
Solve the equations:
1x + 5y = -5
8x + 5y = -5

Output:
1x + 5y = -5
8x + 5y = -5

Using elimination
8*(1x + 5y = -5)
1*(8x + 5y = -5)
8x + 40y = -40
8x + 5y = -5
Subtract equations
35y = -35
y = -35/35
y = -1

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


Input: Solve the equation 7x + 18 = 0

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


Input: Find x in x^3 - 59/90x^2 + 17/162x - 2/405 = 0

Output:
x^3 - 59/90x^2 + 17/162x - 2/405 = 0
(x - 1/9)(x - 4/9)(x - 1/10) = 0
x - 1/9 = 0
x - 4/9 = 0
x - 1/10 = 0
x = 1/9
x = 4/9
x = 1/10


Input: Solve 1x - 16/3 = 0

Output:
1x - 16/3 = 0
1x = 16/3
x = 16/3 / 1
x = 16/3


Input:
Solve simultaneously:
7x + 4y = 128/9
3x + 6y = 44/3

Output:
7x + 4y = 128/9
3x + 6y = 44/3

Using elimination
3*(7x + 4y = 128/9)
7*(3x + 6y = 44/3)
21x + 12y = 128/3
21x + 42y = 308/3
Subtract equations
-30y = -60
y = -60/-30
y = 2

Substitute y
7x + 4(2) = 128/9
7x = 56/9
x = 56/9/7
x = 8/9


Input:
Solve the equations:
9x + 10y = -81
9x + 8y = -63

Output:
9x + 10y = -81
9x + 8y = -63

Using elimination
9*(9x + 10y = -81)
9*(9x + 8y = -63)
81x + 90y = -729
81x + 72y = -567
Subtract equations
18y = -162
y = -162/18
y = -9

Substitute y
9x + 10(-9) = -81
9x = 9
x = 9/9
x = 1


Input: What value of x satisfies 1x + 13/7 = 0

Output:
1x + 13/7 = 0
1x = -13/7
x = -13/7 / 1
x = -13/7


Input: What value of x satisfies x^3 - 115/9x^2 - 143/27x + 845/27 = 0

Output:
x^3 - 115/9x^2 - 143/27x + 845/27 = 0
(x - 13/9)(x - 13)(x - -5/3) = 0
x - 13/9 = 0
x - 13 = 0
x - -5/3 = 0
x = 13/9
x = 13
x = -5/3


Input:
Solve the equations:
3x + 4y = 21/5
10x + 7y = 51/5

Output:
3x + 4y = 21/5
10x + 7y = 51/5

Using elimination
10*(3x + 4y = 21/5)
3*(10x + 7y = 51/5)
30x + 40y = 42
30x + 21y = 153/5
Subtract equations
19y = 57/5
y = 57/5/19
y = 3/5

Substitute y
3x + 4(3/5) = 21/5
3x = 9/5
x = 9/5/3
x = 3/5


Input: Solve the equation x^3 + 271/42x^2 + 559/42x + 60/7 = 0

Output:
x^3 + 271/42x^2 + 559/42x + 60/7 = 0
(x - -8/3)(x - -9/7)(x - -5/2) = 0
x - -8/3 = 0
x - -9/7 = 0
x - -5/2 = 0
x = -8/3
x = -9/7
x = -5/2


Input: Solve quickly: 2x - 2 = 0

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


Input: What value of x satisfies 7x - 35/4 = 0

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


Input: Solve the equation x^3 + 31/10x^2 + 3/10x  = 0

Output:
x^3 + 31/10x^2 + 3/10x  = 0
(x - 0)(x - -3)(x - -1/10) = 0
x - 0 = 0
x - -3 = 0
x - -1/10 = 0
x = 0
x = -3
x = -1/10


Input: Compute the solution of x^2 - 7/3x - 40/3 = 0

Output:
x^2 - 7/3x - 40/3 = 0
(x - 5)(x - -8/3) = 0
x - 5 = 0  or  x - -8/3 = 0
x = 5
x = -8/3


Input: Compute the solution of 4x - 80/7 = 0

Output:
4x - 80/7 = 0
4x = 80/7
x = 80/7 / 4
x = 20/7


Input: Find the solution to 8x - 64 = 0

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


Input: Find x for 9x + 54 = 0

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


Input:
Solve the equations:
6x + 3y = -237/10
7x + 10y = -27

Output:
6x + 3y = -237/10
7x + 10y = -27

Using elimination
7*(6x + 3y = -237/10)
6*(7x + 10y = -27)
42x + 21y = -1659/10
42x + 60y = -162
Subtract equations
-39y = -39/10
y = -39/10/-39
y = 1/10

Substitute y
6x + 3(1/10) = -237/10
6x = -24
x = -24/6
x = -4


Input: Determine x in 5x - 5/4 = 0

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


Input: Find x in x^3 + 10x^2 - 4x - 40 = 0

Output:
x^3 + 10x^2 - 4x - 40 = 0
(x - 2)(x - -10)(x - -2) = 0
x - 2 = 0
x - -10 = 0
x - -2 = 0
x = 2
x = -10
x = -2


Input: Solve the equation 9x - 99 = 0

Output:
9x - 99 = 0
9x = 99
x = 99 / 9
x = 11


Input: Find x in x^2 - 6x + 8 = 0

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


Input: Find x in x^2 - 13/2x - 35 = 0

Output:
x^2 - 13/2x - 35 = 0
(x - 10)(x - -7/2) = 0
x - 10 = 0  or  x - -7/2 = 0
x = 10
x = -7/2


Input: Find x for x^3 + 18x^2 + 89x + 132 = 0

Output:
x^3 + 18x^2 + 89x + 132 = 0
(x - -4)(x - -3)(x - -11) = 0
x - -4 = 0
x - -3 = 0
x - -11 = 0
x = -4
x = -3
x = -11


Input: Compute the solution of x^3 + 34/21x^2 - 667/567x - 130/63 = 0

Output:
x^3 + 34/21x^2 - 667/567x - 130/63 = 0
(x - -9/7)(x - 10/9)(x - -13/9) = 0
x - -9/7 = 0
x - 10/9 = 0
x - -13/9 = 0
x = -9/7
x = 10/9
x = -13/9


Input: Find x in 8x + 1 = 0

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


Input:
Find x and y such that
5x + 3y = 35/2
1x + 1y = 5/2

Output:
5x + 3y = 35/2
1x + 1y = 5/2

Using elimination
1*(5x + 3y = 35/2)
5*(1x + 1y = 5/2)
5x + 3y = 35/2
5x + 5y = 25/2
Subtract equations
-2y = 5
y = 5/-2
y = -5/2

Substitute y
5x + 3(-5/2) = 35/2
5x = 25
x = 25/5
x = 5


Input:
Solve the system:
3x + 7y = -17/9
8x + 4y = 116/9

Output:
3x + 7y = -17/9
8x + 4y = 116/9

Using elimination
8*(3x + 7y = -17/9)
3*(8x + 4y = 116/9)
24x + 56y = -136/9
24x + 12y = 116/3
Subtract equations
44y = -484/9
y = -484/9/44
y = -11/9

Substitute y
3x + 7(-11/9) = -17/9
3x = 20/3
x = 20/3/3
x = 20/9


Input: Solve 7x - 63/5 = 0

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


Input: Compute the solution of x^2 + 116/5x + 64 = 0

Output:
x^2 + 116/5x + 64 = 0
(x - -16/5)(x - -20) = 0
x - -16/5 = 0  or  x - -20 = 0
x = -16/5
x = -20


Input: Determine x in x^2 - 31/21x + 8/21 = 0

Output:
x^2 - 31/21x + 8/21 = 0
(x - 1/3)(x - 8/7) = 0
x - 1/3 = 0  or  x - 8/7 = 0
x = 1/3
x = 8/7


Input: Solve quickly: x^2 + 83/10x - 17/10 = 0

Output:
x^2 + 83/10x - 17/10 = 0
(x - 1/5)(x - -17/2) = 0
x - 1/5 = 0  or  x - -17/2 = 0
x = 1/5
x = -17/2


Input: Find x in 2x + 4/3 = 0

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


Input: Solve quickly: x^3 - 8/35x^2 - 27/5x + 162/35 = 0

Output:
x^3 - 8/35x^2 - 27/5x + 162/35 = 0
(x - -18/7)(x - 1)(x - 9/5) = 0
x - -18/7 = 0
x - 1 = 0
x - 9/5 = 0
x = -18/7
x = 1
x = 9/5


Input: Find the solution to 10x - 14 = 0

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


Input: Solve the equation x^3 + 220/9x^2 + 3379/27x + 494/3 = 0

Output:
x^3 + 220/9x^2 + 3379/27x + 494/3 = 0
(x - -13/3)(x - -18)(x - -19/9) = 0
x - -13/3 = 0
x - -18 = 0
x - -19/9 = 0
x = -13/3
x = -18
x = -19/9


Input: Find x for x^2 - 9/14x - 65/14 = 0

Output:
x^2 - 9/14x - 65/14 = 0
(x - 5/2)(x - -13/7) = 0
x - 5/2 = 0  or  x - -13/7 = 0
x = 5/2
x = -13/7


Input: Find x for x^3 - 221/40x^2 + 1589/160x - 931/160 = 0

Output:
x^3 - 221/40x^2 + 1589/160x - 931/160 = 0
(x - 19/8)(x - 7/4)(x - 7/5) = 0
x - 19/8 = 0
x - 7/4 = 0
x - 7/5 = 0
x = 19/8
x = 7/4
x = 7/5


Input:
Solve the equations:
7x + 10y = -281/18
10x + 3y = -97/3

Output:
7x + 10y = -281/18
10x + 3y = -97/3

Using elimination
10*(7x + 10y = -281/18)
7*(10x + 3y = -97/3)
70x + 100y = -1405/9
70x + 21y = -679/3
Subtract equations
79y = 632/9
y = 632/9/79
y = 8/9

Substitute y
7x + 10(8/9) = -281/18
7x = -49/2
x = -49/2/7
x = -7/2


Input: Find x in 7x + 77/3 = 0

Output:
7x + 77/3 = 0
7x = -77/3
x = -77/3 / 7
x = -11/3


Input: Solve quickly: x^3 - 104/45x^2 + 19/45x  = 0

Output:
x^3 - 104/45x^2 + 19/45x  = 0
(x - 0)(x - 1/5)(x - 19/9) = 0
x - 0 = 0
x - 1/5 = 0
x - 19/9 = 0
x = 0
x = 1/5
x = 19/9


Input: Find x in 9x + 144/5 = 0

Output:
9x + 144/5 = 0
9x = -144/5
x = -144/5 / 9
x = -16/5


Input: Find x in 8x + 120/7 = 0

Output:
8x + 120/7 = 0
8x = -120/7
x = -120/7 / 8
x = -15/7


Input: Solve the equation x^3 + 17/15x^2 - 8/5x + 4/15 = 0

Output:
x^3 + 17/15x^2 - 8/5x + 4/15 = 0
(x - 2/3)(x - -2)(x - 1/5) = 0
x - 2/3 = 0
x - -2 = 0
x - 1/5 = 0
x = 2/3
x = -2
x = 1/5


Input: Solve quickly: x^3 - 3/28x^2 - 99/28x - 1/2 = 0

Output:
x^3 - 3/28x^2 - 99/28x - 1/2 = 0
(x - -7/4)(x - 2)(x - -1/7) = 0
x - -7/4 = 0
x - 2 = 0
x - -1/7 = 0
x = -7/4
x = 2
x = -1/7


Input: What value of x satisfies x^3 + 9x^2 - 10x  = 0

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


Input:
Solve the system:
7x + 8y = 7/9
10x + 2y = -122/9

Output:
7x + 8y = 7/9
10x + 2y = -122/9

Using elimination
10*(7x + 8y = 7/9)
7*(10x + 2y = -122/9)
70x + 80y = 70/9
70x + 14y = -854/9
Subtract equations
66y = 308/3
y = 308/3/66
y = 14/9

Substitute y
7x + 8(14/9) = 7/9
7x = -35/3
x = -35/3/7
x = -5/3


Input: What value of x satisfies x^3 + 83/10x^2 + 229/10x + 21 = 0

Output:
x^3 + 83/10x^2 + 229/10x + 21 = 0
(x - -5/2)(x - -14/5)(x - -3) = 0
x - -5/2 = 0
x - -14/5 = 0
x - -3 = 0
x = -5/2
x = -14/5
x = -3


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

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


Input: Find the solution to x^2 - 19/9x - 154/27 = 0

Output:
x^2 - 19/9x - 154/27 = 0
(x - -14/9)(x - 11/3) = 0
x - -14/9 = 0  or  x - 11/3 = 0
x = -14/9
x = 11/3


Input: Compute the solution of x^3 - 1327/210x^2 - 62/105x + 19/6 = 0

Output:
x^3 - 1327/210x^2 - 62/105x + 19/6 = 0
(x - 19/3)(x - -5/7)(x - 7/10) = 0
x - 19/3 = 0
x - -5/7 = 0
x - 7/10 = 0
x = 19/3
x = -5/7
x = 7/10


Input: Compute the solution of x^3 + 52/15x^2 + 89/60x - 26/15 = 0

Output:
x^3 + 52/15x^2 + 89/60x - 26/15 = 0
(x - -8/3)(x - 1/2)(x - -13/10) = 0
x - -8/3 = 0
x - 1/2 = 0
x - -13/10 = 0
x = -8/3
x = 1/2
x = -13/10


Input:
Find x and y such that
4x + 1y = -152/9
4x + 8y = -208/9

Output:
4x + 1y = -152/9
4x + 8y = -208/9

Using elimination
4*(4x + 1y = -152/9)
4*(4x + 8y = -208/9)
16x + 4y = -608/9
16x + 32y = -832/9
Subtract equations
-28y = 224/9
y = 224/9/-28
y = -8/9

Substitute y
4x + 1(-8/9) = -152/9
4x = -16
x = -16/4
x = -4


Input: Find the solution to x^3 + 7/2x^2 - 119x + 117/2 = 0

Output:
x^3 + 7/2x^2 - 119x + 117/2 = 0
(x - 9)(x - 1/2)(x - -13) = 0
x - 9 = 0
x - 1/2 = 0
x - -13 = 0
x = 9
x = 1/2
x = -13


Input:
Find x and y such that
1x + 6y = 41/4
10x + 7y = 191/6

Output:
1x + 6y = 41/4
10x + 7y = 191/6

Using elimination
10*(1x + 6y = 41/4)
1*(10x + 7y = 191/6)
10x + 60y = 205/2
10x + 7y = 191/6
Subtract equations
53y = 212/3
y = 212/3/53
y = 4/3

Substitute y
1x + 6(4/3) = 41/4
1x = 9/4
x = 9/4/1
x = 9/4


Input: Solve the equation x^2 + 159/28x + 85/14 = 0

Output:
x^2 + 159/28x + 85/14 = 0
(x - -17/4)(x - -10/7) = 0
x - -17/4 = 0  or  x - -10/7 = 0
x = -17/4
x = -10/7


Input: Solve the equation x^2 - 15/2x - 19 = 0

Output:
x^2 - 15/2x - 19 = 0
(x - 19/2)(x - -2) = 0
x - 19/2 = 0  or  x - -2 = 0
x = 19/2
x = -2


Input:
Find x and y such that
10x + 1y = -533/12
2x + 8y = 26/3

Output:
10x + 1y = -533/12
2x + 8y = 26/3

Using elimination
2*(10x + 1y = -533/12)
10*(2x + 8y = 26/3)
20x + 2y = -533/6
20x + 80y = 260/3
Subtract equations
-78y = -351/2
y = -351/2/-78
y = 9/4

Substitute y
10x + 1(9/4) = -533/12
10x = -140/3
x = -140/3/10
x = -14/3


Input:
Solve the system:
6x + 1y = 13
9x + 6y = 42

Output:
6x + 1y = 13
9x + 6y = 42

Using elimination
9*(6x + 1y = 13)
6*(9x + 6y = 42)
54x + 9y = 117
54x + 36y = 252
Subtract equations
-27y = -135
y = -135/-27
y = 5

