Input:
Solve the system:
10x + 1y = 46/3
3x + 2y = -9

Output:
10x + 1y = 46/3
3x + 2y = -9

Using elimination
3*(10x + 1y = 46/3)
10*(3x + 2y = -9)
30x + 3y = 46
30x + 20y = -90
Subtract equations
-17y = 136
y = 136/-17
y = -8

Substitute y
10x + 1(-8) = 46/3
10x = 70/3
x = 70/3/10
x = 7/3


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

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


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

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


Input:
Find x and y such that
2x + 9y = -23/3
1x + 4y = -11/3

Output:
2x + 9y = -23/3
1x + 4y = -11/3

Using elimination
1*(2x + 9y = -23/3)
2*(1x + 4y = -11/3)
2x + 9y = -23/3
2x + 8y = -22/3
Subtract equations
1y = -1/3
y = -1/3/1
y = -1/3

Substitute y
2x + 9(-1/3) = -23/3
2x = -14/3
x = -14/3/2
x = -7/3


Input: Find the solution to x^2 + 51/35x - 26/35 = 0

Output:
x^2 + 51/35x - 26/35 = 0
(x - 2/5)(x - -13/7) = 0
x - 2/5 = 0  or  x - -13/7 = 0
x = 2/5
x = -13/7


Input: What value of x satisfies 9x + 60 = 0

Output:
9x + 60 = 0
9x = -60
x = -60 / 9
x = -20/3


Input:
Find x and y such that
3x + 1y = 61/9
6x + 7y = 157/9

Output:
3x + 1y = 61/9
6x + 7y = 157/9

Using elimination
6*(3x + 1y = 61/9)
3*(6x + 7y = 157/9)
18x + 6y = 122/3
18x + 21y = 157/3
Subtract equations
-15y = -35/3
y = -35/3/-15
y = 7/9

Substitute y
3x + 1(7/9) = 61/9
3x = 6
x = 6/3
x = 2


Input:
Solve the equations:
3x + 10y = -81
1x + 6y = -39

Output:
3x + 10y = -81
1x + 6y = -39

Using elimination
1*(3x + 10y = -81)
3*(1x + 6y = -39)
3x + 10y = -81
3x + 18y = -117
Subtract equations
-8y = 36
y = 36/-8
y = -9/2

Substitute y
3x + 10(-9/2) = -81
3x = -36
x = -36/3
x = -12


Input: Compute the solution of x^2 - 64/9x + 20/3 = 0

Output:
x^2 - 64/9x + 20/3 = 0
(x - 6)(x - 10/9) = 0
x - 6 = 0  or  x - 10/9 = 0
x = 6
x = 10/9


Input: Find x for 3x - 33/7 = 0

Output:
3x - 33/7 = 0
3x = 33/7
x = 33/7 / 3
x = 11/7


Input: Find x in 1x - 8/7 = 0

Output:
1x - 8/7 = 0
1x = 8/7
x = 8/7 / 1
x = 8/7


Input: Find the solution to x^2 - 23/6x + 11/3 = 0

Output:
x^2 - 23/6x + 11/3 = 0
(x - 11/6)(x - 2) = 0
x - 11/6 = 0  or  x - 2 = 0
x = 11/6
x = 2


Input:
Solve the equations:
10x + 6y = 6
7x + 5y = 5

Output:
10x + 6y = 6
7x + 5y = 5

Using elimination
7*(10x + 6y = 6)
10*(7x + 5y = 5)
70x + 42y = 42
70x + 50y = 50
Subtract equations
-8y = -8
y = -8/-8
y = 1

Substitute y
10x + 6(1) = 6
10x = 0
x = 0/10
x = 0


Input: What value of x satisfies x^3 - 229/12x^2 - 109/6x - 10/3 = 0

Output:
x^3 - 229/12x^2 - 109/6x - 10/3 = 0
(x - 20)(x - -1/4)(x - -2/3) = 0
x - 20 = 0
x - -1/4 = 0
x - -2/3 = 0
x = 20
x = -1/4
x = -2/3


Input:
Solve simultaneously:
10x + 6y = 37/2
9x + 8y = 179/12

Output:
10x + 6y = 37/2
9x + 8y = 179/12

Using elimination
9*(10x + 6y = 37/2)
10*(9x + 8y = 179/12)
90x + 54y = 333/2
90x + 80y = 895/6
Subtract equations
-26y = 52/3
y = 52/3/-26
y = -2/3

Substitute y
10x + 6(-2/3) = 37/2
10x = 45/2
x = 45/2/10
x = 9/4


Input:
Find x and y such that
1x + 4y = 3/10
4x + 2y = -29/5

Output:
1x + 4y = 3/10
4x + 2y = -29/5

Using elimination
4*(1x + 4y = 3/10)
1*(4x + 2y = -29/5)
4x + 16y = 6/5
4x + 2y = -29/5
Subtract equations
14y = 7
y = 7/14
y = 1/2

Substitute y
1x + 4(1/2) = 3/10
1x = -17/10
x = -17/10/1
x = -17/10


Input:
Solve the system:
7x + 10y = -153
10x + 5y = -70

Output:
7x + 10y = -153
10x + 5y = -70

Using elimination
10*(7x + 10y = -153)
7*(10x + 5y = -70)
70x + 100y = -1530
70x + 35y = -490
Subtract equations
65y = -1040
y = -1040/65
y = -16

Substitute y
7x + 10(-16) = -153
7x = 7
x = 7/7
x = 1


Input: Find the solution to 2x + 1 = 0

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


Input: Determine x in 6x - 3/4 = 0

Output:
6x - 3/4 = 0
6x = 3/4
x = 3/4 / 6
x = 1/8


Input: Solve quickly: 5x - 5 = 0

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


Input: Determine x in x^2 - 26/7x + 15/7 = 0

Output:
x^2 - 26/7x + 15/7 = 0
(x - 3)(x - 5/7) = 0
x - 3 = 0  or  x - 5/7 = 0
x = 3
x = 5/7


Input:
Solve the system:
3x + 8y = -86/5
3x + 7y = -76/5

Output:
3x + 8y = -86/5
3x + 7y = -76/5

Using elimination
3*(3x + 8y = -86/5)
3*(3x + 7y = -76/5)
9x + 24y = -258/5
9x + 21y = -228/5
Subtract equations
3y = -6
y = -6/3
y = -2

Substitute y
3x + 8(-2) = -86/5
3x = -6/5
x = -6/5/3
x = -2/5


Input: Solve 5x - 25/6 = 0

Output:
5x - 25/6 = 0
5x = 25/6
x = 25/6 / 5
x = 5/6


Input:
Find x and y such that
6x + 5y = 1/10
2x + 2y = 0

Output:
6x + 5y = 1/10
2x + 2y = 0

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

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


Input: Determine x in x^3 - 451/60x^2 + 331/20x - 34/3 = 0

Output:
x^3 - 451/60x^2 + 331/20x - 34/3 = 0
(x - 5/3)(x - 8/5)(x - 17/4) = 0
x - 5/3 = 0
x - 8/5 = 0
x - 17/4 = 0
x = 5/3
x = 8/5
x = 17/4


Input: Compute the solution of 5x + 20/3 = 0

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


Input: What value of x satisfies x^3 - 281/12x^2 + 1037/12x - 95/2 = 0

Output:
x^3 - 281/12x^2 + 1037/12x - 95/2 = 0
(x - 15/4)(x - 2/3)(x - 19) = 0
x - 15/4 = 0
x - 2/3 = 0
x - 19 = 0
x = 15/4
x = 2/3
x = 19


Input: Determine x in x^3 - 22/7x^2 + 1/7x + 30/7 = 0

Output:
x^3 - 22/7x^2 + 1/7x + 30/7 = 0
(x - 2)(x - -1)(x - 15/7) = 0
x - 2 = 0
x - -1 = 0
x - 15/7 = 0
x = 2
x = -1
x = 15/7


Input:
Solve simultaneously:
3x + 6y = -129/14
6x + 10y = -181/14

Output:
3x + 6y = -129/14
6x + 10y = -181/14

Using elimination
6*(3x + 6y = -129/14)
3*(6x + 10y = -181/14)
18x + 36y = -387/7
18x + 30y = -543/14
Subtract equations
6y = -33/2
y = -33/2/6
y = -11/4

Substitute y
3x + 6(-11/4) = -129/14
3x = 51/7
x = 51/7/3
x = 17/7


Input:
Solve the system:
9x + 10y = -29
3x + 1y = -17/2

Output:
9x + 10y = -29
3x + 1y = -17/2

Using elimination
3*(9x + 10y = -29)
9*(3x + 1y = -17/2)
27x + 30y = -87
27x + 9y = -153/2
Subtract equations
21y = -21/2
y = -21/2/21
y = -1/2

Substitute y
9x + 10(-1/2) = -29
9x = -24
x = -24/9
x = -8/3


Input: Find x for 7x + 70/9 = 0

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


Input: Determine x in x^3 - 203/90x^2 - 11/18x + 119/45 = 0

Output:
x^3 - 203/90x^2 - 11/18x + 119/45 = 0
(x - 17/10)(x - 14/9)(x - -1) = 0
x - 17/10 = 0
x - 14/9 = 0
x - -1 = 0
x = 17/10
x = 14/9
x = -1


Input:
Solve simultaneously:
5x + 10y = -40/3
5x + 2y = -88/3

Output:
5x + 10y = -40/3
5x + 2y = -88/3

Using elimination
5*(5x + 10y = -40/3)
5*(5x + 2y = -88/3)
25x + 50y = -200/3
25x + 10y = -440/3
Subtract equations
40y = 80
y = 80/40
y = 2

Substitute y
5x + 10(2) = -40/3
5x = -100/3
x = -100/3/5
x = -20/3


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

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


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

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


Input:
Solve the system:
8x + 3y = -121/3
5x + 5y = -230/9

Output:
8x + 3y = -121/3
5x + 5y = -230/9

Using elimination
5*(8x + 3y = -121/3)
8*(5x + 5y = -230/9)
40x + 15y = -605/3
40x + 40y = -1840/9
Subtract equations
-25y = 25/9
y = 25/9/-25
y = -1/9

Substitute y
8x + 3(-1/9) = -121/3
8x = -40
x = -40/8
x = -5


Input: Solve x^2 + 2x - 15 = 0

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


Input: Compute the solution of x^3 + 7/10x^2 - 9/50x  = 0

Output:
x^3 + 7/10x^2 - 9/50x  = 0
(x - 0)(x - -9/10)(x - 1/5) = 0
x - 0 = 0
x - -9/10 = 0
x - 1/5 = 0
x = 0
x = -9/10
x = 1/5


Input: Find x for x^3 + 116/105x^2 - 44/7x + 80/21 = 0

Output:
x^3 + 116/105x^2 - 44/7x + 80/21 = 0
(x - 4/5)(x - -10/3)(x - 10/7) = 0
x - 4/5 = 0
x - -10/3 = 0
x - 10/7 = 0
x = 4/5
x = -10/3
x = 10/7


Input: What value of x satisfies x^2 - 19/9x + 26/27 = 0

Output:
x^2 - 19/9x + 26/27 = 0
(x - 13/9)(x - 2/3) = 0
x - 13/9 = 0  or  x - 2/3 = 0
x = 13/9
x = 2/3


Input: Compute the solution of x^3 - 73/60x^2 - 113/60x + 3/2 = 0

Output:
x^3 - 73/60x^2 - 113/60x + 3/2 = 0
(x - 9/5)(x - -5/4)(x - 2/3) = 0
x - 9/5 = 0
x - -5/4 = 0
x - 2/3 = 0
x = 9/5
x = -5/4
x = 2/3


Input:
Solve the system:
3x + 7y = -17/3
1x + 10y = -809/63

Output:
3x + 7y = -17/3
1x + 10y = -809/63

Using elimination
1*(3x + 7y = -17/3)
3*(1x + 10y = -809/63)
3x + 7y = -17/3
3x + 30y = -809/21
Subtract equations
-23y = 230/7
y = 230/7/-23
y = -10/7

Substitute y
3x + 7(-10/7) = -17/3
3x = 13/3
x = 13/3/3
x = 13/9


Input: Solve quickly: x^3 + 23/18x^2 - 491/18x + 130/3 = 0

Output:
x^3 + 23/18x^2 - 491/18x + 130/3 = 0
(x - 20/9)(x - -13/2)(x - 3) = 0
x - 20/9 = 0
x - -13/2 = 0
x - 3 = 0
x = 20/9
x = -13/2
x = 3


Input:
Solve simultaneously:
4x + 5y = 22
4x + 9y = 182/5

Output:
4x + 5y = 22
4x + 9y = 182/5

Using elimination
4*(4x + 5y = 22)
4*(4x + 9y = 182/5)
16x + 20y = 88
16x + 36y = 728/5
Subtract equations
-16y = -288/5
y = -288/5/-16
y = 18/5

Substitute y
4x + 5(18/5) = 22
4x = 4
x = 4/4
x = 1


Input: Determine x in x^3 - 113/4x^2 + 343/2x + 392 = 0

Output:
x^3 - 113/4x^2 + 343/2x + 392 = 0
(x - -7/4)(x - 16)(x - 14) = 0
x - -7/4 = 0
x - 16 = 0
x - 14 = 0
x = -7/4
x = 16
x = 14


Input: Compute the solution of x^3 + 2/5x^2 - 311/100x - 153/100 = 0

Output:
x^3 + 2/5x^2 - 311/100x - 153/100 = 0
(x - -1/2)(x - -17/10)(x - 9/5) = 0
x - -1/2 = 0
x - -17/10 = 0
x - 9/5 = 0
x = -1/2
x = -17/10
x = 9/5


Input: Find x for x^3 - 408/35x^2 - 2304/35x - 2048/35 = 0

Output:
x^3 - 408/35x^2 - 2304/35x - 2048/35 = 0
(x - 16)(x - -8/7)(x - -16/5) = 0
x - 16 = 0
x - -8/7 = 0
x - -16/5 = 0
x = 16
x = -8/7
x = -16/5


Input: Determine x in x^2 + 62/7x - 80/7 = 0

Output:
x^2 + 62/7x - 80/7 = 0
(x - 8/7)(x - -10) = 0
x - 8/7 = 0  or  x - -10 = 0
x = 8/7
x = -10


Input:
Solve the system:
8x + 2y = -295/4
6x + 9y = -495/8

Output:
8x + 2y = -295/4
6x + 9y = -495/8

Using elimination
6*(8x + 2y = -295/4)
8*(6x + 9y = -495/8)
48x + 12y = -885/2
48x + 72y = -495
Subtract equations
-60y = 105/2
y = 105/2/-60
y = -7/8

Substitute y
8x + 2(-7/8) = -295/4
8x = -72
x = -72/8
x = -9


Input: Compute the solution of x^3 + 167/90x^2 + 5/18x - 26/45 = 0

Output:
x^3 + 167/90x^2 + 5/18x - 26/45 = 0
(x - 4/9)(x - -13/10)(x - -1) = 0
x - 4/9 = 0
x - -13/10 = 0
x - -1 = 0
x = 4/9
x = -13/10
x = -1


Input:
Find x and y such that
7x + 7y = 16/3
5x + 8y = 101/21

Output:
7x + 7y = 16/3
5x + 8y = 101/21

Using elimination
5*(7x + 7y = 16/3)
7*(5x + 8y = 101/21)
35x + 35y = 80/3
35x + 56y = 101/3
Subtract equations
-21y = -7
y = -7/-21
y = 1/3

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


Input:
Solve simultaneously:
10x + 5y = 2
7x + 2y = -2/5

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

Using elimination
7*(10x + 5y = 2)
10*(7x + 2y = -2/5)
70x + 35y = 14
70x + 20y = -4
Subtract equations
15y = 18
y = 18/15
y = 6/5

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


Input: Solve x^2 - 103/24x - 95/6 = 0

Output:
x^2 - 103/24x - 95/6 = 0
(x - -19/8)(x - 20/3) = 0
x - -19/8 = 0  or  x - 20/3 = 0
x = -19/8
x = 20/3


Input: Find x in x^2 + 22x + 85 = 0

Output:
x^2 + 22x + 85 = 0
(x - -17)(x - -5) = 0
x - -17 = 0  or  x - -5 = 0
x = -17
x = -5


Input: Solve quickly: x^2 - 34/15x - 13/15 = 0

Output:
x^2 - 34/15x - 13/15 = 0
(x - 13/5)(x - -1/3) = 0
x - 13/5 = 0  or  x - -1/3 = 0
x = 13/5
x = -1/3


Input: Find x for x^2 + 31/3x + 95/12 = 0

Output:
x^2 + 31/3x + 95/12 = 0
(x - -5/6)(x - -19/2) = 0
x - -5/6 = 0  or  x - -19/2 = 0
x = -5/6
x = -19/2


Input:
Find x and y such that
1x + 5y = 68/3
4x + 3y = 544/15

Output:
1x + 5y = 68/3
4x + 3y = 544/15

Using elimination
4*(1x + 5y = 68/3)
1*(4x + 3y = 544/15)
4x + 20y = 272/3
4x + 3y = 544/15
Subtract equations
17y = 272/5
y = 272/5/17
y = 16/5