Substitute y
6x + 1(5) = 13
6x = 8
x = 8/6
x = 4/3


Input: Solve the equation x^3 + 83/36x^2 - 1163/108x + 7/6 = 0

Output:
x^3 + 83/36x^2 - 1163/108x + 7/6 = 0
(x - 9/4)(x - 1/9)(x - -14/3) = 0
x - 9/4 = 0
x - 1/9 = 0
x - -14/3 = 0
x = 9/4
x = 1/9
x = -14/3


Input: Solve the equation 7x - 91/10 = 0

Output:
7x - 91/10 = 0
7x = 91/10
x = 91/10 / 7
x = 13/10


Input:
Find x and y such that
10x + 7y = -145/12
3x + 10y = -27/2

Output:
10x + 7y = -145/12
3x + 10y = -27/2

Using elimination
3*(10x + 7y = -145/12)
10*(3x + 10y = -27/2)
30x + 21y = -145/4
30x + 100y = -135
Subtract equations
-79y = 395/4
y = 395/4/-79
y = -5/4

Substitute y
10x + 7(-5/4) = -145/12
10x = -10/3
x = -10/3/10
x = -1/3


Input:
Solve the system:
6x + 10y = -37/6
2x + 8y = -8/9

Output:
6x + 10y = -37/6
2x + 8y = -8/9

Using elimination
2*(6x + 10y = -37/6)
6*(2x + 8y = -8/9)
12x + 20y = -37/3
12x + 48y = -16/3
Subtract equations
-28y = -7
y = -7/-28
y = 1/4

Substitute y
6x + 10(1/4) = -37/6
6x = -26/3
x = -26/3/6
x = -13/9


Input: Determine x in x^3 + 3/8x^2 - 19/16x - 9/16 = 0

Output:
x^3 + 3/8x^2 - 19/16x - 9/16 = 0
(x - 9/8)(x - -1/2)(x - -1) = 0
x - 9/8 = 0
x - -1/2 = 0
x - -1 = 0
x = 9/8
x = -1/2
x = -1


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

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


Input: Solve the equation x^2 + 21/10x + 4/5 = 0

Output:
x^2 + 21/10x + 4/5 = 0
(x - -1/2)(x - -8/5) = 0
x - -1/2 = 0  or  x - -8/5 = 0
x = -1/2
x = -8/5


Input: What value of x satisfies x^2 + 17/8x + 15/32 = 0

Output:
x^2 + 17/8x + 15/32 = 0
(x - -1/4)(x - -15/8) = 0
x - -1/4 = 0  or  x - -15/8 = 0
x = -1/4
x = -15/8


Input: Find x for x^2 - 19/6x - 11/6 = 0

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


Input: Determine x in x^3 - 101/84x^2 - 289/42x + 285/28 = 0

Output:
x^3 - 101/84x^2 - 289/42x + 285/28 = 0
(x - -19/7)(x - 5/3)(x - 9/4) = 0
x - -19/7 = 0
x - 5/3 = 0
x - 9/4 = 0
x = -19/7
x = 5/3
x = 9/4


Input: Solve quickly: 10x + 50 = 0

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


Input: Find x in x^3 - 57/28x^2 - 247/28x + 132/7 = 0

Output:
x^3 - 57/28x^2 - 247/28x + 132/7 = 0
(x - -3)(x - 11/4)(x - 16/7) = 0
x - -3 = 0
x - 11/4 = 0
x - 16/7 = 0
x = -3
x = 11/4
x = 16/7


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

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


Input: Solve x^3 + 251/90x^2 + 4/5x - 17/10 = 0

Output:
x^3 + 251/90x^2 + 4/5x - 17/10 = 0
(x - -17/9)(x - 3/5)(x - -3/2) = 0
x - -17/9 = 0
x - 3/5 = 0
x - -3/2 = 0
x = -17/9
x = 3/5
x = -3/2


Input: Determine x in x^2 + 6/5x - 7/25 = 0

Output:
x^2 + 6/5x - 7/25 = 0
(x - -7/5)(x - 1/5) = 0
x - -7/5 = 0  or  x - 1/5 = 0
x = -7/5
x = 1/5


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

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


Input:
Solve the equations:
2x + 4y = 148/9
3x + 10y = 110/3

Output:
2x + 4y = 148/9
3x + 10y = 110/3

Using elimination
3*(2x + 4y = 148/9)
2*(3x + 10y = 110/3)
6x + 12y = 148/3
6x + 20y = 220/3
Subtract equations
-8y = -24
y = -24/-8
y = 3

Substitute y
2x + 4(3) = 148/9
2x = 40/9
x = 40/9/2
x = 20/9


Input: Solve the equation x^3 + 3/5x^2 - 49/25x + 9/25 = 0

Output:
x^3 + 3/5x^2 - 49/25x + 9/25 = 0
(x - 1/5)(x - 1)(x - -9/5) = 0
x - 1/5 = 0
x - 1 = 0
x - -9/5 = 0
x = 1/5
x = 1
x = -9/5


Input: Find x in x^2 + 41/10x + 33/10 = 0

Output:
x^2 + 41/10x + 33/10 = 0
(x - -3)(x - -11/10) = 0
x - -3 = 0  or  x - -11/10 = 0
x = -3
x = -11/10


Input: Find the solution to 5x - 10/3 = 0

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


Input:
Solve the system:
1x + 9y = -47/2
2x + 3y = -46/3

Output:
1x + 9y = -47/2
2x + 3y = -46/3

Using elimination
2*(1x + 9y = -47/2)
1*(2x + 3y = -46/3)
2x + 18y = -47
2x + 3y = -46/3
Subtract equations
15y = -95/3
y = -95/3/15
y = -19/9

Substitute y
1x + 9(-19/9) = -47/2
1x = -9/2
x = -9/2/1
x = -9/2


Input: Compute the solution of x^3 - 14x^2 + 275/9x + 242/9 = 0

Output:
x^3 - 14x^2 + 275/9x + 242/9 = 0
(x - 11)(x - -2/3)(x - 11/3) = 0
x - 11 = 0
x - -2/3 = 0
x - 11/3 = 0
x = 11
x = -2/3
x = 11/3


Input: Solve x^2 - 185/42x + 33/7 = 0

Output:
x^2 - 185/42x + 33/7 = 0
(x - 11/6)(x - 18/7) = 0
x - 11/6 = 0  or  x - 18/7 = 0
x = 11/6
x = 18/7


Input: Solve quickly: x^2 + 90/7x - 16 = 0

Output:
x^2 + 90/7x - 16 = 0
(x - -14)(x - 8/7) = 0
x - -14 = 0  or  x - 8/7 = 0
x = -14
x = 8/7


Input: Solve the equation 5x + 85/7 = 0

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


Input: Solve the equation x^2 + 125/18x + 26/9 = 0

Output:
x^2 + 125/18x + 26/9 = 0
(x - -4/9)(x - -13/2) = 0
x - -4/9 = 0  or  x - -13/2 = 0
x = -4/9
x = -13/2


Input: Find x in 7x - 63 = 0

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


Input: Solve x^3 + 17/18x^2 - 317/6x + 260/9 = 0

Output:
x^3 + 17/18x^2 - 317/6x + 260/9 = 0
(x - 5/9)(x - -8)(x - 13/2) = 0
x - 5/9 = 0
x - -8 = 0
x - 13/2 = 0
x = 5/9
x = -8
x = 13/2


Input: Find x in x^3 + 68/5x^2 - 439/20x - 57/4 = 0

Output:
x^3 + 68/5x^2 - 439/20x - 57/4 = 0
(x - 19/10)(x - -15)(x - -1/2) = 0
x - 19/10 = 0
x - -15 = 0
x - -1/2 = 0
x = 19/10
x = -15
x = -1/2


Input: Solve x^3 - 2x^2 - 49/36x + 49/18 = 0

Output:
x^3 - 2x^2 - 49/36x + 49/18 = 0
(x - 7/6)(x - -7/6)(x - 2) = 0
x - 7/6 = 0
x - -7/6 = 0
x - 2 = 0
x = 7/6
x = -7/6
x = 2


Input: Solve x^3 + 73/24x^2 + 65/96x - 169/64 = 0

Output:
x^3 + 73/24x^2 + 65/96x - 169/64 = 0
(x - -13/8)(x - -13/6)(x - 3/4) = 0
x - -13/8 = 0
x - -13/6 = 0
x - 3/4 = 0
x = -13/8
x = -13/6
x = 3/4


Input:
Solve the equations:
3x + 5y = -32
6x + 2y = -304/5

Output:
3x + 5y = -32
6x + 2y = -304/5

Using elimination
6*(3x + 5y = -32)
3*(6x + 2y = -304/5)
18x + 30y = -192
18x + 6y = -912/5
Subtract equations
24y = -48/5
y = -48/5/24
y = -2/5

Substitute y
3x + 5(-2/5) = -32
3x = -30
x = -30/3
x = -10


Input:
Find x and y such that
8x + 7y = 45/7
8x + 1y = 75/7

Output:
8x + 7y = 45/7
8x + 1y = 75/7

Using elimination
8*(8x + 7y = 45/7)
8*(8x + 1y = 75/7)
64x + 56y = 360/7
64x + 8y = 600/7
Subtract equations
48y = -240/7
y = -240/7/48
y = -5/7

Substitute y
8x + 7(-5/7) = 45/7
8x = 80/7
x = 80/7/8
x = 10/7


Input: What value of x satisfies x^3 - 47/12x^2 + 113/24x - 7/4 = 0

Output:
x^3 - 47/12x^2 + 113/24x - 7/4 = 0
(x - 2)(x - 3/4)(x - 7/6) = 0
x - 2 = 0
x - 3/4 = 0
x - 7/6 = 0
x = 2
x = 3/4
x = 7/6


Input:
Find x and y such that
1x + 8y = 64/3
2x + 5y = 29/3

Output:
1x + 8y = 64/3
2x + 5y = 29/3

Using elimination
2*(1x + 8y = 64/3)
1*(2x + 5y = 29/3)
2x + 16y = 128/3
2x + 5y = 29/3
Subtract equations
11y = 33
y = 33/11
y = 3

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


Input: Find x in 5x - 35/8 = 0

Output:
5x - 35/8 = 0
5x = 35/8
x = 35/8 / 5
x = 7/8


Input: Determine x in 2x - 10 = 0

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


Input:
Solve the system:
2x + 9y = 223/9
9x + 8y = 14

Output:
2x + 9y = 223/9
9x + 8y = 14

Using elimination
9*(2x + 9y = 223/9)
2*(9x + 8y = 14)
18x + 81y = 223
18x + 16y = 28
Subtract equations
65y = 195
y = 195/65
y = 3

Substitute y
2x + 9(3) = 223/9
2x = -20/9
x = -20/9/2
x = -10/9


Input: Determine x in x^2 - 11/18x - 85/18 = 0

Output:
x^2 - 11/18x - 85/18 = 0
(x - 5/2)(x - -17/9) = 0
x - 5/2 = 0  or  x - -17/9 = 0
x = 5/2
x = -17/9


Input: Solve the equation x^2 + 3/8x - 1/16 = 0

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


Input: Solve quickly: x^3 + 7/9x^2 - 86/27x - 40/27 = 0

Output:
x^3 + 7/9x^2 - 86/27x - 40/27 = 0
(x - 5/3)(x - -4/9)(x - -2) = 0
x - 5/3 = 0
x - -4/9 = 0
x - -2 = 0
x = 5/3
x = -4/9
x = -2


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

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


Input:
Solve simultaneously:
9x + 2y = -20
6x + 6y = -18

Output:
9x + 2y = -20
6x + 6y = -18

Using elimination
6*(9x + 2y = -20)
9*(6x + 6y = -18)
54x + 12y = -120
54x + 54y = -162
Subtract equations
-42y = 42
y = 42/-42
y = -1

Substitute y
9x + 2(-1) = -20
9x = -18
x = -18/9
x = -2


Input: Find x in x^2 + 18/35x - 32/5 = 0

Output:
x^2 + 18/35x - 32/5 = 0
(x - 16/7)(x - -14/5) = 0
x - 16/7 = 0  or  x - -14/5 = 0
x = 16/7
x = -14/5


Input: Compute the solution of x^2 + 15x + 26 = 0

Output:
x^2 + 15x + 26 = 0
(x - -2)(x - -13) = 0
x - -2 = 0  or  x - -13 = 0
x = -2
x = -13


Input: Compute the solution of x^2 - 19/9x + 2/9 = 0

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


Input: Solve the equation x^2 - 10/9x + 1/9 = 0

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


Input:
Solve the equations:
7x + 9y = -40
3x + 4y = -35/2

Output:
7x + 9y = -40
3x + 4y = -35/2

Using elimination
3*(7x + 9y = -40)
7*(3x + 4y = -35/2)
21x + 27y = -120
21x + 28y = -245/2
Subtract equations
-1y = 5/2
y = 5/2/-1
y = -5/2

Substitute y
7x + 9(-5/2) = -40
7x = -35/2
x = -35/2/7
x = -5/2


Input: Solve x^2 - 18/7x - 9/7 = 0

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


Input: Find x for x^3 + 5/2x^2 - 4x - 10 = 0

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


Input: Find x in 3x - 20 = 0

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


Input: Solve the equation x^3 + 23/10x^2 - 337/50x - 78/5 = 0

Output:
x^3 + 23/10x^2 - 337/50x - 78/5 = 0
(x - -12/5)(x - 13/5)(x - -5/2) = 0
x - -12/5 = 0
x - 13/5 = 0
x - -5/2 = 0
x = -12/5
x = 13/5
x = -5/2


Input: Solve the equation x^3 - 44/5x^2 + 92/5x - 48/5 = 0

Output:
x^3 - 44/5x^2 + 92/5x - 48/5 = 0
(x - 6)(x - 2)(x - 4/5) = 0
x - 6 = 0
x - 2 = 0
x - 4/5 = 0
x = 6
x = 2
x = 4/5


Input: Determine x in 5x + 65/2 = 0

Output:
5x + 65/2 = 0
5x = -65/2
x = -65/2 / 5
x = -13/2


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

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


Input:
Solve simultaneously:
6x + 1y = 21/2
2x + 9y = 85/2

Output:
6x + 1y = 21/2
2x + 9y = 85/2

Using elimination
2*(6x + 1y = 21/2)
6*(2x + 9y = 85/2)
12x + 2y = 21
12x + 54y = 255
Subtract equations
-52y = -234
y = -234/-52
y = 9/2

Substitute y
6x + 1(9/2) = 21/2
6x = 6
x = 6/6
x = 1


Input: Determine x in 6x + 12/5 = 0

Output:
6x + 12/5 = 0
6x = -12/5
x = -12/5 / 6
x = -2/5


Input:
Solve simultaneously:
10x + 5y = -205/3
10x + 9y = -75

Output:
10x + 5y = -205/3
10x + 9y = -75

Using elimination
10*(10x + 5y = -205/3)
10*(10x + 9y = -75)
100x + 50y = -2050/3
100x + 90y = -750
Subtract equations
-40y = 200/3
y = 200/3/-40
y = -5/3

Substitute y
10x + 5(-5/3) = -205/3
10x = -60
x = -60/10
x = -6


Input: Find x in x^2 + 27/10x + 1/2 = 0

Output:
x^2 + 27/10x + 1/2 = 0
(x - -5/2)(x - -1/5) = 0
x - -5/2 = 0  or  x - -1/5 = 0
x = -5/2
x = -1/5


Input:
Solve the equations:
5x + 6y = 36/5
6x + 1y = -5

Output:
5x + 6y = 36/5
6x + 1y = -5

Using elimination
6*(5x + 6y = 36/5)
5*(6x + 1y = -5)
30x + 36y = 216/5
30x + 5y = -25
Subtract equations
31y = 341/5
y = 341/5/31
y = 11/5