Substitute y
1x + 5(16/5) = 68/3
1x = 20/3
x = 20/3/1
x = 20/3


Input: Solve quickly: x^3 - 159/20x^2 + 63/5x - 27/5 = 0

Output:
x^3 - 159/20x^2 + 63/5x - 27/5 = 0
(x - 6/5)(x - 6)(x - 3/4) = 0
x - 6/5 = 0
x - 6 = 0
x - 3/4 = 0
x = 6/5
x = 6
x = 3/4


Input:
Solve the equations:
4x + 3y = -113/10
5x + 1y = -89/10

Output:
4x + 3y = -113/10
5x + 1y = -89/10

Using elimination
5*(4x + 3y = -113/10)
4*(5x + 1y = -89/10)
20x + 15y = -113/2
20x + 4y = -178/5
Subtract equations
11y = -209/10
y = -209/10/11
y = -19/10

Substitute y
4x + 3(-19/10) = -113/10
4x = -28/5
x = -28/5/4
x = -7/5


Input: Find x in x^3 + 605/72x^2 - 221/36x - 55/8 = 0

Output:
x^3 + 605/72x^2 - 221/36x - 55/8 = 0
(x - 11/9)(x - -5/8)(x - -9) = 0
x - 11/9 = 0
x - -5/8 = 0
x - -9 = 0
x = 11/9
x = -5/8
x = -9


Input: Find x in x^3 - 134/45x^2 + 77/45x  = 0

Output:
x^3 - 134/45x^2 + 77/45x  = 0
(x - 11/5)(x - 7/9)(x - 0) = 0
x - 11/5 = 0
x - 7/9 = 0
x - 0 = 0
x = 11/5
x = 7/9
x = 0


Input: Find x in 5x  = 0

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


Input: Solve the equation 1x - 9/7 = 0

Output:
1x - 9/7 = 0
1x = 9/7
x = 9/7 / 1
x = 9/7


Input: Solve the equation x^3 - 91/10x^2 + 23x - 88/5 = 0

Output:
x^3 - 91/10x^2 + 23x - 88/5 = 0
(x - 11/2)(x - 2)(x - 8/5) = 0
x - 11/2 = 0
x - 2 = 0
x - 8/5 = 0
x = 11/2
x = 2
x = 8/5


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

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


Input: Solve 4x - 5 = 0

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


Input: Solve 10x - 35 = 0

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


Input:
Solve simultaneously:
9x + 7y = 311/4
7x + 7y = 273/4

Output:
9x + 7y = 311/4
7x + 7y = 273/4

Using elimination
7*(9x + 7y = 311/4)
9*(7x + 7y = 273/4)
63x + 49y = 2177/4
63x + 63y = 2457/4
Subtract equations
-14y = -70
y = -70/-14
y = 5

Substitute y
9x + 7(5) = 311/4
9x = 171/4
x = 171/4/9
x = 19/4


Input: Determine x in 4x - 6 = 0

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


Input: Determine x in x^2 + 13/21x - 20/21 = 0

Output:
x^2 + 13/21x - 20/21 = 0
(x - -4/3)(x - 5/7) = 0
x - -4/3 = 0  or  x - 5/7 = 0
x = -4/3
x = 5/7


Input: Solve quickly: x^2 + 23/10x - 21/10 = 0

Output:
x^2 + 23/10x - 21/10 = 0
(x - 7/10)(x - -3) = 0
x - 7/10 = 0  or  x - -3 = 0
x = 7/10
x = -3


Input: Find x for 3x - 21/5 = 0

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


Input: What value of x satisfies x^3 - 17/5x^2 + 43/20x + 1/4 = 0

Output:
x^3 - 17/5x^2 + 43/20x + 1/4 = 0
(x - 1)(x - 5/2)(x - -1/10) = 0
x - 1 = 0
x - 5/2 = 0
x - -1/10 = 0
x = 1
x = 5/2
x = -1/10


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

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


Input: Find x for x^2 - 9/5x + 9/20 = 0

Output:
x^2 - 9/5x + 9/20 = 0
(x - 3/10)(x - 3/2) = 0
x - 3/10 = 0  or  x - 3/2 = 0
x = 3/10
x = 3/2


Input:
Solve the equations:
2x + 3y = -291/35
3x + 8y = -1503/70

Output:
2x + 3y = -291/35
3x + 8y = -1503/70

Using elimination
3*(2x + 3y = -291/35)
2*(3x + 8y = -1503/70)
6x + 9y = -873/35
6x + 16y = -1503/35
Subtract equations
-7y = 18
y = 18/-7
y = -18/7

Substitute y
2x + 3(-18/7) = -291/35
2x = -3/5
x = -3/5/2
x = -3/10


Input:
Solve simultaneously:
5x + 6y = -43
5x + 3y = -39

Output:
5x + 6y = -43
5x + 3y = -39

Using elimination
5*(5x + 6y = -43)
5*(5x + 3y = -39)
25x + 30y = -215
25x + 15y = -195
Subtract equations
15y = -20
y = -20/15
y = -4/3

Substitute y
5x + 6(-4/3) = -43
5x = -35
x = -35/5
x = -7


Input: Find x for x^2 - 41/3x - 380/3 = 0

Output:
x^2 - 41/3x - 380/3 = 0
(x - 20)(x - -19/3) = 0
x - 20 = 0  or  x - -19/3 = 0
x = 20
x = -19/3


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

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


Input: Compute the solution of x^2 - 166/63x + 13/9 = 0

Output:
x^2 - 166/63x + 13/9 = 0
(x - 7/9)(x - 13/7) = 0
x - 7/9 = 0  or  x - 13/7 = 0
x = 7/9
x = 13/7


Input: Find x for x^3 - 49/18x^2 - 1187/18x + 133/9 = 0

Output:
x^3 - 49/18x^2 - 1187/18x + 133/9 = 0
(x - 19/2)(x - 2/9)(x - -7) = 0
x - 19/2 = 0
x - 2/9 = 0
x - -7 = 0
x = 19/2
x = 2/9
x = -7


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

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


Input: Find the solution to 4x - 19 = 0

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


Input: Find x in x^3 - 8/9x^2 - 1/9x  = 0

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


Input:
Solve the equations:
7x + 8y = 44/5
7x + 7y = 42/5

Output:
7x + 8y = 44/5
7x + 7y = 42/5

Using elimination
7*(7x + 8y = 44/5)
7*(7x + 7y = 42/5)
49x + 56y = 308/5
49x + 49y = 294/5
Subtract equations
7y = 14/5
y = 14/5/7
y = 2/5

Substitute y
7x + 8(2/5) = 44/5
7x = 28/5
x = 28/5/7
x = 4/5


Input: Compute the solution of x^2 - 65/12x + 77/12 = 0

Output:
x^2 - 65/12x + 77/12 = 0
(x - 7/4)(x - 11/3) = 0
x - 7/4 = 0  or  x - 11/3 = 0
x = 7/4
x = 11/3


Input: Solve the equation x^3 - 109/10x^2 - 1043/25x - 588/25 = 0

Output:
x^3 - 109/10x^2 - 1043/25x - 588/25 = 0
(x - -12/5)(x - -7/10)(x - 14) = 0
x - -12/5 = 0
x - -7/10 = 0
x - 14 = 0
x = -12/5
x = -7/10
x = 14


Input: Find x for x^2 - 15/7x + 8/7 = 0

Output:
x^2 - 15/7x + 8/7 = 0
(x - 8/7)(x - 1) = 0
x - 8/7 = 0  or  x - 1 = 0
x = 8/7
x = 1


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

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

Using elimination
2*(3x + 1y = 5/3)
3*(2x + 2y = 10/3)
6x + 2y = 10/3
6x + 6y = 10
Subtract equations
-4y = -20/3
y = -20/3/-4
y = 5/3

Substitute y
3x + 1(5/3) = 5/3
3x = 0
x = 0/3
x = 0


Input: Find x in x^2 - 127/40x - 19/8 = 0

Output:
x^2 - 127/40x - 19/8 = 0
(x - 19/5)(x - -5/8) = 0
x - 19/5 = 0  or  x - -5/8 = 0
x = 19/5
x = -5/8


Input:
Solve the system:
4x + 8y = -14
1x + 7y = 13/2

Output:
4x + 8y = -14
1x + 7y = 13/2

Using elimination
1*(4x + 8y = -14)
4*(1x + 7y = 13/2)
4x + 8y = -14
4x + 28y = 26
Subtract equations
-20y = -40
y = -40/-20
y = 2

Substitute y
4x + 8(2) = -14
4x = -30
x = -30/4
x = -15/2


Input: Find x for 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
8x + 6y = 5
10x + 1y = -33/2

Output:
8x + 6y = 5
10x + 1y = -33/2

Using elimination
10*(8x + 6y = 5)
8*(10x + 1y = -33/2)
80x + 60y = 50
80x + 8y = -132
Subtract equations
52y = 182
y = 182/52
y = 7/2

Substitute y
8x + 6(7/2) = 5
8x = -16
x = -16/8
x = -2


Input: What value of x satisfies 4x - 16/3 = 0

Output:
4x - 16/3 = 0
4x = 16/3
x = 16/3 / 4
x = 4/3


Input: Find x in x^2 + 31/6x + 11/2 = 0

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


Input: Solve the equation 8x + 136/9 = 0

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


Input: Compute the solution of x^3 - 38/3x^2 + 85/3x - 50/3 = 0

Output:
x^3 - 38/3x^2 + 85/3x - 50/3 = 0
(x - 10)(x - 1)(x - 5/3) = 0
x - 10 = 0
x - 1 = 0
x - 5/3 = 0
x = 10
x = 1
x = 5/3


Input: Solve quickly: x^2 + 17x + 16 = 0

Output:
x^2 + 17x + 16 = 0
(x - -16)(x - -1) = 0
x - -16 = 0  or  x - -1 = 0
x = -16
x = -1


Input: Find x in x^2 - 13/3x + 14/3 = 0

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


Input: Solve x^2 - 79/9x + 56/9 = 0

Output:
x^2 - 79/9x + 56/9 = 0
(x - 7/9)(x - 8) = 0
x - 7/9 = 0  or  x - 8 = 0
x = 7/9
x = 8


Input: Find x in x^2 + 27/14x - 11/2 = 0

Output:
x^2 + 27/14x - 11/2 = 0
(x - -7/2)(x - 11/7) = 0
x - -7/2 = 0  or  x - 11/7 = 0
x = -7/2
x = 11/7


Input:
Solve the equations:
5x + 4y = -11/2
4x + 6y = -38

Output:
5x + 4y = -11/2
4x + 6y = -38

Using elimination
4*(5x + 4y = -11/2)
5*(4x + 6y = -38)
20x + 16y = -22
20x + 30y = -190
Subtract equations
-14y = 168
y = 168/-14
y = -12

Substitute y
5x + 4(-12) = -11/2
5x = 85/2
x = 85/2/5
x = 17/2


Input: Find x in x^2 - 16/45x - 1/9 = 0

Output:
x^2 - 16/45x - 1/9 = 0
(x - -1/5)(x - 5/9) = 0
x - -1/5 = 0  or  x - 5/9 = 0
x = -1/5
x = 5/9


Input:
Solve the system:
4x + 1y = -91/15
6x + 9y = -173/5

Output:
4x + 1y = -91/15
6x + 9y = -173/5

Using elimination
6*(4x + 1y = -91/15)
4*(6x + 9y = -173/5)
24x + 6y = -182/5
24x + 36y = -692/5
Subtract equations
-30y = 102
y = 102/-30
y = -17/5

Substitute y
4x + 1(-17/5) = -91/15
4x = -8/3
x = -8/3/4
x = -2/3


Input: Solve x^3 + 137/42x^2 + 61/42x - 5/3 = 0

Output:
x^3 + 137/42x^2 + 61/42x - 5/3 = 0
(x - -7/3)(x - 1/2)(x - -10/7) = 0
x - -7/3 = 0
x - 1/2 = 0
x - -10/7 = 0
x = -7/3
x = 1/2
x = -10/7


Input:
Solve simultaneously:
5x + 6y = -77/3
8x + 7y = -92/3

Output:
5x + 6y = -77/3
8x + 7y = -92/3

Using elimination
8*(5x + 6y = -77/3)
5*(8x + 7y = -92/3)
40x + 48y = -616/3
40x + 35y = -460/3
Subtract equations
13y = -52
y = -52/13
y = -4

Substitute y
5x + 6(-4) = -77/3
5x = -5/3
x = -5/3/5
x = -1/3


Input: What value of x satisfies x^3 - 425/84x^2 + 691/84x - 30/7 = 0

Output:
x^3 - 425/84x^2 + 691/84x - 30/7 = 0
(x - 9/4)(x - 8/7)(x - 5/3) = 0
x - 9/4 = 0
x - 8/7 = 0
x - 5/3 = 0
x = 9/4
x = 8/7
x = 5/3


Input: Compute the solution of x^2 + 12/7x - 27/7 = 0

Output:
x^2 + 12/7x - 27/7 = 0
(x - 9/7)(x - -3) = 0
x - 9/7 = 0  or  x - -3 = 0
x = 9/7
x = -3


Input: Solve the equation x^3 + 28/45x^2 - 28/135x - 16/135 = 0

Output:
x^3 + 28/45x^2 - 28/135x - 16/135 = 0
(x - -2/3)(x - -2/5)(x - 4/9) = 0
x - -2/3 = 0
x - -2/5 = 0
x - 4/9 = 0
x = -2/3
x = -2/5
x = 4/9


Input: Solve x^2 + 15/28x - 27/28 = 0

Output:
x^2 + 15/28x - 27/28 = 0
(x - 3/4)(x - -9/7) = 0
x - 3/4 = 0  or  x - -9/7 = 0
x = 3/4
x = -9/7


Input: Find x for x^2 + 112/45x - 4 = 0

Output:
x^2 + 112/45x - 4 = 0
(x - -18/5)(x - 10/9) = 0
x - -18/5 = 0  or  x - 10/9 = 0
x = -18/5
x = 10/9


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

Output:
x^2 + 5/14x - 3/7 = 0
(x - 1/2)(x - -6/7) = 0
x - 1/2 = 0  or  x - -6/7 = 0
x = 1/2
x = -6/7


Input:
Solve the equations:
8x + 9y = -439/7
5x + 4y = -607/21

Output:
8x + 9y = -439/7
5x + 4y = -607/21

Using elimination
5*(8x + 9y = -439/7)
8*(5x + 4y = -607/21)
40x + 45y = -2195/7
40x + 32y = -4856/21
Subtract equations
13y = -247/3
y = -247/3/13
y = -19/3

Substitute y
8x + 9(-19/3) = -439/7
8x = -40/7
x = -40/7/8
x = -5/7


Input:
Find x and y such that
6x + 2y = -69/4
2x + 10y = -65/4

Output:
6x + 2y = -69/4
2x + 10y = -65/4

Using elimination
2*(6x + 2y = -69/4)
6*(2x + 10y = -65/4)
12x + 4y = -69/2
12x + 60y = -195/2
Subtract equations
-56y = 63
y = 63/-56
y = -9/8

Substitute y
6x + 2(-9/8) = -69/4
6x = -15
x = -15/6
x = -5/2


Input:
Solve the system:
7x + 1y = -96/5
2x + 9y = -193/5

Output:
7x + 1y = -96/5
2x + 9y = -193/5

Using elimination
2*(7x + 1y = -96/5)
7*(2x + 9y = -193/5)
14x + 2y = -192/5
14x + 63y = -1351/5
Subtract equations
-61y = 1159/5
y = 1159/5/-61
y = -19/5

Substitute y
7x + 1(-19/5) = -96/5
7x = -77/5
x = -77/5/7
x = -11/5


Input: Compute the solution of x^2 + 59/8x + 33/4 = 0

Output:
x^2 + 59/8x + 33/4 = 0
(x - -6)(x - -11/8) = 0
x - -6 = 0  or  x - -11/8 = 0
x = -6
x = -11/8


Input: Find x in 5x + 5/7 = 0

Output:
5x + 5/7 = 0
5x = -5/7
x = -5/7 / 5
x = -1/7


Input: Compute the solution of x^3 + 13/10x^2 - 39/2x + 99/5 = 0

Output:
x^3 + 13/10x^2 - 39/2x + 99/5 = 0
(x - -11/2)(x - 3)(x - 6/5) = 0
x - -11/2 = 0
x - 3 = 0
x - 6/5 = 0
x = -11/2
x = 3
x = 6/5


Input: Solve the equation 8x - 16 = 0

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


Input: Find the solution to x^3 + 81/10x^2 + 512/25x + 408/25 = 0

Output:
x^3 + 81/10x^2 + 512/25x + 408/25 = 0
(x - -12/5)(x - -4)(x - -17/10) = 0
x - -12/5 = 0
x - -4 = 0
x - -17/10 = 0
x = -12/5
x = -4
x = -17/10


Input: Solve x^2 - 29/10x - 117/5 = 0

Output:
x^2 - 29/10x - 117/5 = 0
(x - 13/2)(x - -18/5) = 0
x - 13/2 = 0  or  x - -18/5 = 0
x = 13/2
x = -18/5


Input: Find x for x^3 + 1/5x^2 - 669/100x + 513/100 = 0

Output:
x^3 + 1/5x^2 - 669/100x + 513/100 = 0
(x - 9/10)(x - -3)(x - 19/10) = 0
x - 9/10 = 0
x - -3 = 0
x - 19/10 = 0
x = 9/10
x = -3
x = 19/10


Input: Solve quickly: x^3 + 151/168x^2 - 1535/336x - 221/56 = 0

Output:
x^3 + 151/168x^2 - 1535/336x - 221/56 = 0
(x - -6/7)(x - -13/6)(x - 17/8) = 0
x - -6/7 = 0
x - -13/6 = 0
x - 17/8 = 0
x = -6/7
x = -13/6
x = 17/8


Input:
Find x and y such that
8x + 2y = -139/9
5x + 2y = -88/9

Output:
8x + 2y = -139/9
5x + 2y = -88/9

Using elimination
5*(8x + 2y = -139/9)
8*(5x + 2y = -88/9)
40x + 10y = -695/9
40x + 16y = -704/9
Subtract equations
-6y = 1
y = 1/-6
y = -1/6

Substitute y
8x + 2(-1/6) = -139/9
8x = -136/9
x = -136/9/8
x = -17/9


Input: Compute the solution of x^3 + 8/15x^2 + 37/405x + 2/405 = 0

Output:
x^3 + 8/15x^2 + 37/405x + 2/405 = 0
(x - -2/9)(x - -1/9)(x - -1/5) = 0
x - -2/9 = 0
x - -1/9 = 0
x - -1/5 = 0
x = -2/9
x = -1/9
x = -1/5


Input: Solve x^3 - 17/2x^2 + 247/18x  = 0

Output:
x^3 - 17/2x^2 + 247/18x  = 0
(x - 0)(x - 13/6)(x - 19/3) = 0
x - 0 = 0
x - 13/6 = 0
x - 19/3 = 0
x = 0
x = 13/6
x = 19/3


Input: Determine x in x^3 + 1/10x^2 - 15/2x + 18/5 = 0

Output:
x^3 + 1/10x^2 - 15/2x + 18/5 = 0
(x - -3)(x - 12/5)(x - 1/2) = 0
x - -3 = 0
x - 12/5 = 0
x - 1/2 = 0
x = -3
x = 12/5
x = 1/2


Input:
Find x and y such that
1x + 10y = 31/4
5x + 9y = -9/4

Output:
1x + 10y = 31/4
5x + 9y = -9/4

Using elimination
5*(1x + 10y = 31/4)
1*(5x + 9y = -9/4)
5x + 50y = 155/4
5x + 9y = -9/4
Subtract equations
41y = 41
y = 41/41
y = 1

Substitute y
1x + 10(1) = 31/4
1x = -9/4
x = -9/4/1
x = -9/4


Input: Find x for x^2 + 32/15x + 16/15 = 0

Output:
x^2 + 32/15x + 16/15 = 0
(x - -4/3)(x - -4/5) = 0
x - -4/3 = 0  or  x - -4/5 = 0
x = -4/3
x = -4/5


Input:
Solve simultaneously:
3x + 1y = -2
6x + 1y = 1

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

Using elimination
6*(3x + 1y = -2)
3*(6x + 1y = 1)
18x + 6y = -12
18x + 3y = 3
Subtract equations
3y = -15
y = -15/3
y = -5

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


Input:
Solve simultaneously:
5x + 2y = -119/4
5x + 10y = -115/4

Output:
5x + 2y = -119/4
5x + 10y = -115/4

Using elimination
5*(5x + 2y = -119/4)
5*(5x + 10y = -115/4)
25x + 10y = -595/4
25x + 50y = -575/4
Subtract equations
-40y = -5
y = -5/-40
y = 1/8

Substitute y
5x + 2(1/8) = -119/4
5x = -30
x = -30/5
x = -6


Input:
Solve simultaneously:
2x + 2y = -7/9
10x + 7y = -83/9

Output:
2x + 2y = -7/9
10x + 7y = -83/9

Using elimination
10*(2x + 2y = -7/9)
2*(10x + 7y = -83/9)
20x + 20y = -70/9
20x + 14y = -166/9
Subtract equations
6y = 32/3
y = 32/3/6
y = 16/9

Substitute y
2x + 2(16/9) = -7/9
2x = -13/3
x = -13/3/2
x = -13/6


Input: Determine x in x^2 - 7/9x - 22/9 = 0

Output:
x^2 - 7/9x - 22/9 = 0
(x - 2)(x - -11/9) = 0
x - 2 = 0  or  x - -11/9 = 0
x = 2
x = -11/9


Input: What value of x satisfies x^2 + 13/2x + 15/2 = 0

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


Input:
Solve the system:
10x + 10y = -45
3x + 5y = -39/2

Output:
10x + 10y = -45
3x + 5y = -39/2

Using elimination
3*(10x + 10y = -45)
10*(3x + 5y = -39/2)
30x + 30y = -135
30x + 50y = -195
Subtract equations
-20y = 60
y = 60/-20
y = -3

Substitute y
10x + 10(-3) = -45
10x = -15
x = -15/10
x = -3/2


Input: Determine x in x^3 + 44/9x^2 + 68/9x + 32/9 = 0

Output:
x^3 + 44/9x^2 + 68/9x + 32/9 = 0
(x - -2)(x - -8/9)(x - -2) = 0
x - -2 = 0
x - -8/9 = 0
x - -2 = 0
x = -2
x = -8/9
x = -2


Input:
Solve the system:
10x + 7y = 116/3
3x + 1y = 26/3

Output:
10x + 7y = 116/3
3x + 1y = 26/3

Using elimination
3*(10x + 7y = 116/3)
10*(3x + 1y = 26/3)
30x + 21y = 116
30x + 10y = 260/3
Subtract equations
11y = 88/3
y = 88/3/11
y = 8/3

Substitute y
10x + 7(8/3) = 116/3
10x = 20
x = 20/10
x = 2


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

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

Using elimination
3*(2x + 3y = -7/3)
2*(3x + 6y = -6)
6x + 9y = -7
6x + 12y = -12
Subtract equations
-3y = 5
y = 5/-3
y = -5/3

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


Input: Solve x^3 - 19/2x^2 + 12x  = 0

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


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

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


Input:
Solve the equations:
3x + 10y = -25
7x + 9y = -45/2

Output:
3x + 10y = -25
7x + 9y = -45/2

Using elimination
7*(3x + 10y = -25)
3*(7x + 9y = -45/2)
21x + 70y = -175
21x + 27y = -135/2
Subtract equations
43y = -215/2
y = -215/2/43
y = -5/2

Substitute y
3x + 10(-5/2) = -25
3x = 0
x = 0/3
x = 0


Input:
Solve simultaneously:
3x + 6y = -8
3x + 9y = -11

Output:
3x + 6y = -8
3x + 9y = -11

Using elimination
3*(3x + 6y = -8)
3*(3x + 9y = -11)
9x + 18y = -24
9x + 27y = -33
Subtract equations
-9y = 9
y = 9/-9
y = -1

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


Input:
Solve simultaneously:
9x + 1y = 83/10
10x + 7y = 95/2

Output:
9x + 1y = 83/10
10x + 7y = 95/2

Using elimination
10*(9x + 1y = 83/10)
9*(10x + 7y = 95/2)
90x + 10y = 83
90x + 63y = 855/2
Subtract equations
-53y = -689/2
y = -689/2/-53
y = 13/2

Substitute y
9x + 1(13/2) = 83/10
9x = 9/5
x = 9/5/9
x = 1/5


Input:
Solve simultaneously:
10x + 4y = -189/10
10x + 5y = -18

Output:
10x + 4y = -189/10
10x + 5y = -18

Using elimination
10*(10x + 4y = -189/10)
10*(10x + 5y = -18)
100x + 40y = -189
100x + 50y = -180
Subtract equations
-10y = -9
y = -9/-10
y = 9/10

Substitute y
10x + 4(9/10) = -189/10
10x = -45/2
x = -45/2/10
x = -9/4


Input:
Solve the system:
3x + 5y = 41/10
9x + 1y = -17/10

Output:
3x + 5y = 41/10
9x + 1y = -17/10

Using elimination
9*(3x + 5y = 41/10)
3*(9x + 1y = -17/10)
27x + 45y = 369/10
27x + 3y = -51/10
Subtract equations
42y = 42
y = 42/42
y = 1

Substitute y
3x + 5(1) = 41/10
3x = -9/10
x = -9/10/3
x = -3/10


Input: Find x for 10x + 170 = 0

Output:
10x + 170 = 0
10x = -170
x = -170 / 10
x = -17


Input: Compute the solution of x^3 + 57/10x^2 - 152/5x - 63/10 = 0

Output:
x^3 + 57/10x^2 - 152/5x - 63/10 = 0
(x - -1/5)(x - -9)(x - 7/2) = 0
x - -1/5 = 0
x - -9 = 0
x - 7/2 = 0
x = -1/5
x = -9
x = 7/2


Input: Solve quickly: x^3 - 27/10x^2 - 89/45x + 68/15 = 0

Output:
x^3 - 27/10x^2 - 89/45x + 68/15 = 0
(x - 17/6)(x - 6/5)(x - -4/3) = 0
x - 17/6 = 0
x - 6/5 = 0
x - -4/3 = 0
x = 17/6
x = 6/5
x = -4/3


Input: Solve x^2 + 23/3x - 12 = 0

Output:
x^2 + 23/3x - 12 = 0
(x - -9)(x - 4/3) = 0
x - -9 = 0  or  x - 4/3 = 0
x = -9
x = 4/3


Input: Find x for x^3 - 3/2x^2 - 31/25x + 12/25 = 0

Output:
x^3 - 3/2x^2 - 31/25x + 12/25 = 0
(x - 3/10)(x - 2)(x - -4/5) = 0
x - 3/10 = 0
x - 2 = 0
x - -4/5 = 0
x = 3/10
x = 2
x = -4/5


Input: Solve the equation 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: Determine x in x^3 + 23/20x^2 - 19/8x + 9/40 = 0

Output:
x^3 + 23/20x^2 - 19/8x + 9/40 = 0
(x - 1/10)(x - 1)(x - -9/4) = 0
x - 1/10 = 0
x - 1 = 0
x - -9/4 = 0
x = 1/10
x = 1
x = -9/4


Input: Find the solution to x^3 - 27x^2 + 1610/9x - 304 = 0

Output:
x^3 - 27x^2 + 1610/9x - 304 = 0
(x - 8/3)(x - 19/3)(x - 18) = 0
x - 8/3 = 0
x - 19/3 = 0
x - 18 = 0
x = 8/3
x = 19/3
x = 18


Input:
Solve simultaneously:
4x + 1y = -23/2
4x + 10y = -97

Output:
4x + 1y = -23/2
4x + 10y = -97

Using elimination
4*(4x + 1y = -23/2)
4*(4x + 10y = -97)
16x + 4y = -46
16x + 40y = -388
Subtract equations
-36y = 342
y = 342/-36
y = -19/2

Substitute y
4x + 1(-19/2) = -23/2
4x = -2
x = -2/4
x = -1/2


Input:
Solve the equations:
7x + 7y = 19
8x + 7y = 150/7

Output:
7x + 7y = 19
8x + 7y = 150/7

Using elimination
8*(7x + 7y = 19)
7*(8x + 7y = 150/7)
56x + 56y = 152
56x + 49y = 150
Subtract equations
7y = 2
y = 2/7
y = 2/7

Substitute y
7x + 7(2/7) = 19
7x = 17
x = 17/7
x = 17/7


Input: Solve quickly: x^3 - 17/7x^2 - 44/7x  = 0

Output:
x^3 - 17/7x^2 - 44/7x  = 0
(x - -11/7)(x - 4)(x - 0) = 0
x - -11/7 = 0
x - 4 = 0
x - 0 = 0
x = -11/7
x = 4
x = 0


Input: Solve the equation x^3 + 2/3x^2 - 103/3x - 190/3 = 0

Output:
x^3 + 2/3x^2 - 103/3x - 190/3 = 0
(x - 19/3)(x - -5)(x - -2) = 0
x - 19/3 = 0
x - -5 = 0
x - -2 = 0
x = 19/3
x = -5
x = -2


Input:
Solve the system:
1x + 4y = -2
4x + 10y = -2

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

Using elimination
4*(1x + 4y = -2)
1*(4x + 10y = -2)
4x + 16y = -8
4x + 10y = -2
Subtract equations
6y = -6
y = -6/6
y = -1

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


Input: Solve the equation x^2 - 39/8x + 7/2 = 0

Output:
x^2 - 39/8x + 7/2 = 0
(x - 7/8)(x - 4) = 0
x - 7/8 = 0  or  x - 4 = 0
x = 7/8
x = 4


Input:
Solve the equations:
7x + 2y = -29/10
4x + 5y = -14

Output:
7x + 2y = -29/10
4x + 5y = -14

Using elimination
4*(7x + 2y = -29/10)
7*(4x + 5y = -14)
28x + 8y = -58/5
28x + 35y = -98
Subtract equations
-27y = 432/5
y = 432/5/-27
y = -16/5

Substitute y
7x + 2(-16/5) = -29/10
7x = 7/2
x = 7/2/7
x = 1/2


Input: Find x for 7x + 77 = 0

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


Input: Find the solution to 3x + 6/5 = 0

Output:
3x + 6/5 = 0
3x = -6/5
x = -6/5 / 3
x = -2/5


Input: Solve quickly: x^3 - 47/10x^2 + 179/25x - 88/25 = 0

Output:
x^3 - 47/10x^2 + 179/25x - 88/25 = 0
(x - 2)(x - 8/5)(x - 11/10) = 0
x - 2 = 0
x - 8/5 = 0
x - 11/10 = 0
x = 2
x = 8/5
x = 11/10


Input: Find the solution to x^3 - 5x^2 - 22x + 56 = 0

Output:
x^3 - 5x^2 - 22x + 56 = 0
(x - -4)(x - 7)(x - 2) = 0
x - -4 = 0
x - 7 = 0
x - 2 = 0
x = -4
x = 7
x = 2


Input:
Solve the equations:
10x + 3y = -959/72
10x + 8y = -103/9

Output:
10x + 3y = -959/72
10x + 8y = -103/9

Using elimination
10*(10x + 3y = -959/72)
10*(10x + 8y = -103/9)
100x + 30y = -4795/36
100x + 80y = -1030/9
Subtract equations
-50y = -75/4
y = -75/4/-50
y = 3/8

Substitute y
10x + 3(3/8) = -959/72
10x = -130/9
x = -130/9/10
x = -13/9


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

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


Input: Solve the equation x^3 - 443/24x^2 + 113/24x + 255/4 = 0

Output:
x^3 - 443/24x^2 + 113/24x + 255/4 = 0
(x - -5/3)(x - 18)(x - 17/8) = 0
x - -5/3 = 0
x - 18 = 0
x - 17/8 = 0
x = -5/3
x = 18
x = 17/8


Input: Find x for x^3 + 43/14x^2 - 10/7x - 50/7 = 0

Output:
x^3 + 43/14x^2 - 10/7x - 50/7 = 0
(x - 10/7)(x - -2)(x - -5/2) = 0
x - 10/7 = 0
x - -2 = 0
x - -5/2 = 0
x = 10/7
x = -2
x = -5/2


Input: Determine x in 1x - 2 = 0

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


Input: Find x in x^3 - 279/14x^2 + 51x - 289/14 = 0

Output:
x^3 - 279/14x^2 + 51x - 289/14 = 0
(x - 17)(x - 1/2)(x - 17/7) = 0
x - 17 = 0
x - 1/2 = 0
x - 17/7 = 0
x = 17
x = 1/2
x = 17/7


Input: Determine x in 10x - 5/2 = 0

Output:
10x - 5/2 = 0
10x = 5/2
x = 5/2 / 10
x = 1/4


Input: Determine x in 6x - 72 = 0

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


Input:
Find x and y such that
10x + 3y = -37/2
1x + 6y = -53/4

Output:
10x + 3y = -37/2
1x + 6y = -53/4

Using elimination
1*(10x + 3y = -37/2)
10*(1x + 6y = -53/4)
10x + 3y = -37/2
10x + 60y = -265/2
Subtract equations
-57y = 114
y = 114/-57
y = -2

Substitute y
10x + 3(-2) = -37/2
10x = -25/2
x = -25/2/10
x = -5/4


Input:
Solve the system:
8x + 1y = 16/3
7x + 5y = 61/6

Output:
8x + 1y = 16/3
7x + 5y = 61/6

Using elimination
7*(8x + 1y = 16/3)
8*(7x + 5y = 61/6)
56x + 7y = 112/3
56x + 40y = 244/3
Subtract equations
-33y = -44
y = -44/-33
y = 4/3