Substitute y
5x + 6(11/5) = 36/5
5x = -6
x = -6/5
x = -6/5


Input:
Solve the equations:
4x + 2y = 116/5
1x + 8y = 733/10

Output:
4x + 2y = 116/5
1x + 8y = 733/10

Using elimination
1*(4x + 2y = 116/5)
4*(1x + 8y = 733/10)
4x + 2y = 116/5
4x + 32y = 1466/5
Subtract equations
-30y = -270
y = -270/-30
y = 9

Substitute y
4x + 2(9) = 116/5
4x = 26/5
x = 26/5/4
x = 13/10


Input: Compute the solution of 2x + 20 = 0

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


Input: Solve quickly: x^3 + 78/5x^2 + 153/20x - 81/4 = 0

Output:
x^3 + 78/5x^2 + 153/20x - 81/4 = 0
(x - 9/10)(x - -15)(x - -3/2) = 0
x - 9/10 = 0
x - -15 = 0
x - -3/2 = 0
x = 9/10
x = -15
x = -3/2


Input:
Solve simultaneously:
6x + 4y = -22/35
7x + 8y = -9/35

Output:
6x + 4y = -22/35
7x + 8y = -9/35

Using elimination
7*(6x + 4y = -22/35)
6*(7x + 8y = -9/35)
42x + 28y = -22/5
42x + 48y = -54/35
Subtract equations
-20y = -20/7
y = -20/7/-20
y = 1/7

Substitute y
6x + 4(1/7) = -22/35
6x = -6/5
x = -6/5/6
x = -1/5


Input: Solve quickly: x^2 - 68/35x + 32/35 = 0

Output:
x^2 - 68/35x + 32/35 = 0
(x - 4/5)(x - 8/7) = 0
x - 4/5 = 0  or  x - 8/7 = 0
x = 4/5
x = 8/7


Input: What value of x satisfies x^3 + 104/45x^2 - 128/45x  = 0

Output:
x^3 + 104/45x^2 - 128/45x  = 0
(x - -16/5)(x - 0)(x - 8/9) = 0
x - -16/5 = 0
x - 0 = 0
x - 8/9 = 0
x = -16/5
x = 0
x = 8/9


Input: Determine x in x^3 + 3x^2 - 13/16x - 45/8 = 0

Output:
x^3 + 3x^2 - 13/16x - 45/8 = 0
(x - 5/4)(x - -2)(x - -9/4) = 0
x - 5/4 = 0
x - -2 = 0
x - -9/4 = 0
x = 5/4
x = -2
x = -9/4


Input: What value of x satisfies x^3 - 29/5x^2 - 31/20x + 21/10 = 0

Output:
x^3 - 29/5x^2 - 31/20x + 21/10 = 0
(x - 1/2)(x - 6)(x - -7/10) = 0
x - 1/2 = 0
x - 6 = 0
x - -7/10 = 0
x = 1/2
x = 6
x = -7/10


Input: Find x for x^2 - 55/18x - 14/9 = 0

Output:
x^2 - 55/18x - 14/9 = 0
(x - -4/9)(x - 7/2) = 0
x - -4/9 = 0  or  x - 7/2 = 0
x = -4/9
x = 7/2


Input:
Solve simultaneously:
1x + 10y = -51
10x + 8y = -50

Output:
1x + 10y = -51
10x + 8y = -50

Using elimination
10*(1x + 10y = -51)
1*(10x + 8y = -50)
10x + 100y = -510
10x + 8y = -50
Subtract equations
92y = -460
y = -460/92
y = -5

Substitute y
1x + 10(-5) = -51
1x = -1
x = -1/1
x = -1


Input:
Solve the system:
8x + 3y = 31/3
2x + 1y = 10/3

Output:
8x + 3y = 31/3
2x + 1y = 10/3

Using elimination
2*(8x + 3y = 31/3)
8*(2x + 1y = 10/3)
16x + 6y = 62/3
16x + 8y = 80/3
Subtract equations
-2y = -6
y = -6/-2
y = 3

Substitute y
8x + 3(3) = 31/3
8x = 4/3
x = 4/3/8
x = 1/6


Input:
Solve the equations:
9x + 5y = -800/21
6x + 2y = -356/21

Output:
9x + 5y = -800/21
6x + 2y = -356/21

Using elimination
6*(9x + 5y = -800/21)
9*(6x + 2y = -356/21)
54x + 30y = -1600/7
54x + 18y = -1068/7
Subtract equations
12y = -76
y = -76/12
y = -19/3

Substitute y
9x + 5(-19/3) = -800/21
9x = -45/7
x = -45/7/9
x = -5/7


Input: What value of x satisfies x^3 - 197/18x^2 + 326/9x - 65/2 = 0

Output:
x^3 - 197/18x^2 + 326/9x - 65/2 = 0
(x - 9/2)(x - 5)(x - 13/9) = 0
x - 9/2 = 0
x - 5 = 0
x - 13/9 = 0
x = 9/2
x = 5
x = 13/9


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

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


Input:
Solve the equations:
7x + 5y = 215/24
8x + 10y = 20/3

Output:
7x + 5y = 215/24
8x + 10y = 20/3

Using elimination
8*(7x + 5y = 215/24)
7*(8x + 10y = 20/3)
56x + 40y = 215/3
56x + 70y = 140/3
Subtract equations
-30y = 25
y = 25/-30
y = -5/6

Substitute y
7x + 5(-5/6) = 215/24
7x = 105/8
x = 105/8/7
x = 15/8


Input: Find x in x^3 + 17/5x^2 - 37/5x + 3 = 0

Output:
x^3 + 17/5x^2 - 37/5x + 3 = 0
(x - 3/5)(x - 1)(x - -5) = 0
x - 3/5 = 0
x - 1 = 0
x - -5 = 0
x = 3/5
x = 1
x = -5


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

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


Input: Find x in 3x - 9 = 0

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


Input:
Solve the system:
9x + 9y = 486/7
6x + 8y = 334/7

Output:
9x + 9y = 486/7
6x + 8y = 334/7

Using elimination
6*(9x + 9y = 486/7)
9*(6x + 8y = 334/7)
54x + 54y = 2916/7
54x + 72y = 3006/7
Subtract equations
-18y = -90/7
y = -90/7/-18
y = 5/7

Substitute y
9x + 9(5/7) = 486/7
9x = 63
x = 63/9
x = 7


Input: Compute the solution of x^3 + 67/6x^2 + 10x - 50/3 = 0

Output:
x^3 + 67/6x^2 + 10x - 50/3 = 0
(x - 5/6)(x - -10)(x - -2) = 0
x - 5/6 = 0
x - -10 = 0
x - -2 = 0
x = 5/6
x = -10
x = -2


Input: Compute the solution of 5x  = 0

Output:
5x  = 0
5x = 0
x = 0 / 5
x = 0


Input: Solve the equation x^2 - 5x - 36 = 0

Output:
x^2 - 5x - 36 = 0
(x - 9)(x - -4) = 0
x - 9 = 0  or  x - -4 = 0
x = 9
x = -4


Input:
Solve the system:
9x + 7y = -5/3
8x + 3y = -52/9

Output:
9x + 7y = -5/3
8x + 3y = -52/9

Using elimination
8*(9x + 7y = -5/3)
9*(8x + 3y = -52/9)
72x + 56y = -40/3
72x + 27y = -52
Subtract equations
29y = 116/3
y = 116/3/29
y = 4/3

Substitute y
9x + 7(4/3) = -5/3
9x = -11
x = -11/9
x = -11/9


Input: Determine x in x^3 + 89/10x^2 - 64/5x - 18 = 0

Output:
x^3 + 89/10x^2 - 64/5x - 18 = 0
(x - -9/10)(x - 2)(x - -10) = 0
x - -9/10 = 0
x - 2 = 0
x - -10 = 0
x = -9/10
x = 2
x = -10


Input: Solve quickly: x^2 - 49/4x + 285/8 = 0

Output:
x^2 - 49/4x + 285/8 = 0
(x - 15/2)(x - 19/4) = 0
x - 15/2 = 0  or  x - 19/4 = 0
x = 15/2
x = 19/4


Input: Find x in x^3 + 7/4x^2 - 607/8x - 765/8 = 0

Output:
x^3 + 7/4x^2 - 607/8x - 765/8 = 0
(x - 17/2)(x - -9)(x - -5/4) = 0
x - 17/2 = 0
x - -9 = 0
x - -5/4 = 0
x = 17/2
x = -9
x = -5/4


Input:
Find x and y such that
7x + 2y = 0
6x + 7y = 37/7

Output:
7x + 2y = 0
6x + 7y = 37/7

Using elimination
6*(7x + 2y = 0)
7*(6x + 7y = 37/7)
42x + 12y = 0
42x + 49y = 37
Subtract equations
-37y = -37
y = -37/-37
y = 1

Substitute y
7x + 2(1) = 0
7x = -2
x = -2/7
x = -2/7


Input:
Solve the equations:
8x + 6y = -25
8x + 8y = -27

Output:
8x + 6y = -25
8x + 8y = -27

Using elimination
8*(8x + 6y = -25)
8*(8x + 8y = -27)
64x + 48y = -200
64x + 64y = -216
Subtract equations
-16y = 16
y = 16/-16
y = -1

Substitute y
8x + 6(-1) = -25
8x = -19
x = -19/8
x = -19/8


Input:
Solve simultaneously:
9x + 4y = -177/5
6x + 9y = -213/5

Output:
9x + 4y = -177/5
6x + 9y = -213/5

Using elimination
6*(9x + 4y = -177/5)
9*(6x + 9y = -213/5)
54x + 24y = -1062/5
54x + 81y = -1917/5
Subtract equations
-57y = 171
y = 171/-57
y = -3

Substitute y
9x + 4(-3) = -177/5
9x = -117/5
x = -117/5/9
x = -13/5


Input: Find the solution to x^2 - 221/70x + 169/70 = 0

Output:
x^2 - 221/70x + 169/70 = 0
(x - 13/7)(x - 13/10) = 0
x - 13/7 = 0  or  x - 13/10 = 0
x = 13/7
x = 13/10


Input: Solve x^3 + 5/6x^2 - 493/3x + 1445/2 = 0

Output:
x^3 + 5/6x^2 - 493/3x + 1445/2 = 0
(x - -15)(x - 17/2)(x - 17/3) = 0
x - -15 = 0
x - 17/2 = 0
x - 17/3 = 0
x = -15
x = 17/2
x = 17/3


Input: Find x for x^2 - 115/12x + 68/3 = 0

Output:
x^2 - 115/12x + 68/3 = 0
(x - 17/4)(x - 16/3) = 0
x - 17/4 = 0  or  x - 16/3 = 0
x = 17/4
x = 16/3


Input:
Solve simultaneously:
6x + 9y = -142/5
4x + 7y = -922/45

Output:
6x + 9y = -142/5
4x + 7y = -922/45

Using elimination
4*(6x + 9y = -142/5)
6*(4x + 7y = -922/45)
24x + 36y = -568/5
24x + 42y = -1844/15
Subtract equations
-6y = 28/3
y = 28/3/-6
y = -14/9

Substitute y
6x + 9(-14/9) = -142/5
6x = -72/5
x = -72/5/6
x = -12/5


Input:
Find x and y such that
6x + 10y = -58/3
1x + 7y = 17/3

Output:
6x + 10y = -58/3
1x + 7y = 17/3

Using elimination
1*(6x + 10y = -58/3)
6*(1x + 7y = 17/3)
6x + 10y = -58/3
6x + 42y = 34
Subtract equations
-32y = -160/3
y = -160/3/-32
y = 5/3

Substitute y
6x + 10(5/3) = -58/3
6x = -36
x = -36/6
x = -6


Input:
Solve the system:
10x + 9y = 88
4x + 8y = 77

Output:
10x + 9y = 88
4x + 8y = 77

Using elimination
4*(10x + 9y = 88)
10*(4x + 8y = 77)
40x + 36y = 352
40x + 80y = 770
Subtract equations
-44y = -418
y = -418/-44
y = 19/2

Substitute y
10x + 9(19/2) = 88
10x = 5/2
x = 5/2/10
x = 1/4


Input: Solve quickly: 8x - 112/9 = 0

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


Input:
Solve the system:
1x + 1y = 11/3
7x + 2y = 67/3

Output:
1x + 1y = 11/3
7x + 2y = 67/3

Using elimination
7*(1x + 1y = 11/3)
1*(7x + 2y = 67/3)
7x + 7y = 77/3
7x + 2y = 67/3
Subtract equations
5y = 10/3
y = 10/3/5
y = 2/3

Substitute y
1x + 1(2/3) = 11/3
1x = 3
x = 3/1
x = 3


Input:
Solve simultaneously:
1x + 8y = 129
4x + 7y = 116

Output:
1x + 8y = 129
4x + 7y = 116

Using elimination
4*(1x + 8y = 129)
1*(4x + 7y = 116)
4x + 32y = 516
4x + 7y = 116
Subtract equations
25y = 400
y = 400/25
y = 16

Substitute y
1x + 8(16) = 129
1x = 1
x = 1/1
x = 1


Input: Compute the solution of x^2 - 11/3x - 48 = 0

Output:
x^2 - 11/3x - 48 = 0
(x - -16/3)(x - 9) = 0
x - -16/3 = 0  or  x - 9 = 0
x = -16/3
x = 9


Input: Determine x in 9x + 20 = 0

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


Input: Compute the solution of 9x + 108/5 = 0

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


Input: Determine x in x^2 - 112/15x + 196/15 = 0

Output:
x^2 - 112/15x + 196/15 = 0
(x - 14/3)(x - 14/5) = 0
x - 14/3 = 0  or  x - 14/5 = 0
x = 14/3
x = 14/5


Input: Compute the solution of 6x - 48/5 = 0

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


Input:
Solve the system:
1x + 3y = -43/10
7x + 10y = -191/10

Output:
1x + 3y = -43/10
7x + 10y = -191/10

Using elimination
7*(1x + 3y = -43/10)
1*(7x + 10y = -191/10)
7x + 21y = -301/10
7x + 10y = -191/10
Subtract equations
11y = -11
y = -11/11
y = -1

Substitute y
1x + 3(-1) = -43/10
1x = -13/10
x = -13/10/1
x = -13/10


Input: Find the solution to x^2 - 47/9x + 44/9 = 0

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


Input: Solve x^2 + 15/4x - 17/8 = 0

Output:
x^2 + 15/4x - 17/8 = 0
(x - -17/4)(x - 1/2) = 0
x - -17/4 = 0  or  x - 1/2 = 0
x = -17/4
x = 1/2


Input:
Solve the equations:
8x + 9y = -871/14
4x + 5y = -467/14

Output:
8x + 9y = -871/14
4x + 5y = -467/14

Using elimination
4*(8x + 9y = -871/14)
8*(4x + 5y = -467/14)
32x + 36y = -1742/7
32x + 40y = -1868/7
Subtract equations
-4y = 18
y = 18/-4
y = -9/2

Substitute y
8x + 9(-9/2) = -871/14
8x = -152/7
x = -152/7/8
x = -19/7


Input: Find the solution to 5x + 15/2 = 0

Output:
5x + 15/2 = 0
5x = -15/2
x = -15/2 / 5
x = -3/2


Input: Solve quickly: x^3 + 11/7x^2   = 0

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


Input: Find the solution to x^3 - 38/5x^2 - 19/5x + 24/5 = 0

Output:
x^3 - 38/5x^2 - 19/5x + 24/5 = 0
(x - 3/5)(x - 8)(x - -1) = 0
x - 3/5 = 0
x - 8 = 0
x - -1 = 0
x = 3/5
x = 8
x = -1