Substitute y
8x + 1(4/3) = 16/3
8x = 4
x = 4/8
x = 1/2


Input: Solve 1x - 17/10 = 0

Output:
1x - 17/10 = 0
1x = 17/10
x = 17/10 / 1
x = 17/10


Input: Solve quickly: 1x - 8/7 = 0

Output:
1x - 8/7 = 0
1x = 8/7
x = 8/7 / 1
x = 8/7


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

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


Input: Find x for x^3 + 1/2x^2 - 149/18x + 35/9 = 0

Output:
x^3 + 1/2x^2 - 149/18x + 35/9 = 0
(x - 7/3)(x - 1/2)(x - -10/3) = 0
x - 7/3 = 0
x - 1/2 = 0
x - -10/3 = 0
x = 7/3
x = 1/2
x = -10/3


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

Output:
8x + 5y = -1
5x + 6y = 8

Using elimination
5*(8x + 5y = -1)
8*(5x + 6y = 8)
40x + 25y = -5
40x + 48y = 64
Subtract equations
-23y = -69
y = -69/-23
y = 3

Substitute y
8x + 5(3) = -1
8x = -16
x = -16/8
x = -2


Input: Find x for 9x - 63/5 = 0

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


Input: Solve quickly: 10x + 13 = 0

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


Input: Find x for x^2 + 19/2x + 22 = 0

Output:
x^2 + 19/2x + 22 = 0
(x - -11/2)(x - -4) = 0
x - -11/2 = 0  or  x - -4 = 0
x = -11/2
x = -4


Input:
Find x and y such that
9x + 6y = -72
3x + 7y = -84

Output:
9x + 6y = -72
3x + 7y = -84

Using elimination
3*(9x + 6y = -72)
9*(3x + 7y = -84)
27x + 18y = -216
27x + 63y = -756
Subtract equations
-45y = 540
y = 540/-45
y = -12

Substitute y
9x + 6(-12) = -72
9x = 0
x = 0/9
x = 0


Input:
Solve the system:
5x + 3y = -17/2
10x + 4y = -18

Output:
5x + 3y = -17/2
10x + 4y = -18

Using elimination
10*(5x + 3y = -17/2)
5*(10x + 4y = -18)
50x + 30y = -85
50x + 20y = -90
Subtract equations
10y = 5
y = 5/10
y = 1/2

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


Input: What value of x satisfies 10x + 140/3 = 0

Output:
10x + 140/3 = 0
10x = -140/3
x = -140/3 / 10
x = -14/3


Input:
Solve the equations:
7x + 4y = 106/5
2x + 4y = 76/5

Output:
7x + 4y = 106/5
2x + 4y = 76/5

Using elimination
2*(7x + 4y = 106/5)
7*(2x + 4y = 76/5)
14x + 8y = 212/5
14x + 28y = 532/5
Subtract equations
-20y = -64
y = -64/-20
y = 16/5

Substitute y
7x + 4(16/5) = 106/5
7x = 42/5
x = 42/5/7
x = 6/5


Input: Determine x in 8x + 76/5 = 0

Output:
8x + 76/5 = 0
8x = -76/5
x = -76/5 / 8
x = -19/10


Input: Find the solution to x^2 + 91/40x - 19/80 = 0

Output:
x^2 + 91/40x - 19/80 = 0
(x - 1/10)(x - -19/8) = 0
x - 1/10 = 0  or  x - -19/8 = 0
x = 1/10
x = -19/8


Input: Solve quickly: 5x + 2 = 0

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


Input: Compute the solution of 4x - 48/5 = 0

Output:
4x - 48/5 = 0
4x = 48/5
x = 48/5 / 4
x = 12/5


Input: Determine x in x^2 - 23/6x + 11/3 = 0

Output:
x^2 - 23/6x + 11/3 = 0
(x - 2)(x - 11/6) = 0
x - 2 = 0  or  x - 11/6 = 0
x = 2
x = 11/6


Input:
Solve simultaneously:
3x + 5y = -173/2
7x + 1y = -59/6

Output:
3x + 5y = -173/2
7x + 1y = -59/6

Using elimination
7*(3x + 5y = -173/2)
3*(7x + 1y = -59/6)
21x + 35y = -1211/2
21x + 3y = -59/2
Subtract equations
32y = -576
y = -576/32
y = -18

Substitute y
3x + 5(-18) = -173/2
3x = 7/2
x = 7/2/3
x = 7/6


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

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


Input: Compute the solution of x^3 - 21/40x^2 - 79/10x - 51/8 = 0

Output:
x^3 - 21/40x^2 - 79/10x - 51/8 = 0
(x - -1)(x - -15/8)(x - 17/5) = 0
x - -1 = 0
x - -15/8 = 0
x - 17/5 = 0
x = -1
x = -15/8
x = 17/5


Input: Find the solution to 8x - 12/5 = 0

Output:
8x - 12/5 = 0
8x = 12/5
x = 12/5 / 8
x = 3/10


Input:
Solve the equations:
3x + 10y = 73/7
2x + 6y = 44/7

Output:
3x + 10y = 73/7
2x + 6y = 44/7

Using elimination
2*(3x + 10y = 73/7)
3*(2x + 6y = 44/7)
6x + 20y = 146/7
6x + 18y = 132/7
Subtract equations
2y = 2
y = 2/2
y = 1

Substitute y
3x + 10(1) = 73/7
3x = 3/7
x = 3/7/3
x = 1/7


Input: Solve x^3 + 124/9x^2 + 77/3x - 484/9 = 0

Output:
x^3 + 124/9x^2 + 77/3x - 484/9 = 0
(x - -11)(x - -4)(x - 11/9) = 0
x - -11 = 0
x - -4 = 0
x - 11/9 = 0
x = -11
x = -4
x = 11/9


Input: Compute the solution of x^2 + 89/56x - 15/28 = 0

Output:
x^2 + 89/56x - 15/28 = 0
(x - -15/8)(x - 2/7) = 0
x - -15/8 = 0  or  x - 2/7 = 0
x = -15/8
x = 2/7


Input:
Solve the equations:
2x + 10y = -255/7
10x + 3y = -247/14

Output:
2x + 10y = -255/7
10x + 3y = -247/14

Using elimination
10*(2x + 10y = -255/7)
2*(10x + 3y = -247/14)
20x + 100y = -2550/7
20x + 6y = -247/7
Subtract equations
94y = -329
y = -329/94
y = -7/2

Substitute y
2x + 10(-7/2) = -255/7
2x = -10/7
x = -10/7/2
x = -5/7


Input: Solve 2x - 3 = 0

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


Input: Solve x^3 - 301/30x^2 + 773/30x - 91/5 = 0

Output:
x^3 - 301/30x^2 + 773/30x - 91/5 = 0
(x - 6/5)(x - 13/2)(x - 7/3) = 0
x - 6/5 = 0
x - 13/2 = 0
x - 7/3 = 0
x = 6/5
x = 13/2
x = 7/3


Input: Solve the equation x^2 - 19/42x - 88/21 = 0

Output:
x^2 - 19/42x - 88/21 = 0
(x - 16/7)(x - -11/6) = 0
x - 16/7 = 0  or  x - -11/6 = 0
x = 16/7
x = -11/6


Input: Solve x^3 - 157/9x^2 + 1378/27x - 1064/27 = 0

Output:
x^3 - 157/9x^2 + 1378/27x - 1064/27 = 0
(x - 4/3)(x - 14)(x - 19/9) = 0
x - 4/3 = 0
x - 14 = 0
x - 19/9 = 0
x = 4/3
x = 14
x = 19/9


Input:
Solve the system:
1x + 9y = -145/8
7x + 8y = -10

Output:
1x + 9y = -145/8
7x + 8y = -10

Using elimination
7*(1x + 9y = -145/8)
1*(7x + 8y = -10)
7x + 63y = -1015/8
7x + 8y = -10
Subtract equations
55y = -935/8
y = -935/8/55
y = -17/8

Substitute y
1x + 9(-17/8) = -145/8
1x = 1
x = 1/1
x = 1


Input: What value of x satisfies x^2 - 73/15x + 22/5 = 0

Output:
x^2 - 73/15x + 22/5 = 0
(x - 11/3)(x - 6/5) = 0
x - 11/3 = 0  or  x - 6/5 = 0
x = 11/3
x = 6/5


Input: Find x for x^2 + 22/9x + 8/9 = 0

Output:
x^2 + 22/9x + 8/9 = 0
(x - -2)(x - -4/9) = 0
x - -2 = 0  or  x - -4/9 = 0
x = -2
x = -4/9


Input: Find x in x^2 + 30/7x + 216/49 = 0

Output:
x^2 + 30/7x + 216/49 = 0
(x - -18/7)(x - -12/7) = 0
x - -18/7 = 0  or  x - -12/7 = 0
x = -18/7
x = -12/7


Input: Find x for x^2 + 81/5x - 76 = 0

Output:
x^2 + 81/5x - 76 = 0
(x - 19/5)(x - -20) = 0
x - 19/5 = 0  or  x - -20 = 0
x = 19/5
x = -20


Input:
Solve the system:
1x + 1y = -53/10
5x + 8y = -40

Output:
1x + 1y = -53/10
5x + 8y = -40

Using elimination
5*(1x + 1y = -53/10)
1*(5x + 8y = -40)
5x + 5y = -53/2
5x + 8y = -40
Subtract equations
-3y = 27/2
y = 27/2/-3
y = -9/2

Substitute y
1x + 1(-9/2) = -53/10
1x = -4/5
x = -4/5/1
x = -4/5


Input: Find the solution to x^3 + 71/10x^2 + 51/10x - 27 = 0

Output:
x^3 + 71/10x^2 + 51/10x - 27 = 0
(x - -5)(x - -18/5)(x - 3/2) = 0
x - -5 = 0
x - -18/5 = 0
x - 3/2 = 0
x = -5
x = -18/5
x = 3/2


Input:
Solve the equations:
8x + 1y = 18/5
1x + 1y = -33/20

Output:
8x + 1y = 18/5
1x + 1y = -33/20

Using elimination
1*(8x + 1y = 18/5)
8*(1x + 1y = -33/20)
8x + 1y = 18/5
8x + 8y = -66/5
Subtract equations
-7y = 84/5
y = 84/5/-7
y = -12/5

Substitute y
8x + 1(-12/5) = 18/5
8x = 6
x = 6/8
x = 3/4


Input: Solve quickly: 2x - 12/5 = 0

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


Input: Solve x^2 - 103/5x + 12 = 0

Output:
x^2 - 103/5x + 12 = 0
(x - 20)(x - 3/5) = 0
x - 20 = 0  or  x - 3/5 = 0
x = 20
x = 3/5


Input: Find the solution to x^3 - 1249/252x^2 + 15/2x - 119/36 = 0

Output:
x^3 - 1249/252x^2 + 15/2x - 119/36 = 0
(x - 17/7)(x - 7/9)(x - 7/4) = 0
x - 17/7 = 0
x - 7/9 = 0
x - 7/4 = 0
x = 17/7
x = 7/9
x = 7/4


Input: Compute the solution of x^2 + 9/5x  = 0

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


Input:
Find x and y such that
1x + 8y = 101
8x + 6y = 54

Output:
1x + 8y = 101
8x + 6y = 54

Using elimination
8*(1x + 8y = 101)
1*(8x + 6y = 54)
8x + 64y = 808
8x + 6y = 54
Subtract equations
58y = 754
y = 754/58
y = 13

Substitute y
1x + 8(13) = 101
1x = -3
x = -3/1
x = -3


Input:
Find x and y such that
9x + 2y = 811/14
8x + 7y = 50

Output:
9x + 2y = 811/14
8x + 7y = 50

Using elimination
8*(9x + 2y = 811/14)
9*(8x + 7y = 50)
72x + 16y = 3244/7
72x + 63y = 450
Subtract equations
-47y = 94/7
y = 94/7/-47
y = -2/7

Substitute y
9x + 2(-2/7) = 811/14
9x = 117/2
x = 117/2/9
x = 13/2


Input:
Find x and y such that
2x + 7y = 47/8
2x + 1y = 41/8

Output:
2x + 7y = 47/8
2x + 1y = 41/8

Using elimination
2*(2x + 7y = 47/8)
2*(2x + 1y = 41/8)
4x + 14y = 47/4
4x + 2y = 41/4
Subtract equations
12y = 3/2
y = 3/2/12
y = 1/8

Substitute y
2x + 7(1/8) = 47/8
2x = 5
x = 5/2
x = 5/2


Input: Solve 1x - 9 = 0

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


Input: Determine x in 2x - 40/3 = 0

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


Input: What value of x satisfies 10x - 65/2 = 0

Output:
10x - 65/2 = 0
10x = 65/2
x = 65/2 / 10
x = 13/4


Input: What value of x satisfies 3x + 33/2 = 0

Output:
3x + 33/2 = 0
3x = -33/2
x = -33/2 / 3
x = -11/2


Input: What value of x satisfies x^3 + 68/21x^2 + 145/63x + 4/9 = 0

Output:
x^3 + 68/21x^2 + 145/63x + 4/9 = 0
(x - -1/3)(x - -4/7)(x - -7/3) = 0
x - -1/3 = 0
x - -4/7 = 0
x - -7/3 = 0
x = -1/3
x = -4/7
x = -7/3


Input: Determine x in x^3 - 31/36x^2 - 185/216x + 25/54 = 0

Output:
x^3 - 31/36x^2 - 185/216x + 25/54 = 0
(x - -5/6)(x - 4/9)(x - 5/4) = 0
x - -5/6 = 0
x - 4/9 = 0
x - 5/4 = 0
x = -5/6
x = 4/9
x = 5/4


Input:
Solve the system:
6x + 3y = -35/2
6x + 6y = -31/2

Output:
6x + 3y = -35/2
6x + 6y = -31/2

Using elimination
6*(6x + 3y = -35/2)
6*(6x + 6y = -31/2)
36x + 18y = -105
36x + 36y = -93
Subtract equations
-18y = -12
y = -12/-18
y = 2/3

Substitute y
6x + 3(2/3) = -35/2
6x = -39/2
x = -39/2/6
x = -13/4


Input: Solve x^2  - 16 = 0

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


Input: Find x in x^3 - 181/20x^2 + 57/10x + 108/5 = 0

Output:
x^3 - 181/20x^2 + 57/10x + 108/5 = 0
(x - 9/4)(x - 8)(x - -6/5) = 0
x - 9/4 = 0
x - 8 = 0
x - -6/5 = 0
x = 9/4
x = 8
x = -6/5


Input: Determine x in x^3 - 5/2x^2 + 17/16x + 7/16 = 0

Output:
x^3 - 5/2x^2 + 17/16x + 7/16 = 0
(x - -1/4)(x - 1)(x - 7/4) = 0
x - -1/4 = 0
x - 1 = 0
x - 7/4 = 0
x = -1/4
x = 1
x = 7/4


Input: Solve the equation x^2 - 3x - 55/4 = 0

Output:
x^2 - 3x - 55/4 = 0
(x - 11/2)(x - -5/2) = 0
x - 11/2 = 0  or  x - -5/2 = 0
x = 11/2
x = -5/2


Input: Find x in x^2 - 3/4x - 7/4 = 0

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


Input: Determine x in 3x - 13/3 = 0

Output:
3x - 13/3 = 0
3x = 13/3
x = 13/3 / 3
x = 13/9


Input:
Solve simultaneously:
6x + 2y = -11/35
5x + 3y = 47/70

Output:
6x + 2y = -11/35
5x + 3y = 47/70

Using elimination
5*(6x + 2y = -11/35)
6*(5x + 3y = 47/70)
30x + 10y = -11/7
30x + 18y = 141/35
Subtract equations
-8y = -28/5
y = -28/5/-8
y = 7/10

Substitute y
6x + 2(7/10) = -11/35
6x = -12/7
x = -12/7/6
x = -2/7


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

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


Input: Solve quickly: x^3 + 17/3x^2 + 65/12x + 3/4 = 0

Output:
x^3 + 17/3x^2 + 65/12x + 3/4 = 0
(x - -1/6)(x - -1)(x - -9/2) = 0
x - -1/6 = 0
x - -1 = 0
x - -9/2 = 0
x = -1/6
x = -1
x = -9/2


Input:
Solve the system:
6x + 10y = -134/9
3x + 2y = -25/9

Output:
6x + 10y = -134/9
3x + 2y = -25/9

Using elimination
3*(6x + 10y = -134/9)
6*(3x + 2y = -25/9)
18x + 30y = -134/3
18x + 12y = -50/3
Subtract equations
18y = -28
y = -28/18
y = -14/9

Substitute y
6x + 10(-14/9) = -134/9
6x = 2/3
x = 2/3/6
x = 1/9


Input: Solve the equation x^3 + 281/12x^2 + 177/2x + 1045/12 = 0

Output:
x^3 + 281/12x^2 + 177/2x + 1045/12 = 0
(x - -5/3)(x - -11/4)(x - -19) = 0
x - -5/3 = 0
x - -11/4 = 0
x - -19 = 0
x = -5/3
x = -11/4
x = -19


Input:
Solve simultaneously:
7x + 7y = -35/8
8x + 7y = -45/8

Output:
7x + 7y = -35/8
8x + 7y = -45/8

Using elimination
8*(7x + 7y = -35/8)
7*(8x + 7y = -45/8)
56x + 56y = -35
56x + 49y = -315/8
Subtract equations
7y = 35/8
y = 35/8/7
y = 5/8

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


Input: Solve the equation 4x - 56/9 = 0

Output:
4x - 56/9 = 0
4x = 56/9
x = 56/9 / 4
x = 14/9


Input: Find the solution to x^3 - 277/30x^2 + 84/5x - 49/6 = 0

Output:
x^3 - 277/30x^2 + 84/5x - 49/6 = 0
(x - 7)(x - 5/6)(x - 7/5) = 0
x - 7 = 0
x - 5/6 = 0
x - 7/5 = 0
x = 7
x = 5/6
x = 7/5


Input: Solve 6x + 51/5 = 0

Output:
6x + 51/5 = 0
6x = -51/5
x = -51/5 / 6
x = -17/10


Input: Solve 6x + 2 = 0

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


Input:
Solve the system:
7x + 1y = 23/6
1x + 4y = -83/21

Output:
7x + 1y = 23/6
1x + 4y = -83/21

Using elimination
1*(7x + 1y = 23/6)
7*(1x + 4y = -83/21)
7x + 1y = 23/6
7x + 28y = -83/3
Subtract equations
-27y = 63/2
y = 63/2/-27
y = -7/6

Substitute y
7x + 1(-7/6) = 23/6
7x = 5
x = 5/7
x = 5/7


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

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


Input:
Find x and y such that
6x + 6y = 90/7
9x + 4y = 160/7

Output:
6x + 6y = 90/7
9x + 4y = 160/7

Using elimination
9*(6x + 6y = 90/7)
6*(9x + 4y = 160/7)
54x + 54y = 810/7
54x + 24y = 960/7
Subtract equations
30y = -150/7
y = -150/7/30
y = -5/7

Substitute y
6x + 6(-5/7) = 90/7
6x = 120/7
x = 120/7/6
x = 20/7


Input:
Find x and y such that
3x + 10y = -82/5
7x + 8y = -38/5

Output:
3x + 10y = -82/5
7x + 8y = -38/5

Using elimination
7*(3x + 10y = -82/5)
3*(7x + 8y = -38/5)
21x + 70y = -574/5
21x + 24y = -114/5
Subtract equations
46y = -92
y = -92/46
y = -2

Substitute y
3x + 10(-2) = -82/5
3x = 18/5
x = 18/5/3
x = 6/5


Input:
Solve simultaneously:
5x + 4y = 13/4
5x + 9y = -1/2

Output:
5x + 4y = 13/4
5x + 9y = -1/2

Using elimination
5*(5x + 4y = 13/4)
5*(5x + 9y = -1/2)
25x + 20y = 65/4
25x + 45y = -5/2
Subtract equations
-25y = 75/4
y = 75/4/-25
y = -3/4

Substitute y
5x + 4(-3/4) = 13/4
5x = 25/4
x = 25/4/5
x = 5/4


Input: Determine x in 5x  = 0

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


Input:
Solve the equations:
5x + 4y = 5
3x + 10y = 201/10

Output:
5x + 4y = 5
3x + 10y = 201/10

Using elimination
3*(5x + 4y = 5)
5*(3x + 10y = 201/10)
15x + 12y = 15
15x + 50y = 201/2
Subtract equations
-38y = -171/2
y = -171/2/-38
y = 9/4

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


Input:
Solve the system:
2x + 8y = 445/21
8x + 3y = 649/21

Output:
2x + 8y = 445/21
8x + 3y = 649/21

Using elimination
8*(2x + 8y = 445/21)
2*(8x + 3y = 649/21)
16x + 64y = 3560/21
16x + 6y = 1298/21
Subtract equations
58y = 754/7
y = 754/7/58
y = 13/7

Substitute y
2x + 8(13/7) = 445/21
2x = 19/3
x = 19/3/2
x = 19/6


Input:
Find x and y such that
7x + 10y = -75/2
5x + 10y = -65/2

Output:
7x + 10y = -75/2
5x + 10y = -65/2

Using elimination
5*(7x + 10y = -75/2)
7*(5x + 10y = -65/2)
35x + 50y = -375/2
35x + 70y = -455/2
Subtract equations
-20y = 40
y = 40/-20
y = -2

Substitute y
7x + 10(-2) = -75/2
7x = -35/2
x = -35/2/7
x = -5/2


Input: Solve quickly: 1x + 11/3 = 0

Output:
1x + 11/3 = 0
1x = -11/3
x = -11/3 / 1
x = -11/3


Input: Compute the solution of 9x + 144 = 0

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


Input: Find x for x^3 + 7/12x^2 - 593/12x + 238/3 = 0

Output:
x^3 + 7/12x^2 - 593/12x + 238/3 = 0
(x - 17/3)(x - -8)(x - 7/4) = 0
x - 17/3 = 0
x - -8 = 0
x - 7/4 = 0
x = 17/3
x = -8
x = 7/4


Input: Find x for 7x + 119/6 = 0

Output:
7x + 119/6 = 0
7x = -119/6
x = -119/6 / 7
x = -17/6


Input: Solve 3x - 51/5 = 0

Output:
3x - 51/5 = 0
3x = 51/5
x = 51/5 / 3
x = 17/5


Input: Find x in x^2 - 4x - 5 = 0

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


Input: Determine x in x^3 - 1/3x^2 - 88/81x  = 0

Output:
x^3 - 1/3x^2 - 88/81x  = 0
(x - 0)(x - 11/9)(x - -8/9) = 0
x - 0 = 0
x - 11/9 = 0
x - -8/9 = 0
x = 0
x = 11/9
x = -8/9


Input: Compute the solution of 2x + 16/7 = 0

Output:
2x + 16/7 = 0
2x = -16/7
x = -16/7 / 2
x = -8/7


Input: Solve quickly: x^2 + 44/9x + 32/9 = 0

Output:
x^2 + 44/9x + 32/9 = 0
(x - -4)(x - -8/9) = 0
x - -4 = 0  or  x - -8/9 = 0
x = -4
x = -8/9


Input:
Find x and y such that
5x + 5y = -85/14
5x + 6y = -39/7

Output:
5x + 5y = -85/14
5x + 6y = -39/7

Using elimination
5*(5x + 5y = -85/14)
5*(5x + 6y = -39/7)
25x + 25y = -425/14
25x + 30y = -195/7
Subtract equations
-5y = -5/2
y = -5/2/-5
y = 1/2

Substitute y
5x + 5(1/2) = -85/14
5x = -60/7
x = -60/7/5
x = -12/7


Input: Solve the equation 8x - 56/9 = 0

Output:
8x - 56/9 = 0
8x = 56/9
x = 56/9 / 8
x = 7/9


Input:
Solve the equations:
6x + 2y = 7
3x + 3y = 29/2

Output:
6x + 2y = 7
3x + 3y = 29/2

Using elimination
3*(6x + 2y = 7)
6*(3x + 3y = 29/2)
18x + 6y = 21
18x + 18y = 87
Subtract equations
-12y = -66
y = -66/-12
y = 11/2

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


Input: Solve the equation 2x + 28/9 = 0

Output:
2x + 28/9 = 0
2x = -28/9
x = -28/9 / 2
x = -14/9


Input: Find x in x^2 + 7/2x - 36 = 0

Output:
x^2 + 7/2x - 36 = 0
(x - 9/2)(x - -8) = 0
x - 9/2 = 0  or  x - -8 = 0
x = 9/2
x = -8


Input: Find x in 5x - 25/3 = 0

Output:
5x - 25/3 = 0
5x = 25/3
x = 25/3 / 5
x = 5/3


Input: Find the solution to x^2 - 9/2x + 187/50 = 0

Output:
x^2 - 9/2x + 187/50 = 0
(x - 17/5)(x - 11/10) = 0
x - 17/5 = 0  or  x - 11/10 = 0
x = 17/5
x = 11/10


Input:
Solve the equations:
5x + 6y = 187/8
7x + 7y = 217/8

Output:
5x + 6y = 187/8
7x + 7y = 217/8

Using elimination
7*(5x + 6y = 187/8)
5*(7x + 7y = 217/8)
35x + 42y = 1309/8
35x + 35y = 1085/8
Subtract equations
7y = 28
y = 28/7
y = 4

Substitute y
5x + 6(4) = 187/8
5x = -5/8
x = -5/8/5
x = -1/8


Input: Solve x^2 + 69/28x + 9/7 = 0

Output:
x^2 + 69/28x + 9/7 = 0
(x - -3/4)(x - -12/7) = 0
x - -3/4 = 0  or  x - -12/7 = 0
x = -3/4
x = -12/7


Input: Find the solution to x^2 + 139/40x + 209/80 = 0

Output:
x^2 + 139/40x + 209/80 = 0
(x - -19/8)(x - -11/10) = 0
x - -19/8 = 0  or  x - -11/10 = 0
x = -19/8
x = -11/10


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

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

Using elimination
2*(5x + 6y = -7/2)
5*(2x + 9y = -8)
10x + 12y = -7
10x + 45y = -40
Subtract equations
-33y = 33
y = 33/-33
y = -1

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


Input: Solve quickly: 5x + 35/6 = 0

Output:
5x + 35/6 = 0
5x = -35/6
x = -35/6 / 5
x = -7/6


Input:
Solve simultaneously:
8x + 1y = 207/7
9x + 10y = 661/14

Output:
8x + 1y = 207/7
9x + 10y = 661/14

Using elimination
9*(8x + 1y = 207/7)
8*(9x + 10y = 661/14)
72x + 9y = 1863/7
72x + 80y = 2644/7
Subtract equations
-71y = -781/7
y = -781/7/-71
y = 11/7

Substitute y
8x + 1(11/7) = 207/7
8x = 28
x = 28/8
x = 7/2


Input:
Solve simultaneously:
5x + 1y = 2/3
4x + 9y = -134/5

Output:
5x + 1y = 2/3
4x + 9y = -134/5

Using elimination
4*(5x + 1y = 2/3)
5*(4x + 9y = -134/5)
20x + 4y = 8/3
20x + 45y = -134
Subtract equations
-41y = 410/3
y = 410/3/-41
y = -10/3

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


Input: Determine x in x^3 - 43/30x^2 - 703/150x + 51/25 = 0

Output:
x^3 - 43/30x^2 - 703/150x + 51/25 = 0
(x - -9/5)(x - 17/6)(x - 2/5) = 0
x - -9/5 = 0
x - 17/6 = 0
x - 2/5 = 0
x = -9/5
x = 17/6
x = 2/5


Input: Find the solution to x^2 - 41/4x + 5/2 = 0

Output:
x^2 - 41/4x + 5/2 = 0
(x - 1/4)(x - 10) = 0
x - 1/4 = 0  or  x - 10 = 0
x = 1/4
x = 10


Input: Solve x^3 + 59/36x^2 - 115/24x - 475/72 = 0

Output:
x^3 + 59/36x^2 - 115/24x - 475/72 = 0
(x - -5/2)(x - 19/9)(x - -5/4) = 0
x - -5/2 = 0
x - 19/9 = 0
x - -5/4 = 0
x = -5/2
x = 19/9
x = -5/4


Input: Compute the solution of 2x  = 0

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


Input: What value of x satisfies x^3 - 77/6x^2 + 107/3x - 21/2 = 0

Output:
x^3 - 77/6x^2 + 107/3x - 21/2 = 0
(x - 9)(x - 7/2)(x - 1/3) = 0
x - 9 = 0
x - 7/2 = 0
x - 1/3 = 0
x = 9
x = 7/2
x = 1/3


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

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


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

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


Input:
Find x and y such that
3x + 4y = 113/6
3x + 10y = 161/6

Output:
3x + 4y = 113/6
3x + 10y = 161/6

Using elimination
3*(3x + 4y = 113/6)
3*(3x + 10y = 161/6)
9x + 12y = 113/2
9x + 30y = 161/2
Subtract equations
-18y = -24
y = -24/-18
y = 4/3

Substitute y
3x + 4(4/3) = 113/6
3x = 27/2
x = 27/2/3
x = 9/2


Input: What value of x satisfies x^2 - 57/35x - 176/35 = 0

Output:
x^2 - 57/35x - 176/35 = 0
(x - 16/5)(x - -11/7) = 0
x - 16/5 = 0  or  x - -11/7 = 0
x = 16/5
x = -11/7


Input:
Solve the equations:
10x + 8y = 329/10
7x + 5y = 89/4

Output:
10x + 8y = 329/10
7x + 5y = 89/4

Using elimination
7*(10x + 8y = 329/10)
10*(7x + 5y = 89/4)
70x + 56y = 2303/10
70x + 50y = 445/2
Subtract equations
6y = 39/5
y = 39/5/6
y = 13/10

Substitute y
10x + 8(13/10) = 329/10
10x = 45/2
x = 45/2/10
x = 9/4


Input: Solve x^2 - 37/7x + 48/7 = 0

Output:
x^2 - 37/7x + 48/7 = 0
(x - 16/7)(x - 3) = 0
x - 16/7 = 0  or  x - 3 = 0
x = 16/7
x = 3


Input: Find x for x^3 - 229/15x^2 + 832/15x - 28 = 0

Output:
x^3 - 229/15x^2 + 832/15x - 28 = 0
(x - 10)(x - 3/5)(x - 14/3) = 0
x - 10 = 0
x - 3/5 = 0
x - 14/3 = 0
x = 10
x = 3/5
x = 14/3


Input:
Solve the equations:
1x + 9y = 83/5
2x + 6y = 46/5

Output:
1x + 9y = 83/5
2x + 6y = 46/5

Using elimination
2*(1x + 9y = 83/5)
1*(2x + 6y = 46/5)
2x + 18y = 166/5
2x + 6y = 46/5
Subtract equations
12y = 24
y = 24/12
y = 2

Substitute y
1x + 9(2) = 83/5
1x = -7/5
x = -7/5/1
x = -7/5


Input:
Solve simultaneously:
7x + 1y = 729/14
5x + 2y = 513/14

Output:
7x + 1y = 729/14
5x + 2y = 513/14

Using elimination
5*(7x + 1y = 729/14)
7*(5x + 2y = 513/14)
35x + 5y = 3645/14
35x + 14y = 513/2
Subtract equations
-9y = 27/7
y = 27/7/-9
y = -3/7

Substitute y
7x + 1(-3/7) = 729/14
7x = 105/2
x = 105/2/7
x = 15/2


Input:
Find x and y such that
5x + 9y = -53
6x + 1y = 5

Output:
5x + 9y = -53
6x + 1y = 5

Using elimination
6*(5x + 9y = -53)
5*(6x + 1y = 5)
30x + 54y = -318
30x + 5y = 25
Subtract equations
49y = -343
y = -343/49
y = -7

Substitute y
5x + 9(-7) = -53
5x = 10
x = 10/5
x = 2


Input:
Solve the equations:
8x + 10y = -264/7
1x + 4y = -110/7

Output:
8x + 10y = -264/7
1x + 4y = -110/7

Using elimination
1*(8x + 10y = -264/7)
8*(1x + 4y = -110/7)
8x + 10y = -264/7
8x + 32y = -880/7
Subtract equations
-22y = 88
y = 88/-22
y = -4

Substitute y
8x + 10(-4) = -264/7
8x = 16/7
x = 16/7/8
x = 2/7


Input:
Solve the system:
5x + 7y = -65/4
4x + 9y = -35/4

Output:
5x + 7y = -65/4
4x + 9y = -35/4

Using elimination
4*(5x + 7y = -65/4)
5*(4x + 9y = -35/4)
20x + 28y = -65
20x + 45y = -175/4
Subtract equations
-17y = -85/4
y = -85/4/-17
y = 5/4

Substitute y
5x + 7(5/4) = -65/4
5x = -25
x = -25/5
x = -5


Input: Determine x in 3x + 21/4 = 0

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


Input: Solve the equation x^2 - 145/36x + 4 = 0

Output:
x^2 - 145/36x + 4 = 0
(x - 9/4)(x - 16/9) = 0
x - 9/4 = 0  or  x - 16/9 = 0
x = 9/4
x = 16/9


Input:
Solve the equations:
10x + 1y = -151/10
7x + 7y = -56/5

Output:
10x + 1y = -151/10
7x + 7y = -56/5

Using elimination
7*(10x + 1y = -151/10)
10*(7x + 7y = -56/5)
70x + 7y = -1057/10
70x + 70y = -112
Subtract equations
-63y = 63/10
y = 63/10/-63
y = -1/10

Substitute y
10x + 1(-1/10) = -151/10
10x = -15
x = -15/10
x = -3/2


Input: Determine x in x^3 - 24/35x^2 - 55/7x + 48/5 = 0

Output:
x^3 - 24/35x^2 - 55/7x + 48/5 = 0
(x - -3)(x - 7/5)(x - 16/7) = 0
x - -3 = 0
x - 7/5 = 0
x - 16/7 = 0
x = -3
x = 7/5
x = 16/7