Input:
Solve the equations:
10x + 10y = 185/3
8x + 7y = 133/3

Output:
10x + 10y = 185/3
8x + 7y = 133/3

Using elimination
8*(10x + 10y = 185/3)
10*(8x + 7y = 133/3)
80x + 80y = 1480/3
80x + 70y = 1330/3
Subtract equations
10y = 50
y = 50/10
y = 5

Substitute y
10x + 10(5) = 185/3
10x = 35/3
x = 35/3/10
x = 7/6


Input: Find the solution to x^3 - 37/6x^2 + 97/12x - 21/8 = 0

Output:
x^3 - 37/6x^2 + 97/12x - 21/8 = 0
(x - 7/6)(x - 9/2)(x - 1/2) = 0
x - 7/6 = 0
x - 9/2 = 0
x - 1/2 = 0
x = 7/6
x = 9/2
x = 1/2


Input: Find x in x^2 - 12/7x - 19/7 = 0

Output:
x^2 - 12/7x - 19/7 = 0
(x - 19/7)(x - -1) = 0
x - 19/7 = 0  or  x - -1 = 0
x = 19/7
x = -1


Input: What value of x satisfies 9x + 3/2 = 0

Output:
9x + 3/2 = 0
9x = -3/2
x = -3/2 / 9
x = -1/6


Input: Solve the equation 3x - 1 = 0

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


Input:
Solve the system:
4x + 7y = -29
6x + 8y = -67/2

Output:
4x + 7y = -29
6x + 8y = -67/2

Using elimination
6*(4x + 7y = -29)
4*(6x + 8y = -67/2)
24x + 42y = -174
24x + 32y = -134
Subtract equations
10y = -40
y = -40/10
y = -4

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


Input: Find x in x^2 - 31/8x + 15/32 = 0

Output:
x^2 - 31/8x + 15/32 = 0
(x - 15/4)(x - 1/8) = 0
x - 15/4 = 0  or  x - 1/8 = 0
x = 15/4
x = 1/8


Input: What value of x satisfies x^2 + 27/2x + 81/2 = 0

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


Input: Determine x in x^3 - 61/20x^2 - 235/8x - 30 = 0

Output:
x^3 - 61/20x^2 - 235/8x - 30 = 0
(x - 15/2)(x - -5/4)(x - -16/5) = 0
x - 15/2 = 0
x - -5/4 = 0
x - -16/5 = 0
x = 15/2
x = -5/4
x = -16/5


Input: Determine x in x^3 - 203/180x^2 - 2537/180x - 133/9 = 0

Output:
x^3 - 203/180x^2 - 2537/180x - 133/9 = 0
(x - -7/5)(x - 19/4)(x - -20/9) = 0
x - -7/5 = 0
x - 19/4 = 0
x - -20/9 = 0
x = -7/5
x = 19/4
x = -20/9


Input: Solve 8x - 144/7 = 0

Output:
8x - 144/7 = 0
8x = 144/7
x = 144/7 / 8
x = 18/7


Input: Solve the equation x^3 + 18/5x^2 - 1563/20x - 4199/20 = 0

Output:
x^3 + 18/5x^2 - 1563/20x - 4199/20 = 0
(x - -13/5)(x - 17/2)(x - -19/2) = 0
x - -13/5 = 0
x - 17/2 = 0
x - -19/2 = 0
x = -13/5
x = 17/2
x = -19/2


Input: Solve 4x - 12 = 0

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


Input:
Solve the equations:
4x + 3y = -195/2
2x + 1y = -89/2

Output:
4x + 3y = -195/2
2x + 1y = -89/2

Using elimination
2*(4x + 3y = -195/2)
4*(2x + 1y = -89/2)
8x + 6y = -195
8x + 4y = -178
Subtract equations
2y = -17
y = -17/2
y = -17/2

Substitute y
4x + 3(-17/2) = -195/2
4x = -72
x = -72/4
x = -18


Input:
Find x and y such that
2x + 5y = -199/12
10x + 1y = -347/12

Output:
2x + 5y = -199/12
10x + 1y = -347/12

Using elimination
10*(2x + 5y = -199/12)
2*(10x + 1y = -347/12)
20x + 50y = -995/6
20x + 2y = -347/6
Subtract equations
48y = -108
y = -108/48
y = -9/4

Substitute y
2x + 5(-9/4) = -199/12
2x = -16/3
x = -16/3/2
x = -8/3


Input: Compute the solution of 7x - 56/3 = 0

Output:
7x - 56/3 = 0
7x = 56/3
x = 56/3 / 7
x = 8/3


Input: Solve quickly: 9x + 99/10 = 0

Output:
9x + 99/10 = 0
9x = -99/10
x = -99/10 / 9
x = -11/10


Input:
Solve the equations:
10x + 9y = 211/7
2x + 3y = 319/35

Output:
10x + 9y = 211/7
2x + 3y = 319/35

Using elimination
2*(10x + 9y = 211/7)
10*(2x + 3y = 319/35)
20x + 18y = 422/7
20x + 30y = 638/7
Subtract equations
-12y = -216/7
y = -216/7/-12
y = 18/7

Substitute y
10x + 9(18/7) = 211/7
10x = 7
x = 7/10
x = 7/10


Input: Find x for 4x - 4 = 0

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


Input: Solve x^3 + 25/18x^2 - 2443/450x - 931/225 = 0

Output:
x^3 + 25/18x^2 - 2443/450x - 931/225 = 0
(x - -14/5)(x - -7/10)(x - 19/9) = 0
x - -14/5 = 0
x - -7/10 = 0
x - 19/9 = 0
x = -14/5
x = -7/10
x = 19/9


Input:
Solve the system:
8x + 9y = 146/7
2x + 4y = 54/7

Output:
8x + 9y = 146/7
2x + 4y = 54/7

Using elimination
2*(8x + 9y = 146/7)
8*(2x + 4y = 54/7)
16x + 18y = 292/7
16x + 32y = 432/7
Subtract equations
-14y = -20
y = -20/-14
y = 10/7

Substitute y
8x + 9(10/7) = 146/7
8x = 8
x = 8/8
x = 1


Input: Solve x^2 - 20/3x + 25/3 = 0

Output:
x^2 - 20/3x + 25/3 = 0
(x - 5/3)(x - 5) = 0
x - 5/3 = 0  or  x - 5 = 0
x = 5/3
x = 5


Input:
Solve the system:
8x + 10y = 160/9
10x + 6y = 200/9

Output:
8x + 10y = 160/9
10x + 6y = 200/9

Using elimination
10*(8x + 10y = 160/9)
8*(10x + 6y = 200/9)
80x + 100y = 1600/9
80x + 48y = 1600/9
Subtract equations
52y = 0
y = 0/52
y = 0

Substitute y
8x + 10(0) = 160/9
8x = 160/9
x = 160/9/8
x = 20/9


Input:
Solve the system:
5x + 3y = 71/3
8x + 2y = 352/9

Output:
5x + 3y = 71/3
8x + 2y = 352/9

Using elimination
8*(5x + 3y = 71/3)
5*(8x + 2y = 352/9)
40x + 24y = 568/3
40x + 10y = 1760/9
Subtract equations
14y = -56/9
y = -56/9/14
y = -4/9

Substitute y
5x + 3(-4/9) = 71/3
5x = 25
x = 25/5
x = 5


Input:
Find x and y such that
5x + 10y = 118/7
2x + 10y = 506/35

Output:
5x + 10y = 118/7
2x + 10y = 506/35

Using elimination
2*(5x + 10y = 118/7)
5*(2x + 10y = 506/35)
10x + 20y = 236/7
10x + 50y = 506/7
Subtract equations
-30y = -270/7
y = -270/7/-30
y = 9/7

Substitute y
5x + 10(9/7) = 118/7
5x = 4
x = 4/5
x = 4/5


Input: Compute the solution of 3x - 1 = 0

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


Input: Solve the equation x^2 + 1/10x - 91/50 = 0

Output:
x^2 + 1/10x - 91/50 = 0
(x - -7/5)(x - 13/10) = 0
x - -7/5 = 0  or  x - 13/10 = 0
x = -7/5
x = 13/10


Input: Find x for x^2 - 37/9x + 104/27 = 0

Output:
x^2 - 37/9x + 104/27 = 0
(x - 13/9)(x - 8/3) = 0
x - 13/9 = 0  or  x - 8/3 = 0
x = 13/9
x = 8/3


Input: Find the solution to 1x - 10/9 = 0

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


Input: Solve quickly: x^2 + 89/30x - 77/30 = 0

Output:
x^2 + 89/30x - 77/30 = 0
(x - -11/3)(x - 7/10) = 0
x - -11/3 = 0  or  x - 7/10 = 0
x = -11/3
x = 7/10


Input: Compute the solution of x^2 + 10/3x + 1 = 0

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


Input:
Find x and y such that
7x + 1y = -65/4
9x + 7y = -135/4

Output:
7x + 1y = -65/4
9x + 7y = -135/4

Using elimination
9*(7x + 1y = -65/4)
7*(9x + 7y = -135/4)
63x + 9y = -585/4
63x + 49y = -945/4
Subtract equations
-40y = 90
y = 90/-40
y = -9/4

Substitute y
7x + 1(-9/4) = -65/4
7x = -14
x = -14/7
x = -2


Input: Solve 5x + 75/8 = 0

Output:
5x + 75/8 = 0
5x = -75/8
x = -75/8 / 5
x = -15/8


Input: Solve the equation 9x - 5 = 0

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


Input: Find the solution to x^2 + 26/9x - 95/9 = 0

Output:
x^2 + 26/9x - 95/9 = 0
(x - 19/9)(x - -5) = 0
x - 19/9 = 0  or  x - -5 = 0
x = 19/9
x = -5


Input: Solve x^3 + 3/2x^2 - 199/16x - 51/16 = 0

Output:
x^3 + 3/2x^2 - 199/16x - 51/16 = 0
(x - -1/4)(x - -17/4)(x - 3) = 0
x - -1/4 = 0
x - -17/4 = 0
x - 3 = 0
x = -1/4
x = -17/4
x = 3


Input: Solve x^2 + 15/4x + 13/8 = 0

Output:
x^2 + 15/4x + 13/8 = 0
(x - -13/4)(x - -1/2) = 0
x - -13/4 = 0  or  x - -1/2 = 0
x = -13/4
x = -1/2


Input:
Solve simultaneously:
4x + 6y = -252/5
4x + 3y = -117/5

Output:
4x + 6y = -252/5
4x + 3y = -117/5

Using elimination
4*(4x + 6y = -252/5)
4*(4x + 3y = -117/5)
16x + 24y = -1008/5
16x + 12y = -468/5
Subtract equations
12y = -108
y = -108/12
y = -9

Substitute y
4x + 6(-9) = -252/5
4x = 18/5
x = 18/5/4
x = 9/10


Input: Determine x in x^2 + 49/18x + 49/27 = 0

Output:
x^2 + 49/18x + 49/27 = 0
(x - -7/6)(x - -14/9) = 0
x - -7/6 = 0  or  x - -14/9 = 0
x = -7/6
x = -14/9


Input: Find x for 8x - 160 = 0

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


Input: Solve quickly: x^2 + 5/2x - 25/2 = 0

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


Input: Determine x in x^3 + 362/63x^2 + 1247/189x + 130/63 = 0

Output:
x^3 + 362/63x^2 + 1247/189x + 130/63 = 0
(x - -5/9)(x - -13/3)(x - -6/7) = 0
x - -5/9 = 0
x - -13/3 = 0
x - -6/7 = 0
x = -5/9
x = -13/3
x = -6/7


Input: Solve quickly: x^3 - 415/72x^2 + 1549/144x - 935/144 = 0

Output:
x^3 - 415/72x^2 + 1549/144x - 935/144 = 0
(x - 11/8)(x - 5/2)(x - 17/9) = 0
x - 11/8 = 0
x - 5/2 = 0
x - 17/9 = 0
x = 11/8
x = 5/2
x = 17/9


Input:
Solve the system:
10x + 5y = 30
5x + 2y = 31/2

Output:
10x + 5y = 30
5x + 2y = 31/2

Using elimination
5*(10x + 5y = 30)
10*(5x + 2y = 31/2)
50x + 25y = 150
50x + 20y = 155
Subtract equations
5y = -5
y = -5/5
y = -1

Substitute y
10x + 5(-1) = 30
10x = 35
x = 35/10
x = 7/2


Input:
Find x and y such that
2x + 8y = -44/3
2x + 5y = -61/6

Output:
2x + 8y = -44/3
2x + 5y = -61/6

Using elimination
2*(2x + 8y = -44/3)
2*(2x + 5y = -61/6)
4x + 16y = -88/3
4x + 10y = -61/3
Subtract equations
6y = -9
y = -9/6
y = -3/2

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


Input:
Solve the equations:
6x + 1y = -217/15
1x + 9y = 91/5

Output:
6x + 1y = -217/15
1x + 9y = 91/5

Using elimination
1*(6x + 1y = -217/15)
6*(1x + 9y = 91/5)
6x + 1y = -217/15
6x + 54y = 546/5
Subtract equations
-53y = -371/3
y = -371/3/-53
y = 7/3

Substitute y
6x + 1(7/3) = -217/15
6x = -84/5
x = -84/5/6
x = -14/5


Input: Determine x in 3x - 12/7 = 0

Output:
3x - 12/7 = 0
3x = 12/7
x = 12/7 / 3
x = 4/7


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

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


Input: Solve x^3 - 19/10x^2 + 73/80x - 1/8 = 0

Output:
x^3 - 19/10x^2 + 73/80x - 1/8 = 0
(x - 2/5)(x - 1/4)(x - 5/4) = 0
x - 2/5 = 0
x - 1/4 = 0
x - 5/4 = 0
x = 2/5
x = 1/4
x = 5/4


Input: What value of x satisfies x^3 + 983/280x^2 + 11/5x - 48/35 = 0

Output:
x^3 + 983/280x^2 + 11/5x - 48/35 = 0
(x - 3/8)(x - -8/5)(x - -16/7) = 0
x - 3/8 = 0
x - -8/5 = 0
x - -16/7 = 0
x = 3/8
x = -8/5
x = -16/7


Input: Find x in x^3 + 37/3x^2 - 140x + 800/3 = 0

Output:
x^3 + 37/3x^2 - 140x + 800/3 = 0
(x - 5)(x - 8/3)(x - -20) = 0
x - 5 = 0
x - 8/3 = 0
x - -20 = 0
x = 5
x = 8/3
x = -20


Input: Find the solution to 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^2 - 37/14x + 15/14 = 0

Output:
x^2 - 37/14x + 15/14 = 0
(x - 1/2)(x - 15/7) = 0
x - 1/2 = 0  or  x - 15/7 = 0
x = 1/2
x = 15/7


Input: Find x for 9x - 54 = 0

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


Input:
Solve the equations:
6x + 3y = 12
8x + 2y = 66/5

Output:
6x + 3y = 12
8x + 2y = 66/5

Using elimination
8*(6x + 3y = 12)
6*(8x + 2y = 66/5)
48x + 24y = 96
48x + 12y = 396/5
Subtract equations
12y = 84/5
y = 84/5/12
y = 7/5

Substitute y
6x + 3(7/5) = 12
6x = 39/5
x = 39/5/6
x = 13/10


Input: Find x for x^3 - 581/72x^2 - 917/144x + 1105/48 = 0

Output:
x^3 - 581/72x^2 - 917/144x + 1105/48 = 0
(x - -15/8)(x - 13/9)(x - 17/2) = 0
x - -15/8 = 0
x - 13/9 = 0
x - 17/2 = 0
x = -15/8
x = 13/9
x = 17/2


Input:
Solve simultaneously:
1x + 5y = -29/6
5x + 8y = -82/15

Output:
1x + 5y = -29/6
5x + 8y = -82/15

Using elimination
5*(1x + 5y = -29/6)
1*(5x + 8y = -82/15)
5x + 25y = -145/6
5x + 8y = -82/15
Subtract equations
17y = -187/10
y = -187/10/17
y = -11/10