Input:
Solve the equations:
7x + 4y = -29/2
5x + 5y = -25/2

Output:
7x + 4y = -29/2
5x + 5y = -25/2

Using elimination
5*(7x + 4y = -29/2)
7*(5x + 5y = -25/2)
35x + 20y = -145/2
35x + 35y = -175/2
Subtract equations
-15y = 15
y = 15/-15
y = -1

Substitute y
7x + 4(-1) = -29/2
7x = -21/2
x = -21/2/7
x = -3/2


Input: Determine x in x^2 - 129/7x + 272/7 = 0

Output:
x^2 - 129/7x + 272/7 = 0
(x - 17/7)(x - 16) = 0
x - 17/7 = 0  or  x - 16 = 0
x = 17/7
x = 16


Input: Determine x in x^2 - 78/7x + 80/7 = 0

Output:
x^2 - 78/7x + 80/7 = 0
(x - 8/7)(x - 10) = 0
x - 8/7 = 0  or  x - 10 = 0
x = 8/7
x = 10


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

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


Input: Compute the solution of x^2 + 83/21x + 24/7 = 0

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


Input: Find x for x^3 + 47/12x^2 + 7/3x - 5/4 = 0

Output:
x^3 + 47/12x^2 + 7/3x - 5/4 = 0
(x - -5/4)(x - 1/3)(x - -3) = 0
x - -5/4 = 0
x - 1/3 = 0
x - -3 = 0
x = -5/4
x = 1/3
x = -3


Input: Solve the equation x^2 + 7x - 8 = 0

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


Input: Solve x^3 + 17/15x^2 - 71/12x - 187/60 = 0

Output:
x^3 + 17/15x^2 - 71/12x - 187/60 = 0
(x - 11/5)(x - -17/6)(x - -1/2) = 0
x - 11/5 = 0
x - -17/6 = 0
x - -1/2 = 0
x = 11/5
x = -17/6
x = -1/2


Input: Compute the solution of 10x + 20 = 0

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


Input: Find x for x^3 - 23/5x^2 - 266/45x + 392/15 = 0

Output:
x^3 - 23/5x^2 - 266/45x + 392/15 = 0
(x - 14/3)(x - -12/5)(x - 7/3) = 0
x - 14/3 = 0
x - -12/5 = 0
x - 7/3 = 0
x = 14/3
x = -12/5
x = 7/3


Input: Solve quickly: x^3 - 83/14x^2 - 1125/14x - 1053/7 = 0

Output:
x^3 - 83/14x^2 - 1125/14x - 1053/7 = 0
(x - -9/2)(x - 13)(x - -18/7) = 0
x - -9/2 = 0
x - 13 = 0
x - -18/7 = 0
x = -9/2
x = 13
x = -18/7


Input: Solve the equation 5x + 100/7 = 0

Output:
5x + 100/7 = 0
5x = -100/7
x = -100/7 / 5
x = -20/7


Input: Solve x^3 + 363/56x^2 - 243/56x - 5 = 0

Output:
x^3 + 363/56x^2 - 243/56x - 5 = 0
(x - -5/8)(x - 8/7)(x - -7) = 0
x - -5/8 = 0
x - 8/7 = 0
x - -7 = 0
x = -5/8
x = 8/7
x = -7


Input: Determine x in x^3 - 8x^2 - 51/4x + 135/4 = 0

Output:
x^3 - 8x^2 - 51/4x + 135/4 = 0
(x - 3/2)(x - -5/2)(x - 9) = 0
x - 3/2 = 0
x - -5/2 = 0
x - 9 = 0
x = 3/2
x = -5/2
x = 9


Input: Find the solution to x^2 - 3/2x - 27 = 0

Output:
x^2 - 3/2x - 27 = 0
(x - -9/2)(x - 6) = 0
x - -9/2 = 0  or  x - 6 = 0
x = -9/2
x = 6


Input: Compute the solution of x^2 - 96/5x + 187/5 = 0

Output:
x^2 - 96/5x + 187/5 = 0
(x - 11/5)(x - 17) = 0
x - 11/5 = 0  or  x - 17 = 0
x = 11/5
x = 17


Input:
Solve the equations:
5x + 10y = -495/14
8x + 3y = -279/7

Output:
5x + 10y = -495/14
8x + 3y = -279/7

Using elimination
8*(5x + 10y = -495/14)
5*(8x + 3y = -279/7)
40x + 80y = -1980/7
40x + 15y = -1395/7
Subtract equations
65y = -585/7
y = -585/7/65
y = -9/7

Substitute y
5x + 10(-9/7) = -495/14
5x = -45/2
x = -45/2/5
x = -9/2


Input:
Find x and y such that
5x + 1y = -319/8
7x + 4y = -62

Output:
5x + 1y = -319/8
7x + 4y = -62

Using elimination
7*(5x + 1y = -319/8)
5*(7x + 4y = -62)
35x + 7y = -2233/8
35x + 20y = -310
Subtract equations
-13y = 247/8
y = 247/8/-13
y = -19/8

Substitute y
5x + 1(-19/8) = -319/8
5x = -75/2
x = -75/2/5
x = -15/2


Input: Find the solution to x^3 + 92/5x^2 + 199/5x + 112/5 = 0

Output:
x^3 + 92/5x^2 + 199/5x + 112/5 = 0
(x - -7/5)(x - -16)(x - -1) = 0
x - -7/5 = 0
x - -16 = 0
x - -1 = 0
x = -7/5
x = -16
x = -1


Input: Solve 5x - 25/4 = 0

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


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

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


Input:
Find x and y such that
2x + 3y = -41/6
8x + 7y = -89/6

Output:
2x + 3y = -41/6
8x + 7y = -89/6

Using elimination
8*(2x + 3y = -41/6)
2*(8x + 7y = -89/6)
16x + 24y = -164/3
16x + 14y = -89/3
Subtract equations
10y = -25
y = -25/10
y = -5/2

Substitute y
2x + 3(-5/2) = -41/6
2x = 2/3
x = 2/3/2
x = 1/3


Input:
Solve the equations:
1x + 3y = 87/35
10x + 7y = 548/35

Output:
1x + 3y = 87/35
10x + 7y = 548/35

Using elimination
10*(1x + 3y = 87/35)
1*(10x + 7y = 548/35)
10x + 30y = 174/7
10x + 7y = 548/35
Subtract equations
23y = 46/5
y = 46/5/23
y = 2/5

Substitute y
1x + 3(2/5) = 87/35
1x = 9/7
x = 9/7/1
x = 9/7


Input: Find the solution to x^3 + 19/140x^2 - 541/140x + 12/5 = 0

Output:
x^3 + 19/140x^2 - 541/140x + 12/5 = 0
(x - 3/4)(x - 7/5)(x - -16/7) = 0
x - 3/4 = 0
x - 7/5 = 0
x - -16/7 = 0
x = 3/4
x = 7/5
x = -16/7


Input:
Solve the system:
1x + 5y = -163/36
5x + 10y = -205/18

Output:
1x + 5y = -163/36
5x + 10y = -205/18

Using elimination
5*(1x + 5y = -163/36)
1*(5x + 10y = -205/18)
5x + 25y = -815/36
5x + 10y = -205/18
Subtract equations
15y = -45/4
y = -45/4/15
y = -3/4

Substitute y
1x + 5(-3/4) = -163/36
1x = -7/9
x = -7/9/1
x = -7/9


Input: Compute the solution of x^2 + 31/12x - 17/24 = 0

Output:
x^2 + 31/12x - 17/24 = 0
(x - 1/4)(x - -17/6) = 0
x - 1/4 = 0  or  x - -17/6 = 0
x = 1/4
x = -17/6


Input: Find the solution to x^2 - 27/40x - 9/4 = 0

Output:
x^2 - 27/40x - 9/4 = 0
(x - -6/5)(x - 15/8) = 0
x - -6/5 = 0  or  x - 15/8 = 0
x = -6/5
x = 15/8


Input:
Solve the system:
9x + 8y = -365/14
8x + 4y = -128/7

Output:
9x + 8y = -365/14
8x + 4y = -128/7

Using elimination
8*(9x + 8y = -365/14)
9*(8x + 4y = -128/7)
72x + 64y = -1460/7
72x + 36y = -1152/7
Subtract equations
28y = -44
y = -44/28
y = -11/7

Substitute y
9x + 8(-11/7) = -365/14
9x = -27/2
x = -27/2/9
x = -3/2


Input:
Solve the system:
10x + 9y = -215/2
8x + 10y = -314/3

Output:
10x + 9y = -215/2
8x + 10y = -314/3

Using elimination
8*(10x + 9y = -215/2)
10*(8x + 10y = -314/3)
80x + 72y = -860
80x + 100y = -3140/3
Subtract equations
-28y = 560/3
y = 560/3/-28
y = -20/3

Substitute y
10x + 9(-20/3) = -215/2
10x = -95/2
x = -95/2/10
x = -19/4


Input:
Solve the equations:
8x + 4y = 36
5x + 9y = 16

Output:
8x + 4y = 36
5x + 9y = 16

Using elimination
5*(8x + 4y = 36)
8*(5x + 9y = 16)
40x + 20y = 180
40x + 72y = 128
Subtract equations
-52y = 52
y = 52/-52
y = -1

Substitute y
8x + 4(-1) = 36
8x = 40
x = 40/8
x = 5


Input:
Solve the equations:
4x + 3y = -19/4
10x + 4y = -11

Output:
4x + 3y = -19/4
10x + 4y = -11

Using elimination
10*(4x + 3y = -19/4)
4*(10x + 4y = -11)
40x + 30y = -95/2
40x + 16y = -44
Subtract equations
14y = -7/2
y = -7/2/14
y = -1/4

Substitute y
4x + 3(-1/4) = -19/4
4x = -4
x = -4/4
x = -1


Input: Find x in 4x - 8/3 = 0

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


Input: Solve quickly: x^2 - 95/9x + 50/9 = 0

Output:
x^2 - 95/9x + 50/9 = 0
(x - 10)(x - 5/9) = 0
x - 10 = 0  or  x - 5/9 = 0
x = 10
x = 5/9


Input:
Solve the system:
2x + 5y = -49/9
8x + 8y = -656/45

Output:
2x + 5y = -49/9
8x + 8y = -656/45

Using elimination
8*(2x + 5y = -49/9)
2*(8x + 8y = -656/45)
16x + 40y = -392/9
16x + 16y = -1312/45
Subtract equations
24y = -72/5
y = -72/5/24
y = -3/5

Substitute y
2x + 5(-3/5) = -49/9
2x = -22/9
x = -22/9/2
x = -11/9


Input: Solve quickly: 8x - 12 = 0

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


Input:
Solve the equations:
10x + 8y = 308/3
5x + 7y = 202/3

Output:
10x + 8y = 308/3
5x + 7y = 202/3

Using elimination
5*(10x + 8y = 308/3)
10*(5x + 7y = 202/3)
50x + 40y = 1540/3
50x + 70y = 2020/3
Subtract equations
-30y = -160
y = -160/-30
y = 16/3

Substitute y
10x + 8(16/3) = 308/3
10x = 60
x = 60/10
x = 6


Input: Find x for x^3 - 13/12x^2 - 1285/324x - 275/162 = 0

Output:
x^3 - 13/12x^2 - 1285/324x - 275/162 = 0
(x - 11/4)(x - -10/9)(x - -5/9) = 0
x - 11/4 = 0
x - -10/9 = 0
x - -5/9 = 0
x = 11/4
x = -10/9
x = -5/9


Input: Find x in x^3 - 53/6x^2 + 43/2x - 26/3 = 0

Output:
x^3 - 53/6x^2 + 43/2x - 26/3 = 0
(x - 4)(x - 13/3)(x - 1/2) = 0
x - 4 = 0
x - 13/3 = 0
x - 1/2 = 0
x = 4
x = 13/3
x = 1/2


Input: Determine x in 1x + 7/8 = 0

Output:
1x + 7/8 = 0
1x = -7/8
x = -7/8 / 1
x = -7/8


Input:
Solve the equations:
3x + 5y = -35/3
7x + 8y = -89/3

Output:
3x + 5y = -35/3
7x + 8y = -89/3

Using elimination
7*(3x + 5y = -35/3)
3*(7x + 8y = -89/3)
21x + 35y = -245/3
21x + 24y = -89
Subtract equations
11y = 22/3
y = 22/3/11
y = 2/3

Substitute y
3x + 5(2/3) = -35/3
3x = -15
x = -15/3
x = -5


Input: Find the solution to 4x - 12 = 0

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


Input: Solve the equation x^3 + 53/8x^2 - 943/8x - 819/4 = 0

Output:
x^3 + 53/8x^2 - 943/8x - 819/4 = 0
(x - 9)(x - -13/8)(x - -14) = 0
x - 9 = 0
x - -13/8 = 0
x - -14 = 0
x = 9
x = -13/8
x = -14


Input: Solve the equation 5x + 35/6 = 0

Output:
5x + 35/6 = 0
5x = -35/6
x = -35/6 / 5
x = -7/6


Input: Find the solution to x^2 - 28/3x - 20/3 = 0

Output:
x^2 - 28/3x - 20/3 = 0
(x - 10)(x - -2/3) = 0
x - 10 = 0  or  x - -2/3 = 0
x = 10
x = -2/3


Input: Solve quickly: x^2 - 161/30x + 209/30 = 0

Output:
x^2 - 161/30x + 209/30 = 0
(x - 19/6)(x - 11/5) = 0
x - 19/6 = 0  or  x - 11/5 = 0
x = 19/6
x = 11/5


Input: Compute the solution of x^3 + 54/7x^2 - 160/7x  = 0

Output:
x^3 + 54/7x^2 - 160/7x  = 0
(x - -10)(x - 16/7)(x - 0) = 0
x - -10 = 0
x - 16/7 = 0
x - 0 = 0
x = -10
x = 16/7
x = 0


Input: Solve quickly: x^2 - 23/4x + 51/8 = 0

Output:
x^2 - 23/4x + 51/8 = 0
(x - 17/4)(x - 3/2) = 0
x - 17/4 = 0  or  x - 3/2 = 0
x = 17/4
x = 3/2


Input: Solve the equation 10x - 160/7 = 0

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


Input: Solve quickly: x^2 + 13/9x - 56/27 = 0

Output:
x^2 + 13/9x - 56/27 = 0
(x - -7/3)(x - 8/9) = 0
x - -7/3 = 0  or  x - 8/9 = 0
x = -7/3
x = 8/9


Input:
Find x and y such that
6x + 6y = 144/7
4x + 5y = 110/7

Output:
6x + 6y = 144/7
4x + 5y = 110/7

Using elimination
4*(6x + 6y = 144/7)
6*(4x + 5y = 110/7)
24x + 24y = 576/7
24x + 30y = 660/7
Subtract equations
-6y = -12
y = -12/-6
y = 2

Substitute y
6x + 6(2) = 144/7
6x = 60/7
x = 60/7/6
x = 10/7


Input: Solve quickly: 9x + 81/5 = 0

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


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

Output:
2x + 7/4 = 0
2x = -7/4
x = -7/4 / 2
x = -7/8


Input: What value of x satisfies x^3 + 83/7x^2 + 320/7x + 400/7 = 0

Output:
x^3 + 83/7x^2 + 320/7x + 400/7 = 0
(x - -5)(x - -20/7)(x - -4) = 0
x - -5 = 0
x - -20/7 = 0
x - -4 = 0
x = -5
x = -20/7
x = -4


Input: Determine x in x^2 + 7/30x - 1/2 = 0

Output:
x^2 + 7/30x - 1/2 = 0
(x - 3/5)(x - -5/6) = 0
x - 3/5 = 0  or  x - -5/6 = 0
x = 3/5
x = -5/6


Input: Solve quickly: x^3 - 163/72x^2 - 617/216x + 665/108 = 0

Output:
x^3 - 163/72x^2 - 617/216x + 665/108 = 0
(x - 19/8)(x - -5/3)(x - 14/9) = 0
x - 19/8 = 0
x - -5/3 = 0
x - 14/9 = 0
x = 19/8
x = -5/3
x = 14/9


Input: Solve the equation 6x + 30 = 0

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


Input: Determine x in 1x + 4 = 0

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


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

Output:
7x - 7/8 = 0
7x = 7/8
x = 7/8 / 7
x = 1/8


Input:
Solve the equations:
4x + 3y = -169/18
3x + 8y = -47/3

Output:
4x + 3y = -169/18
3x + 8y = -47/3

Using elimination
3*(4x + 3y = -169/18)
4*(3x + 8y = -47/3)
12x + 9y = -169/6
12x + 32y = -188/3
Subtract equations
-23y = 69/2
y = 69/2/-23
y = -3/2

Substitute y
4x + 3(-3/2) = -169/18
4x = -44/9
x = -44/9/4
x = -11/9


Input: Find the solution to x^3 - 23/6x^2 - 58/3x + 133/6 = 0

Output:
x^3 - 23/6x^2 - 58/3x + 133/6 = 0
(x - -7/2)(x - 19/3)(x - 1) = 0
x - -7/2 = 0
x - 19/3 = 0
x - 1 = 0
x = -7/2
x = 19/3
x = 1