Substitute y
1x + 5(-11/10) = -29/6
1x = 2/3
x = 2/3/1
x = 2/3


Input: Compute the solution of x^2 + 23/15x + 2/5 = 0

Output:
x^2 + 23/15x + 2/5 = 0
(x - -6/5)(x - -1/3) = 0
x - -6/5 = 0  or  x - -1/3 = 0
x = -6/5
x = -1/3


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

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


Input: Find the solution to x^3 + 10/3x^2 + 28/9x + 8/9 = 0

Output:
x^3 + 10/3x^2 + 28/9x + 8/9 = 0
(x - -2/3)(x - -2)(x - -2/3) = 0
x - -2/3 = 0
x - -2 = 0
x - -2/3 = 0
x = -2/3
x = -2
x = -2/3


Input: Find the solution to x^3 - 377/105x^2 + 4/5x + 4/21 = 0

Output:
x^3 - 377/105x^2 + 4/5x + 4/21 = 0
(x - -1/7)(x - 10/3)(x - 2/5) = 0
x - -1/7 = 0
x - 10/3 = 0
x - 2/5 = 0
x = -1/7
x = 10/3
x = 2/5


Input: Compute the solution of 8x + 40/7 = 0

Output:
8x + 40/7 = 0
8x = -40/7
x = -40/7 / 8
x = -5/7


Input: Solve quickly: x^2 + 7/5x - 51/100 = 0

Output:
x^2 + 7/5x - 51/100 = 0
(x - 3/10)(x - -17/10) = 0
x - 3/10 = 0  or  x - -17/10 = 0
x = 3/10
x = -17/10


Input: Solve x^2 - 32/21x - 64/21 = 0

Output:
x^2 - 32/21x - 64/21 = 0
(x - 8/3)(x - -8/7) = 0
x - 8/3 = 0  or  x - -8/7 = 0
x = 8/3
x = -8/7


Input: Determine x in x^3 - 37/10x^2 - 31/5x - 3/2 = 0

Output:
x^3 - 37/10x^2 - 31/5x - 3/2 = 0
(x - -1)(x - -3/10)(x - 5) = 0
x - -1 = 0
x - -3/10 = 0
x - 5 = 0
x = -1
x = -3/10
x = 5


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

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


Input: Solve x^2 - 7/4x - 11/4 = 0

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


Input: Find x for x^3 - 74/315x^2 - 141/35x + 16/7 = 0

Output:
x^3 - 74/315x^2 - 141/35x + 16/7 = 0
(x - -15/7)(x - 3/5)(x - 16/9) = 0
x - -15/7 = 0
x - 3/5 = 0
x - 16/9 = 0
x = -15/7
x = 3/5
x = 16/9


Input: What value of x satisfies x^2 - 47/3x - 16/3 = 0

Output:
x^2 - 47/3x - 16/3 = 0
(x - 16)(x - -1/3) = 0
x - 16 = 0  or  x - -1/3 = 0
x = 16
x = -1/3


Input: What value of x satisfies 4x + 4/5 = 0

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


Input:
Solve simultaneously:
4x + 10y = 0
2x + 4y = -1

Output:
4x + 10y = 0
2x + 4y = -1

Using elimination
2*(4x + 10y = 0)
4*(2x + 4y = -1)
8x + 20y = 0
8x + 16y = -4
Subtract equations
4y = 4
y = 4/4
y = 1

Substitute y
4x + 10(1) = 0
4x = -10
x = -10/4
x = -5/2


Input: Find x for 10x + 20 = 0

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


Input: Find x in x^2 + 11/15x - 26/3 = 0

Output:
x^2 + 11/15x - 26/3 = 0
(x - -10/3)(x - 13/5) = 0
x - -10/3 = 0  or  x - 13/5 = 0
x = -10/3
x = 13/5


Input: Solve x^3 - 31/6x^2 + 64/9x - 11/6 = 0

Output:
x^3 - 31/6x^2 + 64/9x - 11/6 = 0
(x - 11/6)(x - 3)(x - 1/3) = 0
x - 11/6 = 0
x - 3 = 0
x - 1/3 = 0
x = 11/6
x = 3
x = 1/3


Input:
Solve the equations:
8x + 2y = -32
1x + 6y = -27

Output:
8x + 2y = -32
1x + 6y = -27

Using elimination
1*(8x + 2y = -32)
8*(1x + 6y = -27)
8x + 2y = -32
8x + 48y = -216
Subtract equations
-46y = 184
y = 184/-46
y = -4

Substitute y
8x + 2(-4) = -32
8x = -24
x = -24/8
x = -3


Input: What value of x satisfies x^2 - 8x + 12 = 0

Output:
x^2 - 8x + 12 = 0
(x - 2)(x - 6) = 0
x - 2 = 0  or  x - 6 = 0
x = 2
x = 6


Input: Compute the solution of 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: Find x for x^3 - 183/14x^2 - 885/14x - 425/7 = 0

Output:
x^3 - 183/14x^2 - 885/14x - 425/7 = 0
(x - -10/7)(x - -5/2)(x - 17) = 0
x - -10/7 = 0
x - -5/2 = 0
x - 17 = 0
x = -10/7
x = -5/2
x = 17


Input: Compute the solution of 8x - 64/3 = 0

Output:
8x - 64/3 = 0
8x = 64/3
x = 64/3 / 8
x = 8/3


Input: Solve 6x - 18 = 0

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


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

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


Input:
Solve simultaneously:
4x + 2y = -26/21
7x + 10y = -52/3

Output:
4x + 2y = -26/21
7x + 10y = -52/3

Using elimination
7*(4x + 2y = -26/21)
4*(7x + 10y = -52/3)
28x + 14y = -26/3
28x + 40y = -208/3
Subtract equations
-26y = 182/3
y = 182/3/-26
y = -7/3

Substitute y
4x + 2(-7/3) = -26/21
4x = 24/7
x = 24/7/4
x = 6/7


Input: Find x in x^3 - 16/3x^2 - 212/9x + 160/9 = 0

Output:
x^3 - 16/3x^2 - 212/9x + 160/9 = 0
(x - -10/3)(x - 2/3)(x - 8) = 0
x - -10/3 = 0
x - 2/3 = 0
x - 8 = 0
x = -10/3
x = 2/3
x = 8


Input:
Find x and y such that
9x + 8y = 103/3
8x + 4y = 76/3

Output:
9x + 8y = 103/3
8x + 4y = 76/3

Using elimination
8*(9x + 8y = 103/3)
9*(8x + 4y = 76/3)
72x + 64y = 824/3
72x + 36y = 228
Subtract equations
28y = 140/3
y = 140/3/28
y = 5/3

Substitute y
9x + 8(5/3) = 103/3
9x = 21
x = 21/9
x = 7/3


Input: Solve quickly: 8x - 8 = 0

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


Input: Find x in 9x + 117/8 = 0

Output:
9x + 117/8 = 0
9x = -117/8
x = -117/8 / 9
x = -13/8


Input: Solve the equation x^3 + 133/90x^2 - 247/135x + 7/18 = 0

Output:
x^3 + 133/90x^2 - 247/135x + 7/18 = 0
(x - 3/10)(x - -7/3)(x - 5/9) = 0
x - 3/10 = 0
x - -7/3 = 0
x - 5/9 = 0
x = 3/10
x = -7/3
x = 5/9


Input: Find x in x^3 + 1/3x^2 - 95/48x + 7/8 = 0

Output:
x^3 + 1/3x^2 - 95/48x + 7/8 = 0
(x - 3/4)(x - 2/3)(x - -7/4) = 0
x - 3/4 = 0
x - 2/3 = 0
x - -7/4 = 0
x = 3/4
x = 2/3
x = -7/4


Input: What value of x satisfies x^3 + 13/3x^2 + 4/9x - 32/3 = 0

Output:
x^3 + 13/3x^2 + 4/9x - 32/3 = 0
(x - -3)(x - -8/3)(x - 4/3) = 0
x - -3 = 0
x - -8/3 = 0
x - 4/3 = 0
x = -3
x = -8/3
x = 4/3


Input: What value of x satisfies 2x - 40/3 = 0

Output:
2x - 40/3 = 0
2x = 40/3
x = 40/3 / 2
x = 20/3


Input:
Solve the equations:
8x + 7y = 15
7x + 4y = 11

Output:
8x + 7y = 15
7x + 4y = 11

Using elimination
7*(8x + 7y = 15)
8*(7x + 4y = 11)
56x + 49y = 105
56x + 32y = 88
Subtract equations
17y = 17
y = 17/17
y = 1

Substitute y
8x + 7(1) = 15
8x = 8
x = 8/8
x = 1


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

Output:
3x + 17/2 = 0
3x = -17/2
x = -17/2 / 3
x = -17/6


Input: Solve the equation x^3 + 14/3x^2 - 835/48x - 325/12 = 0

Output:
x^3 + 14/3x^2 - 835/48x - 325/12 = 0
(x - 13/4)(x - -5/4)(x - -20/3) = 0
x - 13/4 = 0
x - -5/4 = 0
x - -20/3 = 0
x = 13/4
x = -5/4
x = -20/3


Input: Solve x^3 - 21/5x^2 - 101/20x + 21/4 = 0

Output:
x^3 - 21/5x^2 - 101/20x + 21/4 = 0
(x - 7/10)(x - -3/2)(x - 5) = 0
x - 7/10 = 0
x - -3/2 = 0
x - 5 = 0
x = 7/10
x = -3/2
x = 5


Input: Solve quickly: 8x + 24/5 = 0

Output:
8x + 24/5 = 0
8x = -24/5
x = -24/5 / 8
x = -3/5


Input: What value of x satisfies 8x + 18 = 0

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


Input: Solve x^3 + 31/2x^2 + 153/2x + 117 = 0

Output:
x^3 + 31/2x^2 + 153/2x + 117 = 0
(x - -13/2)(x - -6)(x - -3) = 0
x - -13/2 = 0
x - -6 = 0
x - -3 = 0
x = -13/2
x = -6
x = -3


Input:
Solve simultaneously:
9x + 3y = 53
9x + 2y = 166/3

Output:
9x + 3y = 53
9x + 2y = 166/3

Using elimination
9*(9x + 3y = 53)
9*(9x + 2y = 166/3)
81x + 27y = 477
81x + 18y = 498
Subtract equations
9y = -21
y = -21/9
y = -7/3

Substitute y
9x + 3(-7/3) = 53
9x = 60
x = 60/9
x = 20/3


Input: Find x in x^2 + 71/4x + 247/4 = 0

Output:
x^2 + 71/4x + 247/4 = 0
(x - -13)(x - -19/4) = 0
x - -13 = 0  or  x - -19/4 = 0
x = -13
x = -19/4


Input: Solve the equation x^3 - 185/24x^2 + 43/3x - 95/24 = 0

Output:
x^3 - 185/24x^2 + 43/3x - 95/24 = 0
(x - 1/3)(x - 5)(x - 19/8) = 0
x - 1/3 = 0
x - 5 = 0
x - 19/8 = 0
x = 1/3
x = 5
x = 19/8


Input: Solve quickly: 10x - 95 = 0

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


Input:
Find x and y such that
9x + 9y = 75/7
3x + 8y = 125/7

Output:
9x + 9y = 75/7
3x + 8y = 125/7

Using elimination
3*(9x + 9y = 75/7)
9*(3x + 8y = 125/7)
27x + 27y = 225/7
27x + 72y = 1125/7
Subtract equations
-45y = -900/7
y = -900/7/-45
y = 20/7

Substitute y
9x + 9(20/7) = 75/7
9x = -15
x = -15/9
x = -5/3


Input: Find x for 1x + 7/9 = 0

Output:
1x + 7/9 = 0
1x = -7/9
x = -7/9 / 1
x = -7/9


Input:
Solve the system:
7x + 3y = -136/5
8x + 10y = -254/5

Output:
7x + 3y = -136/5
8x + 10y = -254/5

Using elimination
8*(7x + 3y = -136/5)
7*(8x + 10y = -254/5)
56x + 24y = -1088/5
56x + 70y = -1778/5
Subtract equations
-46y = 138
y = 138/-46
y = -3

Substitute y
7x + 3(-3) = -136/5
7x = -91/5
x = -91/5/7
x = -13/5


Input: Solve quickly: x^2 - 39/4x - 55/4 = 0

Output:
x^2 - 39/4x - 55/4 = 0
(x - -5/4)(x - 11) = 0
x - -5/4 = 0  or  x - 11 = 0
x = -5/4
x = 11


Input:
Solve the system:
10x + 9y = -1/2
6x + 5y = 3/2

Output:
10x + 9y = -1/2
6x + 5y = 3/2

Using elimination
6*(10x + 9y = -1/2)
10*(6x + 5y = 3/2)
60x + 54y = -3
60x + 50y = 15
Subtract equations
4y = -18
y = -18/4
y = -9/2

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


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

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


Input: Solve the equation x^2 - 187/9x + 304/9 = 0

Output:
x^2 - 187/9x + 304/9 = 0
(x - 19)(x - 16/9) = 0
x - 19 = 0  or  x - 16/9 = 0
x = 19
x = 16/9


Input: Find x for x^3 + 52/3x^2 + 251/81x - 3536/81 = 0

Output:
x^3 + 52/3x^2 + 251/81x - 3536/81 = 0
(x - 13/9)(x - -16/9)(x - -17) = 0
x - 13/9 = 0
x - -16/9 = 0
x - -17 = 0
x = 13/9
x = -16/9
x = -17


Input: Find x in x^2 + 11/3x - 14/3 = 0

Output:
x^2 + 11/3x - 14/3 = 0
(x - 1)(x - -14/3) = 0
x - 1 = 0  or  x - -14/3 = 0
x = 1
x = -14/3


Input:
Solve simultaneously:
5x + 7y = 38/9
10x + 1y = -145/9

Output:
5x + 7y = 38/9
10x + 1y = -145/9

Using elimination
10*(5x + 7y = 38/9)
5*(10x + 1y = -145/9)
50x + 70y = 380/9
50x + 5y = -725/9
Subtract equations
65y = 1105/9
y = 1105/9/65
y = 17/9

Substitute y
5x + 7(17/9) = 38/9
5x = -9
x = -9/5
x = -9/5


Input: Find the solution to 10x + 65/3 = 0

Output:
10x + 65/3 = 0
10x = -65/3
x = -65/3 / 10
x = -13/6


Input: Solve 9x - 18 = 0

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


Input: Determine x in 6x - 60 = 0

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


Input: Solve the equation x^2 - 4/9x - 5/9 = 0

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


Input: Find the solution to x^3 + 77/15x^2 + 70/9x + 16/5 = 0

Output:
x^3 + 77/15x^2 + 70/9x + 16/5 = 0
(x - -2/3)(x - -9/5)(x - -8/3) = 0
x - -2/3 = 0
x - -9/5 = 0
x - -8/3 = 0
x = -2/3
x = -9/5
x = -8/3


Input: Find x for x^2 + 8/15x - 28/3 = 0

Output:
x^2 + 8/15x - 28/3 = 0
(x - 14/5)(x - -10/3) = 0
x - 14/5 = 0  or  x - -10/3 = 0
x = 14/5
x = -10/3


Input:
Find x and y such that
5x + 9y = 23/3
6x + 2y = -4

Output:
5x + 9y = 23/3
6x + 2y = -4

Using elimination
6*(5x + 9y = 23/3)
5*(6x + 2y = -4)
30x + 54y = 46
30x + 10y = -20
Subtract equations
44y = 66
y = 66/44
y = 3/2

Substitute y
5x + 9(3/2) = 23/3
5x = -35/6
x = -35/6/5
x = -7/6


Input: Solve quickly: x^3 - 27/4x^2 + 41/64x + 819/128 = 0

Output:
x^3 - 27/4x^2 + 41/64x + 819/128 = 0
(x - 9/8)(x - -7/8)(x - 13/2) = 0
x - 9/8 = 0
x - -7/8 = 0
x - 13/2 = 0
x = 9/8
x = -7/8
x = 13/2


Input: Determine x in x^2 - 164/63x + 32/21 = 0

Output:
x^2 - 164/63x + 32/21 = 0
(x - 8/9)(x - 12/7) = 0
x - 8/9 = 0  or  x - 12/7 = 0
x = 8/9
x = 12/7


Input: Find x in x^3 - 59/18x^2 - 29/27x + 28/27 = 0

Output:
x^3 - 59/18x^2 - 29/27x + 28/27 = 0
(x - 7/2)(x - -2/3)(x - 4/9) = 0
x - 7/2 = 0
x - -2/3 = 0
x - 4/9 = 0
x = 7/2
x = -2/3
x = 4/9


Input: What value of x satisfies 6x - 15 = 0

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


Input: Determine x in 9x + 9 = 0

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


Input: Solve the equation x^3 - 25/21x^2 - 192/7x + 1360/21 = 0

Output:
x^3 - 25/21x^2 - 192/7x + 1360/21 = 0
(x - 4)(x - -17/3)(x - 20/7) = 0
x - 4 = 0
x - -17/3 = 0
x - 20/7 = 0
x = 4
x = -17/3
x = 20/7


Input:
Find x and y such that
2x + 7y = -14
3x + 9y = -24

Output:
2x + 7y = -14
3x + 9y = -24

Using elimination
3*(2x + 7y = -14)
2*(3x + 9y = -24)
6x + 21y = -42
6x + 18y = -48
Subtract equations
3y = 6
y = 6/3
y = 2

Substitute y
2x + 7(2) = -14
2x = -28
x = -28/2
x = -14


Input:
Solve the system:
2x + 1y = -37/20
5x + 3y = -217/40

Output:
2x + 1y = -37/20
5x + 3y = -217/40

Using elimination
5*(2x + 1y = -37/20)
2*(5x + 3y = -217/40)
10x + 5y = -37/4
10x + 6y = -217/20
Subtract equations
-1y = 8/5
y = 8/5/-1
y = -8/5

Substitute y
2x + 1(-8/5) = -37/20
2x = -1/4
x = -1/4/2
x = -1/8


Input: Find x for x^2 + 69/10x - 68/5 = 0

Output:
x^2 + 69/10x - 68/5 = 0
(x - -17/2)(x - 8/5) = 0
x - -17/2 = 0  or  x - 8/5 = 0
x = -17/2
x = 8/5


Input: Find x in x^2 + 109/45x + 22/45 = 0

Output:
x^2 + 109/45x + 22/45 = 0
(x - -11/5)(x - -2/9) = 0
x - -11/5 = 0  or  x - -2/9 = 0
x = -11/5
x = -2/9


Input:
Solve simultaneously:
6x + 3y = -259/3
9x + 4y = -1162/9

Output:
6x + 3y = -259/3
9x + 4y = -1162/9

Using elimination
9*(6x + 3y = -259/3)
6*(9x + 4y = -1162/9)
54x + 27y = -777
54x + 24y = -2324/3
Subtract equations
3y = -7/3
y = -7/3/3
y = -7/9

Substitute y
6x + 3(-7/9) = -259/3
6x = -84
x = -84/6
x = -14


Input: Determine x in x^2 + 247/63x + 80/21 = 0

Output:
x^2 + 247/63x + 80/21 = 0
(x - -16/9)(x - -15/7) = 0
x - -16/9 = 0  or  x - -15/7 = 0
x = -16/9
x = -15/7


Input: Find x for 4x - 34 = 0

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


Input: Determine x in x^3 - 161/20x^2 + 389/40x + 91/40 = 0

Output:
x^3 - 161/20x^2 + 389/40x + 91/40 = 0
(x - -1/5)(x - 7/4)(x - 13/2) = 0
x - -1/5 = 0
x - 7/4 = 0
x - 13/2 = 0
x = -1/5
x = 7/4
x = 13/2


Input: Find x in x^3 - 3/8x^2 - 117/32x + 35/16 = 0

Output:
x^3 - 3/8x^2 - 117/32x + 35/16 = 0
(x - 5/8)(x - -2)(x - 7/4) = 0
x - 5/8 = 0
x - -2 = 0
x - 7/4 = 0
x = 5/8
x = -2
x = 7/4


Input: Solve the equation x^2 + 17/14x - 6/7 = 0

Output:
x^2 + 17/14x - 6/7 = 0
(x - 1/2)(x - -12/7) = 0
x - 1/2 = 0  or  x - -12/7 = 0
x = 1/2
x = -12/7


Input:
Solve the equations:
4x + 6y = -91/10
7x + 3y = -131/20

Output:
4x + 6y = -91/10
7x + 3y = -131/20

Using elimination
7*(4x + 6y = -91/10)
4*(7x + 3y = -131/20)
28x + 42y = -637/10
28x + 12y = -131/5
Subtract equations
30y = -75/2
y = -75/2/30
y = -5/4

Substitute y
4x + 6(-5/4) = -91/10
4x = -8/5
x = -8/5/4
x = -2/5


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

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


Input: Solve x^2 + 97/10x + 63/10 = 0

Output:
x^2 + 97/10x + 63/10 = 0
(x - -9)(x - -7/10) = 0
x - -9 = 0  or  x - -7/10 = 0
x = -9
x = -7/10


Input: Compute the solution of 7x + 4 = 0

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


Input: Solve x^2 - 16x - 17 = 0

Output:
x^2 - 16x - 17 = 0
(x - -1)(x - 17) = 0
x - -1 = 0  or  x - 17 = 0
x = -1
x = 17


Input: Find the solution to x^3 + 13/28x^2 - 59/7x - 165/28 = 0

Output:
x^3 + 13/28x^2 - 59/7x - 165/28 = 0
(x - -5/7)(x - 3)(x - -11/4) = 0
x - -5/7 = 0
x - 3 = 0
x - -11/4 = 0
x = -5/7
x = 3
x = -11/4


Input:
Find x and y such that
10x + 6y = 147
7x + 10y = 403/2

Output:
10x + 6y = 147
7x + 10y = 403/2

Using elimination
7*(10x + 6y = 147)
10*(7x + 10y = 403/2)
70x + 42y = 1029
70x + 100y = 2015
Subtract equations
-58y = -986
y = -986/-58
y = 17

Substitute y
10x + 6(17) = 147
10x = 45
x = 45/10
x = 9/2


Input:
Solve the system:
5x + 10y = 255/14
6x + 5y = 125/7

Output:
5x + 10y = 255/14
6x + 5y = 125/7

Using elimination
6*(5x + 10y = 255/14)
5*(6x + 5y = 125/7)
30x + 60y = 765/7
30x + 25y = 625/7
Subtract equations
35y = 20
y = 20/35
y = 4/7

Substitute y
5x + 10(4/7) = 255/14
5x = 25/2
x = 25/2/5
x = 5/2


Input: Find x for x^3 - 26/3x^2 - 317/3x - 560/3 = 0

Output:
x^3 - 26/3x^2 - 317/3x - 560/3 = 0
(x - 16)(x - -5)(x - -7/3) = 0
x - 16 = 0
x - -5 = 0
x - -7/3 = 0
x = 16
x = -5
x = -7/3


Input: Find the solution to x^3 + 3/8x^2 - 99/32x + 85/64 = 0

Output:
x^3 + 3/8x^2 - 99/32x + 85/64 = 0
(x - -17/8)(x - 5/4)(x - 1/2) = 0
x - -17/8 = 0
x - 5/4 = 0
x - 1/2 = 0
x = -17/8
x = 5/4
x = 1/2


Input: Solve the equation x^2 - 127/72x - 5/24 = 0

Output:
x^2 - 127/72x - 5/24 = 0
(x - 15/8)(x - -1/9) = 0
x - 15/8 = 0  or  x - -1/9 = 0
x = 15/8
x = -1/9


Input: Solve the equation 3x + 3 = 0

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


Input: Compute the solution of x^2 + 136/21x + 19/21 = 0

Output:
x^2 + 136/21x + 19/21 = 0
(x - -1/7)(x - -19/3) = 0
x - -1/7 = 0  or  x - -19/3 = 0
x = -1/7
x = -19/3


Input: Solve quickly: 6x - 18/5 = 0

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


Input: What value of x satisfies x^3 - 43/9x^2 + 4/3x + 64/9 = 0

Output:
x^3 - 43/9x^2 + 4/3x + 64/9 = 0
(x - -1)(x - 4)(x - 16/9) = 0
x - -1 = 0
x - 4 = 0
x - 16/9 = 0
x = -1
x = 4
x = 16/9


Input: Find x in x^2 - 19/56x - 15/56 = 0

Output:
x^2 - 19/56x - 15/56 = 0
(x - 5/7)(x - -3/8) = 0
x - 5/7 = 0  or  x - -3/8 = 0
x = 5/7
x = -3/8


Input: Determine x in x^2 + 19/3x + 26/3 = 0

Output:
x^2 + 19/3x + 26/3 = 0
(x - -2)(x - -13/3) = 0
x - -2 = 0  or  x - -13/3 = 0
x = -2
x = -13/3


Input: Solve quickly: x^3 - 251/45x^2 + 31/45x + 11 = 0

Output:
x^3 - 251/45x^2 + 31/45x + 11 = 0
(x - 9/5)(x - -11/9)(x - 5) = 0
x - 9/5 = 0
x - -11/9 = 0
x - 5 = 0
x = 9/5
x = -11/9
x = 5


Input: Solve x^2 + 56/15x - 128/15 = 0

Output:
x^2 + 56/15x - 128/15 = 0
(x - 8/5)(x - -16/3) = 0
x - 8/5 = 0  or  x - -16/3 = 0
x = 8/5
x = -16/3


Input: What value of x satisfies x^3 - 24/5x^2 + 37/5x - 18/5 = 0

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


Input:
Solve the system:
5x + 9y = -23/21
9x + 2y = -241/7

Output:
5x + 9y = -23/21
9x + 2y = -241/7

Using elimination
9*(5x + 9y = -23/21)
5*(9x + 2y = -241/7)
45x + 81y = -69/7
45x + 10y = -1205/7
Subtract equations
71y = 1136/7
y = 1136/7/71
y = 16/7

Substitute y
5x + 9(16/7) = -23/21
5x = -65/3
x = -65/3/5
x = -13/3


Input: Solve quickly: 2x - 3 = 0

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


Input:
Solve simultaneously:
2x + 1y = -45/8
10x + 1y = -173/8

Output:
2x + 1y = -45/8
10x + 1y = -173/8

Using elimination
10*(2x + 1y = -45/8)
2*(10x + 1y = -173/8)
20x + 10y = -225/4
20x + 2y = -173/4
Subtract equations
8y = -13
y = -13/8
y = -13/8

Substitute y
2x + 1(-13/8) = -45/8
2x = -4
x = -4/2
x = -2


Input: What value of x satisfies 9x - 54 = 0

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


Input: What value of x satisfies x^3 + 37/20x^2 - 673/40x - 1547/40 = 0

Output:
x^3 + 37/20x^2 - 673/40x - 1547/40 = 0
(x - 17/4)(x - -13/5)(x - -7/2) = 0
x - 17/4 = 0
x - -13/5 = 0
x - -7/2 = 0
x = 17/4
x = -13/5
x = -7/2


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

Output:
x^2 - 3/10x - 2/5 = 0
(x - -1/2)(x - 4/5) = 0
x - -1/2 = 0  or  x - 4/5 = 0
x = -1/2
x = 4/5


Input: Solve the equation x^2 + 35/8x - 25/8 = 0

Output:
x^2 + 35/8x - 25/8 = 0
(x - 5/8)(x - -5) = 0
x - 5/8 = 0  or  x - -5 = 0
x = 5/8
x = -5


Input: Determine x in 8x - 16/5 = 0

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


Input: Find x for 4x + 8/9 = 0

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


Input: Determine x in 3x + 21/10 = 0

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


Input: Find the solution to 6x - 15 = 0

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


Input: Find the solution to 5x + 35/4 = 0

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


Input: Find the solution to x^3 + 13/4x^2 + 9/4x  = 0

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


Input:
Solve the system:
10x + 1y = 11/4
3x + 3y = -213/20

Output:
10x + 1y = 11/4
3x + 3y = -213/20

Using elimination
3*(10x + 1y = 11/4)
10*(3x + 3y = -213/20)
30x + 3y = 33/4
30x + 30y = -213/2
Subtract equations
-27y = 459/4
y = 459/4/-27
y = -17/4

Substitute y
10x + 1(-17/4) = 11/4
10x = 7
x = 7/10
x = 7/10


Input: Find x for x^3 - 2/5x^2 - 57/5x + 54/5 = 0

Output:
x^3 - 2/5x^2 - 57/5x + 54/5 = 0
(x - -18/5)(x - 3)(x - 1) = 0
x - -18/5 = 0
x - 3 = 0
x - 1 = 0
x = -18/5
x = 3
x = 1


Input: Find x for 10x + 36 = 0

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


Input:
Solve simultaneously:
10x + 6y = 247/10
10x + 2y = 199/10

Output:
10x + 6y = 247/10
10x + 2y = 199/10

Using elimination
10*(10x + 6y = 247/10)
10*(10x + 2y = 199/10)
100x + 60y = 247
100x + 20y = 199
Subtract equations
40y = 48
y = 48/40
y = 6/5

Substitute y
10x + 6(6/5) = 247/10
10x = 35/2
x = 35/2/10
x = 7/4


Input: Find x in x^3 + 6/7x^2 - 211/28x + 6 = 0

Output:
x^3 + 6/7x^2 - 211/28x + 6 = 0
(x - -7/2)(x - 8/7)(x - 3/2) = 0
x - -7/2 = 0
x - 8/7 = 0
x - 3/2 = 0
x = -7/2
x = 8/7
x = 3/2


Input:
Solve the equations:
4x + 4y = -39
8x + 9y = -331/4

Output:
4x + 4y = -39
8x + 9y = -331/4

Using elimination
8*(4x + 4y = -39)
4*(8x + 9y = -331/4)
32x + 32y = -312
32x + 36y = -331
Subtract equations
-4y = 19
y = 19/-4
y = -19/4

Substitute y
4x + 4(-19/4) = -39
4x = -20
x = -20/4
x = -5


Input: Find x in 4x - 12/7 = 0

Output:
4x - 12/7 = 0
4x = 12/7
x = 12/7 / 4
x = 3/7


Input: Solve quickly: x^3 - 36/7x^2 + 96/49x + 512/49 = 0

Output:
x^3 - 36/7x^2 + 96/49x + 512/49 = 0
(x - -8/7)(x - 4)(x - 16/7) = 0
x - -8/7 = 0
x - 4 = 0
x - 16/7 = 0
x = -8/7
x = 4
x = 16/7


Input:
Find x and y such that
6x + 3y = 219/4
9x + 6y = 81

Output:
6x + 3y = 219/4
9x + 6y = 81

Using elimination
9*(6x + 3y = 219/4)
6*(9x + 6y = 81)
54x + 27y = 1971/4
54x + 36y = 486
Subtract equations
-9y = 27/4
y = 27/4/-9
y = -3/4

Substitute y
6x + 3(-3/4) = 219/4
6x = 57
x = 57/6
x = 19/2


Input: Solve the equation 1x - 2/9 = 0

Output:
1x - 2/9 = 0
1x = 2/9
x = 2/9 / 1
x = 2/9


Input: Find the solution to x^2 - 73/24x + 19/12 = 0

Output:
x^2 - 73/24x + 19/12 = 0
(x - 2/3)(x - 19/8) = 0
x - 2/3 = 0  or  x - 19/8 = 0
x = 2/3
x = 19/8


Input: Find x in x^2 - 48/35x - 108/35 = 0

Output:
x^2 - 48/35x - 108/35 = 0
(x - -6/5)(x - 18/7) = 0
x - -6/5 = 0  or  x - 18/7 = 0
x = -6/5
x = 18/7