Input:
Solve the equations:
4x + 10y = -1688/63
5x + 1y = -500/63

Output:
4x + 10y = -1688/63
5x + 1y = -500/63

Using elimination
5*(4x + 10y = -1688/63)
4*(5x + 1y = -500/63)
20x + 50y = -8440/63
20x + 4y = -2000/63
Subtract equations
46y = -920/9
y = -920/9/46
y = -20/9

Substitute y
4x + 10(-20/9) = -1688/63
4x = -32/7
x = -32/7/4
x = -8/7


Input: What value of x satisfies 1x - 2/7 = 0

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


Input: Solve quickly: x^2 + 13x + 165/4 = 0

Output:
x^2 + 13x + 165/4 = 0
(x - -11/2)(x - -15/2) = 0
x - -11/2 = 0  or  x - -15/2 = 0
x = -11/2
x = -15/2


Input: Solve the equation x^3 + 39/40x^2 - 621/80x + 243/40 = 0

Output:
x^3 + 39/40x^2 - 621/80x + 243/40 = 0
(x - 9/8)(x - -18/5)(x - 3/2) = 0
x - 9/8 = 0
x - -18/5 = 0
x - 3/2 = 0
x = 9/8
x = -18/5
x = 3/2


Input: Solve quickly: x^2 - 31/40x - 171/80 = 0

Output:
x^2 - 31/40x - 171/80 = 0
(x - -9/8)(x - 19/10) = 0
x - -9/8 = 0  or  x - 19/10 = 0
x = -9/8
x = 19/10


Input:
Solve the system:
3x + 3y = 105/8
4x + 1y = -1/2

Output:
3x + 3y = 105/8
4x + 1y = -1/2

Using elimination
4*(3x + 3y = 105/8)
3*(4x + 1y = -1/2)
12x + 12y = 105/2
12x + 3y = -3/2
Subtract equations
9y = 54
y = 54/9
y = 6

Substitute y
3x + 3(6) = 105/8
3x = -39/8
x = -39/8/3
x = -13/8


Input: Compute the solution of x^3 + 29/4x^2 + 89/8x - 15/2 = 0

Output:
x^3 + 29/4x^2 + 89/8x - 15/2 = 0
(x - 1/2)(x - -15/4)(x - -4) = 0
x - 1/2 = 0
x - -15/4 = 0
x - -4 = 0
x = 1/2
x = -15/4
x = -4


Input:
Find x and y such that
4x + 8y = 2/3
1x + 9y = 71/6

Output:
4x + 8y = 2/3
1x + 9y = 71/6

Using elimination
1*(4x + 8y = 2/3)
4*(1x + 9y = 71/6)
4x + 8y = 2/3
4x + 36y = 142/3
Subtract equations
-28y = -140/3
y = -140/3/-28
y = 5/3

Substitute y
4x + 8(5/3) = 2/3
4x = -38/3
x = -38/3/4
x = -19/6


Input: Solve x^2 + 27/5x + 34/5 = 0

Output:
x^2 + 27/5x + 34/5 = 0
(x - -17/5)(x - -2) = 0
x - -17/5 = 0  or  x - -2 = 0
x = -17/5
x = -2


Input: What value of x satisfies x^2 + 35/3x + 88/3 = 0

Output:
x^2 + 35/3x + 88/3 = 0
(x - -11/3)(x - -8) = 0
x - -11/3 = 0  or  x - -8 = 0
x = -11/3
x = -8


Input: Solve the equation x^2 + 39/4x - 5/2 = 0

Output:
x^2 + 39/4x - 5/2 = 0
(x - -10)(x - 1/4) = 0
x - -10 = 0  or  x - 1/4 = 0
x = -10
x = 1/4


Input: Solve the equation x^2 + 26/3x + 17 = 0

Output:
x^2 + 26/3x + 17 = 0
(x - -17/3)(x - -3) = 0
x - -17/3 = 0  or  x - -3 = 0
x = -17/3
x = -3


Input: Find the solution to x^3 + 28/9x^2 - 89/9x - 76/3 = 0

Output:
x^3 + 28/9x^2 - 89/9x - 76/3 = 0
(x - 3)(x - -19/9)(x - -4) = 0
x - 3 = 0
x - -19/9 = 0
x - -4 = 0
x = 3
x = -19/9
x = -4


Input: What value of x satisfies 10x - 45/4 = 0

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


Input: Determine x in 1x + 7/4 = 0

Output:
1x + 7/4 = 0
1x = -7/4
x = -7/4 / 1
x = -7/4


Input:
Find x and y such that
6x + 8y = 40/3
1x + 9y = 38

Output:
6x + 8y = 40/3
1x + 9y = 38

Using elimination
1*(6x + 8y = 40/3)
6*(1x + 9y = 38)
6x + 8y = 40/3
6x + 54y = 228
Subtract equations
-46y = -644/3
y = -644/3/-46
y = 14/3

Substitute y
6x + 8(14/3) = 40/3
6x = -24
x = -24/6
x = -4


Input:
Solve the system:
10x + 8y = 394/3
10x + 2y = 106/3

Output:
10x + 8y = 394/3
10x + 2y = 106/3

Using elimination
10*(10x + 8y = 394/3)
10*(10x + 2y = 106/3)
100x + 80y = 3940/3
100x + 20y = 1060/3
Subtract equations
60y = 960
y = 960/60
y = 16

Substitute y
10x + 8(16) = 394/3
10x = 10/3
x = 10/3/10
x = 1/3


Input: Compute the solution of x^3 - 9x^2 + 35/4x + 75/4 = 0

Output:
x^3 - 9x^2 + 35/4x + 75/4 = 0
(x - -1)(x - 5/2)(x - 15/2) = 0
x - -1 = 0
x - 5/2 = 0
x - 15/2 = 0
x = -1
x = 5/2
x = 15/2


Input: Solve x^2 - 4/3x - 20/3 = 0

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


Input: Solve the equation 7x + 70/3 = 0

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


Input:
Solve the equations:
1x + 6y = -8
7x + 5y = -1/2

Output:
1x + 6y = -8
7x + 5y = -1/2

Using elimination
7*(1x + 6y = -8)
1*(7x + 5y = -1/2)
7x + 42y = -56
7x + 5y = -1/2
Subtract equations
37y = -111/2
y = -111/2/37
y = -3/2

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


Input:
Solve simultaneously:
9x + 9y = 81/4
1x + 2y = 17/4

Output:
9x + 9y = 81/4
1x + 2y = 17/4

Using elimination
1*(9x + 9y = 81/4)
9*(1x + 2y = 17/4)
9x + 9y = 81/4
9x + 18y = 153/4
Subtract equations
-9y = -18
y = -18/-9
y = 2

Substitute y
9x + 9(2) = 81/4
9x = 9/4
x = 9/4/9
x = 1/4


Input: Find x in 2x - 16 = 0

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


Input: What value of x satisfies x^3 - 107/5x^2 + 692/25x + 32/5 = 0

Output:
x^3 - 107/5x^2 + 692/25x + 32/5 = 0
(x - 20)(x - -1/5)(x - 8/5) = 0
x - 20 = 0
x - -1/5 = 0
x - 8/5 = 0
x = 20
x = -1/5
x = 8/5


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

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


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

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


Input: Solve 1x + 19/10 = 0

Output:
1x + 19/10 = 0
1x = -19/10
x = -19/10 / 1
x = -19/10


Input: Solve x^2 - 29/45x - 52/45 = 0

Output:
x^2 - 29/45x - 52/45 = 0
(x - 13/9)(x - -4/5) = 0
x - 13/9 = 0  or  x - -4/5 = 0
x = 13/9
x = -4/5


Input: Find x for 9x + 24 = 0

Output:
9x + 24 = 0
9x = -24
x = -24 / 9
x = -8/3


Input: Find x for x^2 + 47/28x + 5/14 = 0

Output:
x^2 + 47/28x + 5/14 = 0
(x - -1/4)(x - -10/7) = 0
x - -1/4 = 0  or  x - -10/7 = 0
x = -1/4
x = -10/7


Input: Find x in 4x - 8 = 0

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


Input: Determine x in x^3 - 208/45x^2 + 389/135x + 308/135 = 0

Output:
x^3 - 208/45x^2 + 389/135x + 308/135 = 0
(x - -4/9)(x - 7/5)(x - 11/3) = 0
x - -4/9 = 0
x - 7/5 = 0
x - 11/3 = 0
x = -4/9
x = 7/5
x = 11/3


Input: Find x in x^3 + 13/10x^2 - 38/45x + 1/10 = 0

Output:
x^3 + 13/10x^2 - 38/45x + 1/10 = 0
(x - -9/5)(x - 1/6)(x - 1/3) = 0
x - -9/5 = 0
x - 1/6 = 0
x - 1/3 = 0
x = -9/5
x = 1/6
x = 1/3


Input:
Solve simultaneously:
2x + 5y = -25/2
4x + 5y = -35/2

Output:
2x + 5y = -25/2
4x + 5y = -35/2

Using elimination
4*(2x + 5y = -25/2)
2*(4x + 5y = -35/2)
8x + 20y = -50
8x + 10y = -35
Subtract equations
10y = -15
y = -15/10
y = -3/2

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


Input: Solve 5x - 9/2 = 0

Output:
5x - 9/2 = 0
5x = 9/2
x = 9/2 / 5
x = 9/10


Input: What value of x satisfies x^3 - 19/9x^2 - 152/27x + 140/27 = 0

Output:
x^3 - 19/9x^2 - 152/27x + 140/27 = 0
(x - 10/3)(x - -2)(x - 7/9) = 0
x - 10/3 = 0
x - -2 = 0
x - 7/9 = 0
x = 10/3
x = -2
x = 7/9


Input: Determine x in 3x - 11/3 = 0

Output:
3x - 11/3 = 0
3x = 11/3
x = 11/3 / 3
x = 11/9


Input: Determine x in 3x + 21/4 = 0

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


Input:
Solve simultaneously:
1x + 4y = -71/15
2x + 9y = -49/5

Output:
1x + 4y = -71/15
2x + 9y = -49/5

Using elimination
2*(1x + 4y = -71/15)
1*(2x + 9y = -49/5)
2x + 8y = -142/15
2x + 9y = -49/5
Subtract equations
-1y = 1/3
y = 1/3/-1
y = -1/3

Substitute y
1x + 4(-1/3) = -71/15
1x = -17/5
x = -17/5/1
x = -17/5


Input: Solve quickly: 4x + 15/2 = 0

Output:
4x + 15/2 = 0
4x = -15/2
x = -15/2 / 4
x = -15/8


Input: Solve 1x + 2 = 0

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


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

Output:
2x - 9/2 = 0
2x = 9/2
x = 9/2 / 2
x = 9/4


Input: Determine x in 5x - 55/7 = 0

Output:
5x - 55/7 = 0
5x = 55/7
x = 55/7 / 5
x = 11/7


Input:
Solve simultaneously:
5x + 9y = -182/45
10x + 9y = -607/45

Output:
5x + 9y = -182/45
10x + 9y = -607/45

Using elimination
10*(5x + 9y = -182/45)
5*(10x + 9y = -607/45)
50x + 90y = -364/9
50x + 45y = -607/9
Subtract equations
45y = 27
y = 27/45
y = 3/5

Substitute y
5x + 9(3/5) = -182/45
5x = -85/9
x = -85/9/5
x = -17/9


Input: Solve quickly: x^3 - 143/70x^2 - 242/245x + 1331/490 = 0

Output:
x^3 - 143/70x^2 - 242/245x + 1331/490 = 0
(x - 11/7)(x - 11/7)(x - -11/10) = 0
x - 11/7 = 0
x - 11/7 = 0
x - -11/10 = 0
x = 11/7
x = 11/7
x = -11/10


Input: Solve the equation 4x + 18 = 0

Output:
4x + 18 = 0
4x = -18
x = -18 / 4
x = -9/2


Input: Solve x^2 - 163/90x + 17/90 = 0

Output:
x^2 - 163/90x + 17/90 = 0
(x - 17/10)(x - 1/9) = 0
x - 17/10 = 0  or  x - 1/9 = 0
x = 17/10
x = 1/9


Input: What value of x satisfies x^3 - 11/30x^2 - 56/5x - 33/10 = 0

Output:
x^3 - 11/30x^2 - 56/5x - 33/10 = 0
(x - -3/10)(x - -3)(x - 11/3) = 0
x - -3/10 = 0
x - -3 = 0
x - 11/3 = 0
x = -3/10
x = -3
x = 11/3


Input:
Find x and y such that
3x + 10y = 733/10
6x + 7y = 278/5

Output:
3x + 10y = 733/10
6x + 7y = 278/5

Using elimination
6*(3x + 10y = 733/10)
3*(6x + 7y = 278/5)
18x + 60y = 2199/5
18x + 21y = 834/5
Subtract equations
39y = 273
y = 273/39
y = 7

Substitute y
3x + 10(7) = 733/10
3x = 33/10
x = 33/10/3
x = 11/10


Input: Solve the equation 4x + 44/7 = 0

Output:
4x + 44/7 = 0
4x = -44/7
x = -44/7 / 4
x = -11/7


Input:
Solve simultaneously:
1x + 10y = 152/9
4x + 10y = 98/9

Output:
1x + 10y = 152/9
4x + 10y = 98/9

Using elimination
4*(1x + 10y = 152/9)
1*(4x + 10y = 98/9)
4x + 40y = 608/9
4x + 10y = 98/9
Subtract equations
30y = 170/3
y = 170/3/30
y = 17/9

Substitute y
1x + 10(17/9) = 152/9
1x = -2
x = -2/1
x = -2


Input: Compute the solution of x^2 - 17/12x - 133/24 = 0

Output:
x^2 - 17/12x - 133/24 = 0
(x - 19/6)(x - -7/4) = 0
x - 19/6 = 0  or  x - -7/4 = 0
x = 19/6
x = -7/4


Input:
Solve simultaneously:
2x + 5y = 86
2x + 4y = 68

Output:
2x + 5y = 86
2x + 4y = 68

Using elimination
2*(2x + 5y = 86)
2*(2x + 4y = 68)
4x + 10y = 172
4x + 8y = 136
Subtract equations
2y = 36
y = 36/2
y = 18

Substitute y
2x + 5(18) = 86
2x = -4
x = -4/2
x = -2


Input:
Find x and y such that
7x + 10y = 459/20
2x + 2y = 99/20

Output:
7x + 10y = 459/20
2x + 2y = 99/20

Using elimination
2*(7x + 10y = 459/20)
7*(2x + 2y = 99/20)
14x + 20y = 459/10
14x + 14y = 693/20
Subtract equations
6y = 45/4
y = 45/4/6
y = 15/8

Substitute y
7x + 10(15/8) = 459/20
7x = 21/5
x = 21/5/7
x = 3/5


Input: Compute the solution of x^2 - 20/7x - 75/7 = 0

Output:
x^2 - 20/7x - 75/7 = 0
(x - -15/7)(x - 5) = 0
x - -15/7 = 0  or  x - 5 = 0
x = -15/7
x = 5


Input: Find x for x^3 - 25/6x^2 - 83/6x + 17 = 0

Output:
x^3 - 25/6x^2 - 83/6x + 17 = 0
(x - -17/6)(x - 1)(x - 6) = 0
x - -17/6 = 0
x - 1 = 0
x - 6 = 0
x = -17/6
x = 1
x = 6


Input: Find x in x^3 + 261/20x^2 + 247/20x - 3 = 0

Output:
x^3 + 261/20x^2 + 247/20x - 3 = 0
(x - 1/5)(x - -12)(x - -5/4) = 0
x - 1/5 = 0
x - -12 = 0
x - -5/4 = 0
x = 1/5
x = -12
x = -5/4


Input: Solve quickly: x^3 - 11/2x^2 + 5x + 4 = 0

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


Input:
Solve the system:
3x + 7y = -181/7
8x + 8y = -184/7

Output:
3x + 7y = -181/7
8x + 8y = -184/7

Using elimination
8*(3x + 7y = -181/7)
3*(8x + 8y = -184/7)
24x + 56y = -1448/7
24x + 24y = -552/7
Subtract equations
32y = -128
y = -128/32
y = -4

Substitute y
3x + 7(-4) = -181/7
3x = 15/7
x = 15/7/3
x = 5/7


Input:
Solve simultaneously:
4x + 10y = 39
4x + 1y = 51/2

Output:
4x + 10y = 39
4x + 1y = 51/2

Using elimination
4*(4x + 10y = 39)
4*(4x + 1y = 51/2)
16x + 40y = 156
16x + 4y = 102
Subtract equations
36y = 54
y = 54/36
y = 3/2

Substitute y
4x + 10(3/2) = 39
4x = 24
x = 24/4
x = 6


Input: What value of x satisfies x^3 + 25/3x^2 - 334/3x + 544/3 = 0

Output:
x^3 + 25/3x^2 - 334/3x + 544/3 = 0
(x - -16)(x - 2)(x - 17/3) = 0
x - -16 = 0
x - 2 = 0
x - 17/3 = 0
x = -16
x = 2
x = 17/3