Input: Solve x^2 - 29/10x - 3/10 = 0

Output:
x^2 - 29/10x - 3/10 = 0
(x - -1/10)(x - 3) = 0
x - -1/10 = 0  or  x - 3 = 0
x = -1/10
x = 3


Input: Find x for x^3 + 3/8x^2 - 207/32x - 187/32 = 0

Output:
x^3 + 3/8x^2 - 207/32x - 187/32 = 0
(x - 11/4)(x - -1)(x - -17/8) = 0
x - 11/4 = 0
x - -1 = 0
x - -17/8 = 0
x = 11/4
x = -1
x = -17/8


Input: Find x in 6x - 12/7 = 0

Output:
6x - 12/7 = 0
6x = 12/7
x = 12/7 / 6
x = 2/7


Input: Solve the equation x^3 + 49/4x^2 - 95/4x + 21/2 = 0

Output:
x^3 + 49/4x^2 - 95/4x + 21/2 = 0
(x - -14)(x - 3/4)(x - 1) = 0
x - -14 = 0
x - 3/4 = 0
x - 1 = 0
x = -14
x = 3/4
x = 1


Input: What value of x satisfies 8x - 136/7 = 0

Output:
8x - 136/7 = 0
8x = 136/7
x = 136/7 / 8
x = 17/7


Input: Solve the equation 4x + 26/3 = 0

Output:
4x + 26/3 = 0
4x = -26/3
x = -26/3 / 4
x = -13/6


Input: Find the solution to 9x + 21/2 = 0

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


Input: Find the solution to x^3 - 16/3x^2 - 11/36x + 847/36 = 0

Output:
x^3 - 16/3x^2 - 11/36x + 847/36 = 0
(x - 11/3)(x - 7/2)(x - -11/6) = 0
x - 11/3 = 0
x - 7/2 = 0
x - -11/6 = 0
x = 11/3
x = 7/2
x = -11/6


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

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


Input: Find the solution to 2x + 19/3 = 0

Output:
2x + 19/3 = 0
2x = -19/3
x = -19/3 / 2
x = -19/6


Input: Compute the solution of x^3 + 1/42x^2 - 7/2x + 52/21 = 0

Output:
x^3 + 1/42x^2 - 7/2x + 52/21 = 0
(x - -13/6)(x - 8/7)(x - 1) = 0
x - -13/6 = 0
x - 8/7 = 0
x - 1 = 0
x = -13/6
x = 8/7
x = 1


Input: Solve quickly: x^2 - 15x + 36 = 0

Output:
x^2 - 15x + 36 = 0
(x - 12)(x - 3) = 0
x - 12 = 0  or  x - 3 = 0
x = 12
x = 3


Input:
Find x and y such that
9x + 8y = -1139/90
2x + 2y = -121/45

Output:
9x + 8y = -1139/90
2x + 2y = -121/45

Using elimination
2*(9x + 8y = -1139/90)
9*(2x + 2y = -121/45)
18x + 16y = -1139/45
18x + 18y = -121/5
Subtract equations
-2y = -10/9
y = -10/9/-2
y = 5/9

Substitute y
9x + 8(5/9) = -1139/90
9x = -171/10
x = -171/10/9
x = -19/10


Input: Find the solution to 6x + 38/3 = 0

Output:
6x + 38/3 = 0
6x = -38/3
x = -38/3 / 6
x = -19/9


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

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


Input: Solve quickly: x^2 + 11/7x - 18/7 = 0

Output:
x^2 + 11/7x - 18/7 = 0
(x - -18/7)(x - 1) = 0
x - -18/7 = 0  or  x - 1 = 0
x = -18/7
x = 1


Input: Compute the solution of x^3 - 172/63x^2 - 3/7x + 208/63 = 0

Output:
x^3 - 172/63x^2 - 3/7x + 208/63 = 0
(x - 13/9)(x - 16/7)(x - -1) = 0
x - 13/9 = 0
x - 16/7 = 0
x - -1 = 0
x = 13/9
x = 16/7
x = -1


Input:
Solve the system:
9x + 4y = 665/18
4x + 4y = 130/9

Output:
9x + 4y = 665/18
4x + 4y = 130/9

Using elimination
4*(9x + 4y = 665/18)
9*(4x + 4y = 130/9)
36x + 16y = 1330/9
36x + 36y = 130
Subtract equations
-20y = 160/9
y = 160/9/-20
y = -8/9

Substitute y
9x + 4(-8/9) = 665/18
9x = 81/2
x = 81/2/9
x = 9/2


Input: What value of x satisfies x^2 - 5/12x - 25/12 = 0

Output:
x^2 - 5/12x - 25/12 = 0
(x - -5/4)(x - 5/3) = 0
x - -5/4 = 0  or  x - 5/3 = 0
x = -5/4
x = 5/3


Input: Find x in 9x - 60 = 0

Output:
9x - 60 = 0
9x = 60
x = 60 / 9
x = 20/3


Input: Compute the solution of x^3 - 169/14x^2 + 173/7x + 440/7 = 0

Output:
x^3 - 169/14x^2 + 173/7x + 440/7 = 0
(x - 8)(x - -10/7)(x - 11/2) = 0
x - 8 = 0
x - -10/7 = 0
x - 11/2 = 0
x = 8
x = -10/7
x = 11/2


Input:
Solve the equations:
10x + 3y = -9/4
6x + 6y = -39/4

Output:
10x + 3y = -9/4
6x + 6y = -39/4

Using elimination
6*(10x + 3y = -9/4)
10*(6x + 6y = -39/4)
60x + 18y = -27/2
60x + 60y = -195/2
Subtract equations
-42y = 84
y = 84/-42
y = -2

Substitute y
10x + 3(-2) = -9/4
10x = 15/4
x = 15/4/10
x = 3/8


Input: Solve the equation 10x - 45/2 = 0

Output:
10x - 45/2 = 0
10x = 45/2
x = 45/2 / 10
x = 9/4


Input: Determine x in x^3 + 65/3x^2 + 178/3x - 120 = 0

Output:
x^3 + 65/3x^2 + 178/3x - 120 = 0
(x - -18)(x - -5)(x - 4/3) = 0
x - -18 = 0
x - -5 = 0
x - 4/3 = 0
x = -18
x = -5
x = 4/3


Input: Solve quickly: x^2 + 191/10x - 18 = 0

Output:
x^2 + 191/10x - 18 = 0
(x - 9/10)(x - -20) = 0
x - 9/10 = 0  or  x - -20 = 0
x = 9/10
x = -20


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

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


Input:
Solve simultaneously:
6x + 9y = -8/3
10x + 3y = -112/9

Output:
6x + 9y = -8/3
10x + 3y = -112/9

Using elimination
10*(6x + 9y = -8/3)
6*(10x + 3y = -112/9)
60x + 90y = -80/3
60x + 18y = -224/3
Subtract equations
72y = 48
y = 48/72
y = 2/3

Substitute y
6x + 9(2/3) = -8/3
6x = -26/3
x = -26/3/6
x = -13/9


Input: Compute the solution of 4x + 80/3 = 0

Output:
4x + 80/3 = 0
4x = -80/3
x = -80/3 / 4
x = -20/3


Input: Solve 1x - 19 = 0

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


Input: Find x in 6x - 120 = 0

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


Input: Solve x^2 - 67/21x + 52/21 = 0

Output:
x^2 - 67/21x + 52/21 = 0
(x - 4/3)(x - 13/7) = 0
x - 4/3 = 0  or  x - 13/7 = 0
x = 4/3
x = 13/7


Input: Find x for x^3 + 61/8x^2 + 1099/72x + 245/36 = 0

Output:
x^3 + 61/8x^2 + 1099/72x + 245/36 = 0
(x - -7/3)(x - -14/3)(x - -5/8) = 0
x - -7/3 = 0
x - -14/3 = 0
x - -5/8 = 0
x = -7/3
x = -14/3
x = -5/8


Input: Determine x in 1x - 2 = 0

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


Input: Compute the solution of 10x - 20 = 0

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


Input:
Solve the equations:
9x + 1y = 50/7
8x + 5y = -157/7

Output:
9x + 1y = 50/7
8x + 5y = -157/7

Using elimination
8*(9x + 1y = 50/7)
9*(8x + 5y = -157/7)
72x + 8y = 400/7
72x + 45y = -1413/7
Subtract equations
-37y = 259
y = 259/-37
y = -7

Substitute y
9x + 1(-7) = 50/7
9x = 99/7
x = 99/7/9
x = 11/7


Input: Determine x in x^3 - 23/12x^2 + 3/8x + 3/8 = 0

Output:
x^3 - 23/12x^2 + 3/8x + 3/8 = 0
(x - 3/2)(x - -1/3)(x - 3/4) = 0
x - 3/2 = 0
x - -1/3 = 0
x - 3/4 = 0
x = 3/2
x = -1/3
x = 3/4


Input: Solve quickly: x^3 + 117/56x^2 - 311/224x - 195/56 = 0

Output:
x^3 + 117/56x^2 - 311/224x - 195/56 = 0
(x - -12/7)(x - 5/4)(x - -13/8) = 0
x - -12/7 = 0
x - 5/4 = 0
x - -13/8 = 0
x = -12/7
x = 5/4
x = -13/8


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

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


Input: Find x for 4x - 20/7 = 0

Output:
4x - 20/7 = 0
4x = 20/7
x = 20/7 / 4
x = 5/7


Input:
Solve the system:
10x + 6y = 76
4x + 6y = 16

Output:
10x + 6y = 76
4x + 6y = 16

Using elimination
4*(10x + 6y = 76)
10*(4x + 6y = 16)
40x + 24y = 304
40x + 60y = 160
Subtract equations
-36y = 144
y = 144/-36
y = -4

Substitute y
10x + 6(-4) = 76
10x = 100
x = 100/10
x = 10


Input: Find the solution to 1x + 3 = 0

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


Input: Solve quickly: 4x - 36/7 = 0

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


Input: Solve the equation x^3 - 189/10x^2 + 323/10x  = 0

Output:
x^3 - 189/10x^2 + 323/10x  = 0
(x - 17)(x - 19/10)(x - 0) = 0
x - 17 = 0
x - 19/10 = 0
x - 0 = 0
x = 17
x = 19/10
x = 0


Input: Find x for 9x + 117/10 = 0

Output:
9x + 117/10 = 0
9x = -117/10
x = -117/10 / 9
x = -13/10


Input: Find x for x^3 - 1x^2 - 23/4x + 15/2 = 0

Output:
x^3 - 1x^2 - 23/4x + 15/2 = 0
(x - -5/2)(x - 3/2)(x - 2) = 0
x - -5/2 = 0
x - 3/2 = 0
x - 2 = 0
x = -5/2
x = 3/2
x = 2


Input: Determine x in x^3 - 24/5x^2 - 1x  = 0

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


Input: Determine x in x^3 + 49/6x^2 - 112x + 640/3 = 0

Output:
x^3 + 49/6x^2 - 112x + 640/3 = 0
(x - 16/3)(x - -16)(x - 5/2) = 0
x - 16/3 = 0
x - -16 = 0
x - 5/2 = 0
x = 16/3
x = -16
x = 5/2


Input: Compute the solution of x^3 + 587/140x^2 - 577/70x - 34 = 0

Output:
x^3 + 587/140x^2 - 577/70x - 34 = 0
(x - 20/7)(x - -17/4)(x - -14/5) = 0
x - 20/7 = 0
x - -17/4 = 0
x - -14/5 = 0
x = 20/7
x = -17/4
x = -14/5


Input:
Find x and y such that
3x + 7y = 95/3
4x + 2y = 50/9

Output:
3x + 7y = 95/3
4x + 2y = 50/9

Using elimination
4*(3x + 7y = 95/3)
3*(4x + 2y = 50/9)
12x + 28y = 380/3
12x + 6y = 50/3
Subtract equations
22y = 110
y = 110/22
y = 5

Substitute y
3x + 7(5) = 95/3
3x = -10/3
x = -10/3/3
x = -10/9


Input: Solve the equation x^3 + 131/56x^2 - 239/56x - 247/28 = 0

Output:
x^3 + 131/56x^2 - 239/56x - 247/28 = 0
(x - -19/7)(x - -13/8)(x - 2) = 0
x - -19/7 = 0
x - -13/8 = 0
x - 2 = 0
x = -19/7
x = -13/8
x = 2


Input:
Solve the system:
10x + 9y = 100
9x + 4y = 8

Output:
10x + 9y = 100
9x + 4y = 8

Using elimination
9*(10x + 9y = 100)
10*(9x + 4y = 8)
90x + 81y = 900
90x + 40y = 80
Subtract equations
41y = 820
y = 820/41
y = 20

Substitute y
10x + 9(20) = 100
10x = -80
x = -80/10
x = -8


Input: Solve the equation x^3 + 1/2x^2 - 69/50x - 99/125 = 0

Output:
x^3 + 1/2x^2 - 69/50x - 99/125 = 0
(x - -3/5)(x - 6/5)(x - -11/10) = 0
x - -3/5 = 0
x - 6/5 = 0
x - -11/10 = 0
x = -3/5
x = 6/5
x = -11/10


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 x^3 + 53/40x^2 - 101/80x - 17/16 = 0

Output:
x^3 + 53/40x^2 - 101/80x - 17/16 = 0
(x - 1)(x - -17/10)(x - -5/8) = 0
x - 1 = 0
x - -17/10 = 0
x - -5/8 = 0
x = 1
x = -17/10
x = -5/8


Input:
Find x and y such that
3x + 1y = -295/63
7x + 2y = -101/9

Output:
3x + 1y = -295/63
7x + 2y = -101/9

Using elimination
7*(3x + 1y = -295/63)
3*(7x + 2y = -101/9)
21x + 7y = -295/9
21x + 6y = -101/3
Subtract equations
1y = 8/9
y = 8/9/1
y = 8/9

Substitute y
3x + 1(8/9) = -295/63
3x = -39/7
x = -39/7/3
x = -13/7


Input:
Find x and y such that
6x + 6y = -71/7
7x + 6y = -10

Output:
6x + 6y = -71/7
7x + 6y = -10

Using elimination
7*(6x + 6y = -71/7)
6*(7x + 6y = -10)
42x + 42y = -71
42x + 36y = -60
Subtract equations
6y = -11
y = -11/6
y = -11/6

Substitute y
6x + 6(-11/6) = -71/7
6x = 6/7
x = 6/7/6
x = 1/7


Input:
Solve the system:
1x + 2y = 13/15
4x + 1y = 122/15

Output:
1x + 2y = 13/15
4x + 1y = 122/15

Using elimination
4*(1x + 2y = 13/15)
1*(4x + 1y = 122/15)
4x + 8y = 52/15
4x + 1y = 122/15
Subtract equations
7y = -14/3
y = -14/3/7
y = -2/3

Substitute y
1x + 2(-2/3) = 13/15
1x = 11/5
x = 11/5/1
x = 11/5


Input:
Solve the system:
9x + 8y = -149/2
7x + 5y = -50

Output:
9x + 8y = -149/2
7x + 5y = -50

Using elimination
7*(9x + 8y = -149/2)
9*(7x + 5y = -50)
63x + 56y = -1043/2
63x + 45y = -450
Subtract equations
11y = -143/2
y = -143/2/11
y = -13/2

Substitute y
9x + 8(-13/2) = -149/2
9x = -45/2
x = -45/2/9
x = -5/2


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

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


Input: Compute the solution of x^2 + 37/72x - 65/36 = 0

Output:
x^2 + 37/72x - 65/36 = 0
(x - -13/8)(x - 10/9) = 0
x - -13/8 = 0  or  x - 10/9 = 0
x = -13/8
x = 10/9


Input:
Solve the system:
6x + 7y = -48
2x + 6y = -71

Output:
6x + 7y = -48
2x + 6y = -71

Using elimination
2*(6x + 7y = -48)
6*(2x + 6y = -71)
12x + 14y = -96
12x + 36y = -426
Subtract equations
-22y = 330
y = 330/-22
y = -15

Substitute y
6x + 7(-15) = -48
6x = 57
x = 57/6
x = 19/2


Input: Find x for x^3 + 31/90x^2 - 93/50x + 34/45 = 0

Output:
x^3 + 31/90x^2 - 93/50x + 34/45 = 0
(x - 4/5)(x - 5/9)(x - -17/10) = 0
x - 4/5 = 0
x - 5/9 = 0
x - -17/10 = 0
x = 4/5
x = 5/9
x = -17/10


Input:
Solve the system:
7x + 3y = 55/2
3x + 4y = 49/6

Output:
7x + 3y = 55/2
3x + 4y = 49/6

Using elimination
3*(7x + 3y = 55/2)
7*(3x + 4y = 49/6)
21x + 9y = 165/2
21x + 28y = 343/6
Subtract equations
-19y = 76/3
y = 76/3/-19
y = -4/3

Substitute y
7x + 3(-4/3) = 55/2
7x = 63/2
x = 63/2/7
x = 9/2


Input:
Solve the equations:
9x + 9y = 594/5
1x + 10y = 15

Output:
9x + 9y = 594/5
1x + 10y = 15

Using elimination
1*(9x + 9y = 594/5)
9*(1x + 10y = 15)
9x + 9y = 594/5
9x + 90y = 135
Subtract equations
-81y = -81/5
y = -81/5/-81
y = 1/5

Substitute y
9x + 9(1/5) = 594/5
9x = 117
x = 117/9
x = 13


Input: Find x for x^2 + 29/9x + 2/3 = 0

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


Input:
Solve simultaneously:
3x + 5y = 20
10x + 10y = 60

Output:
3x + 5y = 20
10x + 10y = 60

Using elimination
10*(3x + 5y = 20)
3*(10x + 10y = 60)
30x + 50y = 200
30x + 30y = 180
Subtract equations
20y = 20
y = 20/20
y = 1

Substitute y
3x + 5(1) = 20
3x = 15
x = 15/3
x = 5


Input: Solve the equation x^3 + 6x^2 - 9/4x - 27/2 = 0

Output:
x^3 + 6x^2 - 9/4x - 27/2 = 0
(x - -3/2)(x - 3/2)(x - -6) = 0
x - -3/2 = 0
x - 3/2 = 0
x - -6 = 0
x = -3/2
x = 3/2
x = -6


Input:
Solve simultaneously:
8x + 7y = 46
5x + 1y = -5

Output:
8x + 7y = 46
5x + 1y = -5

Using elimination
5*(8x + 7y = 46)
8*(5x + 1y = -5)
40x + 35y = 230
40x + 8y = -40
Subtract equations
27y = 270
y = 270/27
y = 10

Substitute y
8x + 7(10) = 46
8x = -24
x = -24/8
x = -3


Input: Compute the solution of 10x + 75/2 = 0

Output:
10x + 75/2 = 0
10x = -75/2
x = -75/2 / 10
x = -15/4


Input: What value of x satisfies 9x + 99/10 = 0

Output:
9x + 99/10 = 0
9x = -99/10
x = -99/10 / 9
x = -11/10


Input: Find x for 9x + 15 = 0

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


Input:
Solve simultaneously:
6x + 5y = 425/36
8x + 8y = 143/9

Output:
6x + 5y = 425/36
8x + 8y = 143/9

Using elimination
8*(6x + 5y = 425/36)
6*(8x + 8y = 143/9)
48x + 40y = 850/9
48x + 48y = 286/3
Subtract equations
-8y = -8/9
y = -8/9/-8
y = 1/9

Substitute y
6x + 5(1/9) = 425/36
6x = 45/4
x = 45/4/6
x = 15/8


Input: Solve quickly: x^2 - 17/5x + 16/25 = 0

Output:
x^2 - 17/5x + 16/25 = 0
(x - 1/5)(x - 16/5) = 0
x - 1/5 = 0  or  x - 16/5 = 0
x = 1/5
x = 16/5


Input: Find the solution to x^2 + 18/5x + 81/25 = 0

Output:
x^2 + 18/5x + 81/25 = 0
(x - -9/5)(x - -9/5) = 0
x - -9/5 = 0  or  x - -9/5 = 0
x = -9/5
x = -9/5


Input: Solve quickly: 2x + 2/9 = 0

Output:
2x + 2/9 = 0
2x = -2/9
x = -2/9 / 2
x = -1/9


Input: Solve x^2 - 11/3x + 8/3 = 0

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


Input: Solve the equation x^3 - 136/21x^2 + 739/63x - 110/21 = 0

Output:
x^3 - 136/21x^2 + 739/63x - 110/21 = 0
(x - 2/3)(x - 15/7)(x - 11/3) = 0
x - 2/3 = 0
x - 15/7 = 0
x - 11/3 = 0
x = 2/3
x = 15/7
x = 11/3


Input:
Solve the equations:
3x + 2y = 19/7
3x + 10y = 67/7

Output:
3x + 2y = 19/7
3x + 10y = 67/7

Using elimination
3*(3x + 2y = 19/7)
3*(3x + 10y = 67/7)
9x + 6y = 57/7
9x + 30y = 201/7
Subtract equations
-24y = -144/7
y = -144/7/-24
y = 6/7

Substitute y
3x + 2(6/7) = 19/7
3x = 1
x = 1/3
x = 1/3


Input: Solve x^3 - 823/360x^2 + 289/180x - 1/3 = 0

Output:
x^3 - 823/360x^2 + 289/180x - 1/3 = 0
(x - 4/5)(x - 3/8)(x - 10/9) = 0
x - 4/5 = 0
x - 3/8 = 0
x - 10/9 = 0
x = 4/5
x = 3/8
x = 10/9


Input: Find x for x^3 + 289/30x^2 + 18/5x - 189/10 = 0

Output:
x^3 + 289/30x^2 + 18/5x - 189/10 = 0
(x - 7/6)(x - -9/5)(x - -9) = 0
x - 7/6 = 0
x - -9/5 = 0
x - -9 = 0
x = 7/6
x = -9/5
x = -9


Input: Determine x in x^3 + 479/35x^2 + 1066/35x + 352/35 = 0

Output:
x^3 + 479/35x^2 + 1066/35x + 352/35 = 0
(x - -11)(x - -2/5)(x - -16/7) = 0
x - -11 = 0
x - -2/5 = 0
x - -16/7 = 0
x = -11
x = -2/5
x = -16/7


Input: Find x in x^2 - 2/5x - 51/5 = 0

Output:
x^2 - 2/5x - 51/5 = 0
(x - -3)(x - 17/5) = 0
x - -3 = 0  or  x - 17/5 = 0
x = -3
x = 17/5


Input: Determine x in 3x + 48 = 0

Output:
3x + 48 = 0
3x = -48
x = -48 / 3
x = -16


Input: Determine x in x^2 + 7/5x - 18 = 0

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


Input:
Solve the equations:
1x + 8y = -21/2
3x + 6y = -45/2

Output:
1x + 8y = -21/2
3x + 6y = -45/2

Using elimination
3*(1x + 8y = -21/2)
1*(3x + 6y = -45/2)
3x + 24y = -63/2
3x + 6y = -45/2
Subtract equations
18y = -9
y = -9/18
y = -1/2

Substitute y
1x + 8(-1/2) = -21/2
1x = -13/2
x = -13/2/1
x = -13/2


Input:
Solve simultaneously:
10x + 6y = -47
7x + 9y = -117/2

Output:
10x + 6y = -47
7x + 9y = -117/2

Using elimination
7*(10x + 6y = -47)
10*(7x + 9y = -117/2)
70x + 42y = -329
70x + 90y = -585
Subtract equations
-48y = 256
y = 256/-48
y = -16/3

Substitute y
10x + 6(-16/3) = -47
10x = -15
x = -15/10
x = -3/2


Input: Determine x in x^3 + 13/2x^2 + 2053/162x + 616/81 = 0

Output:
x^3 + 13/2x^2 + 2053/162x + 616/81 = 0
(x - -7/2)(x - -11/9)(x - -16/9) = 0
x - -7/2 = 0
x - -11/9 = 0
x - -16/9 = 0
x = -7/2
x = -11/9
x = -16/9


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

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


Input: Find x for x^3 - 92/15x^2 - 143/3x - 968/15 = 0

Output:
x^3 - 92/15x^2 - 143/3x - 968/15 = 0
(x - -8/3)(x - -11/5)(x - 11) = 0
x - -8/3 = 0
x - -11/5 = 0
x - 11 = 0
x = -8/3
x = -11/5
x = 11


Input: Determine x in 9x - 135 = 0

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


Input:
Solve the system:
6x + 9y = -75/7
3x + 5y = -48/7

Output:
6x + 9y = -75/7
3x + 5y = -48/7

Using elimination
3*(6x + 9y = -75/7)
6*(3x + 5y = -48/7)
18x + 27y = -225/7
18x + 30y = -288/7
Subtract equations
-3y = 9
y = 9/-3
y = -3

Substitute y
6x + 9(-3) = -75/7
6x = 114/7
x = 114/7/6
x = 19/7


Input: Find x in 1x - 12/7 = 0

Output:
1x - 12/7 = 0
1x = 12/7
x = 12/7 / 1
x = 12/7


Input: Solve x^2 - 23/2x - 105/2 = 0

Output:
x^2 - 23/2x - 105/2 = 0
(x - -7/2)(x - 15) = 0
x - -7/2 = 0  or  x - 15 = 0
x = -7/2
x = 15


Input:
Solve the system:
4x + 8y = 76/5
3x + 5y = 52/5

Output:
4x + 8y = 76/5
3x + 5y = 52/5

Using elimination
3*(4x + 8y = 76/5)
4*(3x + 5y = 52/5)
12x + 24y = 228/5
12x + 20y = 208/5
Subtract equations
4y = 4
y = 4/4
y = 1

Substitute y
4x + 8(1) = 76/5
4x = 36/5
x = 36/5/4
x = 9/5


Input: Find x in 10x - 80/3 = 0

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


Input:
Find x and y such that
6x + 6y = -42
9x + 7y = -51

Output:
6x + 6y = -42
9x + 7y = -51

Using elimination
9*(6x + 6y = -42)
6*(9x + 7y = -51)
54x + 54y = -378
54x + 42y = -306
Subtract equations
12y = -72
y = -72/12
y = -6

Substitute y
6x + 6(-6) = -42
6x = -6
x = -6/6
x = -1


Input: Solve 9x + 9/2 = 0

Output:
9x + 9/2 = 0
9x = -9/2
x = -9/2 / 9
x = -1/2


Input: Compute the solution of x^2 - 23/12x + 5/12 = 0

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


Input: Determine x in x^3 - 83/15x^2 + 2201/300x - 57/20 = 0

Output:
x^3 - 83/15x^2 + 2201/300x - 57/20 = 0
(x - 19/5)(x - 5/6)(x - 9/10) = 0
x - 19/5 = 0
x - 5/6 = 0
x - 9/10 = 0
x = 19/5
x = 5/6
x = 9/10


Input: Find x for 5x - 10 = 0

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


Input: Solve the equation x^2 + 11/6x - 7/6 = 0

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


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

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


Input:
Solve the equations:
10x + 7y = -10
4x + 1y = -104/35

Output:
10x + 7y = -10
4x + 1y = -104/35

Using elimination
4*(10x + 7y = -10)
10*(4x + 1y = -104/35)
40x + 28y = -40
40x + 10y = -208/7
Subtract equations
18y = -72/7
y = -72/7/18
y = -4/7

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


Input:
Solve simultaneously:
9x + 4y = 9
1x + 4y = 1

Output:
9x + 4y = 9
1x + 4y = 1

Using elimination
1*(9x + 4y = 9)
9*(1x + 4y = 1)
9x + 4y = 9
9x + 36y = 9
Subtract equations
-32y = 0
y = 0/-32
y = 0

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


Input: Solve quickly: 2x + 11 = 0

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


Input: What value of x satisfies x^3 + 11/15x^2 - 7/15x - 1/5 = 0

Output:
x^3 + 11/15x^2 - 7/15x - 1/5 = 0
(x - 3/5)(x - -1/3)(x - -1) = 0
x - 3/5 = 0
x - -1/3 = 0
x - -1 = 0
x = 3/5
x = -1/3
x = -1


Input: Solve quickly: x^2 - 26/9x - 40/9 = 0

Output:
x^2 - 26/9x - 40/9 = 0
(x - -10/9)(x - 4) = 0
x - -10/9 = 0  or  x - 4 = 0
x = -10/9
x = 4


Input: Find x for 5x + 1 = 0

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


Input: Solve quickly: x^3 - 10/3x^2 - 37/3x + 20 = 0

Output:
x^3 - 10/3x^2 - 37/3x + 20 = 0
(x - -3)(x - 4/3)(x - 5) = 0
x - -3 = 0
x - 4/3 = 0
x - 5 = 0
x = -3
x = 4/3
x = 5


Input: Find the solution to x^3 - 39/7x^2 - 481/49x - 9/7 = 0

Output:
x^3 - 39/7x^2 - 481/49x - 9/7 = 0
(x - -1/7)(x - -9/7)(x - 7) = 0
x - -1/7 = 0
x - -9/7 = 0
x - 7 = 0
x = -1/7
x = -9/7
x = 7


Input: Find the solution to x^3 - 37/8x^2 - 13/4x + 55/8 = 0

Output:
x^3 - 37/8x^2 - 13/4x + 55/8 = 0
(x - 1)(x - -11/8)(x - 5) = 0
x - 1 = 0
x - -11/8 = 0
x - 5 = 0
x = 1
x = -11/8
x = 5


Input: Find x in x^2 - 130/9x + 56/9 = 0

Output:
x^2 - 130/9x + 56/9 = 0
(x - 14)(x - 4/9) = 0
x - 14 = 0  or  x - 4/9 = 0
x = 14
x = 4/9


Input: Solve x^2 - 59/35x + 2/5 = 0

Output:
x^2 - 59/35x + 2/5 = 0
(x - 7/5)(x - 2/7) = 0
x - 7/5 = 0  or  x - 2/7 = 0
x = 7/5
x = 2/7


Input: Find x in 2x + 16/3 = 0

Output:
2x + 16/3 = 0
2x = -16/3
x = -16/3 / 2
x = -8/3


Input: Find x in 7x - 16 = 0

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


Input: Find x in 9x + 12 = 0

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


Input:
Solve the equations:
2x + 7y = 71/8
7x + 2y = 113/4

Output:
2x + 7y = 71/8
7x + 2y = 113/4

Using elimination
7*(2x + 7y = 71/8)
2*(7x + 2y = 113/4)
14x + 49y = 497/8
14x + 4y = 113/2
Subtract equations
45y = 45/8
y = 45/8/45
y = 1/8

Substitute y
2x + 7(1/8) = 71/8
2x = 8
x = 8/2
x = 4


Input:
Find x and y such that
1x + 9y = -53/2
6x + 10y = -71

Output:
1x + 9y = -53/2
6x + 10y = -71

Using elimination
6*(1x + 9y = -53/2)
1*(6x + 10y = -71)
6x + 54y = -159
6x + 10y = -71
Subtract equations
44y = -88
y = -88/44
y = -2

Substitute y
1x + 9(-2) = -53/2
1x = -17/2
x = -17/2/1
x = -17/2


Input: Solve the equation x^3 - 49/12x^2 - 33/2x + 57/4 = 0

Output:
x^3 - 49/12x^2 - 33/2x + 57/4 = 0
(x - 19/3)(x - 3/4)(x - -3) = 0
x - 19/3 = 0
x - 3/4 = 0
x - -3 = 0
x = 19/3
x = 3/4
x = -3


Input: Determine x in 6x  = 0

Output:
6x  = 0
6x = 0
x = 0 / 6
x = 0