Input: Find the solution to x^2 + 14x + 33 = 0

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


Input: Solve x^3 + 61/12x^2 + 47/8x - 9/8 = 0

Output:
x^3 + 61/12x^2 + 47/8x - 9/8 = 0
(x - -9/4)(x - 1/6)(x - -3) = 0
x - -9/4 = 0
x - 1/6 = 0
x - -3 = 0
x = -9/4
x = 1/6
x = -3


Input: Solve the equation x^3 + 71/18x^2 + 109/27x + 65/162 = 0

Output:
x^3 + 71/18x^2 + 109/27x + 65/162 = 0
(x - -1/9)(x - -5/3)(x - -13/6) = 0
x - -1/9 = 0
x - -5/3 = 0
x - -13/6 = 0
x = -1/9
x = -5/3
x = -13/6


Input: Determine x in x^3 - 1x^2 - 16x - 20 = 0

Output:
x^3 - 1x^2 - 16x - 20 = 0
(x - -2)(x - 5)(x - -2) = 0
x - -2 = 0
x - 5 = 0
x - -2 = 0
x = -2
x = 5
x = -2


Input: Solve x^2 - 25/2x + 36 = 0

Output:
x^2 - 25/2x + 36 = 0
(x - 9/2)(x - 8) = 0
x - 9/2 = 0  or  x - 8 = 0
x = 9/2
x = 8


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

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


Input: Determine x in x^3 + 1/2x^2 - 49x - 49/2 = 0

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


Input: Solve the equation x^2 - 43/15x - 76/3 = 0

Output:
x^2 - 43/15x - 76/3 = 0
(x - 20/3)(x - -19/5) = 0
x - 20/3 = 0  or  x - -19/5 = 0
x = 20/3
x = -19/5


Input: Find x in x^3 + 1/2x^2 - 20x - 75/2 = 0

Output:
x^3 + 1/2x^2 - 20x - 75/2 = 0
(x - -3)(x - -5/2)(x - 5) = 0
x - -3 = 0
x - -5/2 = 0
x - 5 = 0
x = -3
x = -5/2
x = 5


Input: Compute the solution of x^2 - 22x + 40 = 0

Output:
x^2 - 22x + 40 = 0
(x - 2)(x - 20) = 0
x - 2 = 0  or  x - 20 = 0
x = 2
x = 20


Input: Find x in x^3 - 15/28x^2 - 29/8x - 6/7 = 0

Output:
x^3 - 15/28x^2 - 29/8x - 6/7 = 0
(x - 16/7)(x - -3/2)(x - -1/4) = 0
x - 16/7 = 0
x - -3/2 = 0
x - -1/4 = 0
x = 16/7
x = -3/2
x = -1/4


Input: Solve the equation x^3 - 989/360x^2 + 53/90x + 187/120 = 0

Output:
x^3 - 989/360x^2 + 53/90x + 187/120 = 0
(x - 11/9)(x - -3/5)(x - 17/8) = 0
x - 11/9 = 0
x - -3/5 = 0
x - 17/8 = 0
x = 11/9
x = -3/5
x = 17/8


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

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


Input: Solve the equation 6x - 36 = 0

Output:
6x - 36 = 0
6x = 36
x = 36 / 6
x = 6


Input: Compute the solution of 4x + 56/5 = 0

Output:
4x + 56/5 = 0
4x = -56/5
x = -56/5 / 4
x = -14/5


Input:
Solve simultaneously:
10x + 6y = 1072/9
4x + 2y = 364/9

Output:
10x + 6y = 1072/9
4x + 2y = 364/9

Using elimination
4*(10x + 6y = 1072/9)
10*(4x + 2y = 364/9)
40x + 24y = 4288/9
40x + 20y = 3640/9
Subtract equations
4y = 72
y = 72/4
y = 18

Substitute y
10x + 6(18) = 1072/9
10x = 100/9
x = 100/9/10
x = 10/9


Input: Determine x in x^2 + 5/4x - 117/8 = 0

Output:
x^2 + 5/4x - 117/8 = 0
(x - 13/4)(x - -9/2) = 0
x - 13/4 = 0  or  x - -9/2 = 0
x = 13/4
x = -9/2


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

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


Input: Find the solution to x^3 - 9/40x^2 - 303/80x + 19/40 = 0

Output:
x^3 - 9/40x^2 - 303/80x + 19/40 = 0
(x - -19/10)(x - 1/8)(x - 2) = 0
x - -19/10 = 0
x - 1/8 = 0
x - 2 = 0
x = -19/10
x = 1/8
x = 2


Input: Determine x in x^3 + 896/45x^2 + 1588/45x + 16 = 0

Output:
x^3 + 896/45x^2 + 1588/45x + 16 = 0
(x - -18)(x - -10/9)(x - -4/5) = 0
x - -18 = 0
x - -10/9 = 0
x - -4/5 = 0
x = -18
x = -10/9
x = -4/5


Input: Find x for 2x - 10 = 0

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


Input:
Solve simultaneously:
5x + 3y = -59/8
9x + 2y = -373/24

Output:
5x + 3y = -59/8
9x + 2y = -373/24

Using elimination
9*(5x + 3y = -59/8)
5*(9x + 2y = -373/24)
45x + 27y = -531/8
45x + 10y = -1865/24
Subtract equations
17y = 34/3
y = 34/3/17
y = 2/3

Substitute y
5x + 3(2/3) = -59/8
5x = -75/8
x = -75/8/5
x = -15/8


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

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


Input: Find x for x^2 + 9/14x - 9/7 = 0

Output:
x^2 + 9/14x - 9/7 = 0
(x - -3/2)(x - 6/7) = 0
x - -3/2 = 0  or  x - 6/7 = 0
x = -3/2
x = 6/7


Input: What value of x satisfies x^3 + 77/5x^2 + 27/5x - 9 = 0

Output:
x^3 + 77/5x^2 + 27/5x - 9 = 0
(x - -1)(x - 3/5)(x - -15) = 0
x - -1 = 0
x - 3/5 = 0
x - -15 = 0
x = -1
x = 3/5
x = -15


Input: Find the solution to x^2 - 19/10x - 3/2 = 0

Output:
x^2 - 19/10x - 3/2 = 0
(x - 5/2)(x - -3/5) = 0
x - 5/2 = 0  or  x - -3/5 = 0
x = 5/2
x = -3/5


Input: Compute the solution of 6x - 120 = 0

Output:
6x - 120 = 0
6x = 120
x = 120 / 6
x = 20


Input: What value of x satisfies 6x + 36/7 = 0

Output:
6x + 36/7 = 0
6x = -36/7
x = -36/7 / 6
x = -6/7


Input: Solve x^2 - 17/21x - 8/21 = 0

Output:
x^2 - 17/21x - 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 the equations:
1x + 9y = 437/90
2x + 3y = -71/90

Output:
1x + 9y = 437/90
2x + 3y = -71/90

Using elimination
2*(1x + 9y = 437/90)
1*(2x + 3y = -71/90)
2x + 18y = 437/45
2x + 3y = -71/90
Subtract equations
15y = 21/2
y = 21/2/15
y = 7/10

Substitute y
1x + 9(7/10) = 437/90
1x = -13/9
x = -13/9/1
x = -13/9


Input: Solve quickly: 6x + 24 = 0

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


Input: Determine x in 5x + 40 = 0

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


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

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


Input:
Solve the system:
8x + 9y = 93/2
8x + 7y = 99/2

Output:
8x + 9y = 93/2
8x + 7y = 99/2

Using elimination
8*(8x + 9y = 93/2)
8*(8x + 7y = 99/2)
64x + 72y = 372
64x + 56y = 396
Subtract equations
16y = -24
y = -24/16
y = -3/2

Substitute y
8x + 9(-3/2) = 93/2
8x = 60
x = 60/8
x = 15/2


Input:
Solve the equations:
5x + 5y = -15/4
1x + 4y = 9/2

Output:
5x + 5y = -15/4
1x + 4y = 9/2

Using elimination
1*(5x + 5y = -15/4)
5*(1x + 4y = 9/2)
5x + 5y = -15/4
5x + 20y = 45/2
Subtract equations
-15y = -105/4
y = -105/4/-15
y = 7/4

Substitute y
5x + 5(7/4) = -15/4
5x = -25/2
x = -25/2/5
x = -5/2


Input: Solve the equation 10x + 15/2 = 0

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


Input: What value of x satisfies x^3 - 69/7x^2 + 153/7x - 13 = 0

Output:
x^3 - 69/7x^2 + 153/7x - 13 = 0
(x - 1)(x - 7)(x - 13/7) = 0
x - 1 = 0
x - 7 = 0
x - 13/7 = 0
x = 1
x = 7
x = 13/7


Input: Find the solution to x^3 - 13/10x^2 - 16x + 104/5 = 0

Output:
x^3 - 13/10x^2 - 16x + 104/5 = 0
(x - 4)(x - 13/10)(x - -4) = 0
x - 4 = 0
x - 13/10 = 0
x - -4 = 0
x = 4
x = 13/10
x = -4


Input:
Solve the equations:
7x + 9y = -27/5
5x + 7y = -5

Output:
7x + 9y = -27/5
5x + 7y = -5

Using elimination
5*(7x + 9y = -27/5)
7*(5x + 7y = -5)
35x + 45y = -27
35x + 49y = -35
Subtract equations
-4y = 8
y = 8/-4
y = -2

Substitute y
7x + 9(-2) = -27/5
7x = 63/5
x = 63/5/7
x = 9/5


Input: Find x for 8x + 64/5 = 0

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


Input: Compute the solution of 8x + 16/7 = 0

Output:
8x + 16/7 = 0
8x = -16/7
x = -16/7 / 8
x = -2/7


Input: Solve x^3 - 83/56x^2 - 461/112x + 15/28 = 0

Output:
x^3 - 83/56x^2 - 461/112x + 15/28 = 0
(x - -3/2)(x - 20/7)(x - 1/8) = 0
x - -3/2 = 0
x - 20/7 = 0
x - 1/8 = 0
x = -3/2
x = 20/7
x = 1/8


Input: What value of x satisfies x^3 - 15/4x^2 - 9/25x + 27/20 = 0

Output:
x^3 - 15/4x^2 - 9/25x + 27/20 = 0
(x - 15/4)(x - -3/5)(x - 3/5) = 0
x - 15/4 = 0
x - -3/5 = 0
x - 3/5 = 0
x = 15/4
x = -3/5
x = 3/5


Input: Find the solution to x^2 + 53/4x - 105/4 = 0

Output:
x^2 + 53/4x - 105/4 = 0
(x - 7/4)(x - -15) = 0
x - 7/4 = 0  or  x - -15 = 0
x = 7/4
x = -15


Input:
Solve the system:
10x + 7y = -397/12
4x + 10y = -263/6

Output:
10x + 7y = -397/12
4x + 10y = -263/6

Using elimination
4*(10x + 7y = -397/12)
10*(4x + 10y = -263/6)
40x + 28y = -397/3
40x + 100y = -1315/3
Subtract equations
-72y = 306
y = 306/-72
y = -17/4

Substitute y
10x + 7(-17/4) = -397/12
10x = -10/3
x = -10/3/10
x = -1/3


Input: Solve quickly: x^3 - 27/5x^2 + 207/25x - 81/25 = 0

Output:
x^3 - 27/5x^2 + 207/25x - 81/25 = 0
(x - 3/5)(x - 9/5)(x - 3) = 0
x - 3/5 = 0
x - 9/5 = 0
x - 3 = 0
x = 3/5
x = 9/5
x = 3


Input: Solve the equation 3x + 33/10 = 0

Output:
3x + 33/10 = 0
3x = -33/10
x = -33/10 / 3
x = -11/10


Input: What value of x satisfies 9x - 99 = 0

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


Input: Find x in 4x + 8/3 = 0

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


Input: Solve x^3 + 21/8x^2 - 463/144x - 1309/144 = 0

Output:
x^3 + 21/8x^2 - 463/144x - 1309/144 = 0
(x - -17/8)(x - -7/3)(x - 11/6) = 0
x - -17/8 = 0
x - -7/3 = 0
x - 11/6 = 0
x = -17/8
x = -7/3
x = 11/6


Input: Solve quickly: 5x + 15/2 = 0

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


Input:
Solve the system:
2x + 9y = 41
7x + 5y = 404/3

Output:
2x + 9y = 41
7x + 5y = 404/3

Using elimination
7*(2x + 9y = 41)
2*(7x + 5y = 404/3)
14x + 63y = 287
14x + 10y = 808/3
Subtract equations
53y = 53/3
y = 53/3/53
y = 1/3

Substitute y
2x + 9(1/3) = 41
2x = 38
x = 38/2
x = 19


Input: Compute the solution of 6x - 39/2 = 0

Output:
6x - 39/2 = 0
6x = 39/2
x = 39/2 / 6
x = 13/4


Input: Determine x in x^2 + 11/10x - 4/5 = 0

Output:
x^2 + 11/10x - 4/5 = 0
(x - -8/5)(x - 1/2) = 0
x - -8/5 = 0  or  x - 1/2 = 0
x = -8/5
x = 1/2


Input: Solve 1x + 1 = 0

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


Input: Compute the solution of x^3 - 253/315x^2 - 2336/315x - 256/315 = 0

Output:
x^3 - 253/315x^2 - 2336/315x - 256/315 = 0
(x - 16/5)(x - -1/9)(x - -16/7) = 0
x - 16/5 = 0
x - -1/9 = 0
x - -16/7 = 0
x = 16/5
x = -1/9
x = -16/7


Input: Solve the equation x^3 - 58/15x^2 + 77/45x + 196/45 = 0

Output:
x^3 - 58/15x^2 + 77/45x + 196/45 = 0
(x - -4/5)(x - 7/3)(x - 7/3) = 0
x - -4/5 = 0
x - 7/3 = 0
x - 7/3 = 0
x = -4/5
x = 7/3
x = 7/3


Input: Solve quickly: x^3 - 38/35x^2 - 311/35x - 38/7 = 0

Output:
x^3 - 38/35x^2 - 311/35x - 38/7 = 0
(x - -5/7)(x - 19/5)(x - -2) = 0
x - -5/7 = 0
x - 19/5 = 0
x - -2 = 0
x = -5/7
x = 19/5
x = -2


Input: What value of x satisfies x^3 + 14x^2 - 49x + 34 = 0

Output:
x^3 + 14x^2 - 49x + 34 = 0
(x - -17)(x - 1)(x - 2) = 0
x - -17 = 0
x - 1 = 0
x - 2 = 0
x = -17
x = 1
x = 2


Input:
Find x and y such that
6x + 8y = -98/5
10x + 9y = -61/2

Output:
6x + 8y = -98/5
10x + 9y = -61/2

Using elimination
10*(6x + 8y = -98/5)
6*(10x + 9y = -61/2)
60x + 80y = -196
60x + 54y = -183
Subtract equations
26y = -13
y = -13/26
y = -1/2

Substitute y
6x + 8(-1/2) = -98/5
6x = -78/5
x = -78/5/6
x = -13/5


Input: Find x for 3x - 11 = 0

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


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

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


Input:
Solve the system:
9x + 6y = 214/5
6x + 3y = 371/15

Output:
9x + 6y = 214/5
6x + 3y = 371/15

Using elimination
6*(9x + 6y = 214/5)
9*(6x + 3y = 371/15)
54x + 36y = 1284/5
54x + 27y = 1113/5
Subtract equations
9y = 171/5
y = 171/5/9
y = 19/5

Substitute y
9x + 6(19/5) = 214/5
9x = 20
x = 20/9
x = 20/9


Input:
Solve simultaneously:
9x + 10y = -46/3
7x + 1y = -119/6

Output:
9x + 10y = -46/3
7x + 1y = -119/6

Using elimination
7*(9x + 10y = -46/3)
9*(7x + 1y = -119/6)
63x + 70y = -322/3
63x + 9y = -357/2
Subtract equations
61y = 427/6
y = 427/6/61
y = 7/6

Substitute y
9x + 10(7/6) = -46/3
9x = -27
x = -27/9
x = -3


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

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


Input: Find x in x^3 + 83/6x^2 - 203/6x + 40/3 = 0

Output:
x^3 + 83/6x^2 - 203/6x + 40/3 = 0
(x - 1/2)(x - 5/3)(x - -16) = 0
x - 1/2 = 0
x - 5/3 = 0
x - -16 = 0
x = 1/2
x = 5/3
x = -16


Input: Solve x^3 + 11/9x^2 - 74/9x - 40/3 = 0

Output:
x^3 + 11/9x^2 - 74/9x - 40/3 = 0
(x - 3)(x - -20/9)(x - -2) = 0
x - 3 = 0
x - -20/9 = 0
x - -2 = 0
x = 3
x = -20/9
x = -2


Input: Solve quickly: x^3 - 4x^2 - 235/4x + 247/4 = 0

Output:
x^3 - 4x^2 - 235/4x + 247/4 = 0
(x - 1)(x - -13/2)(x - 19/2) = 0
x - 1 = 0
x - -13/2 = 0
x - 19/2 = 0
x = 1
x = -13/2
x = 19/2


Input: Find x in x^2 + 35/6x - 49/6 = 0

Output:
x^2 + 35/6x - 49/6 = 0
(x - 7/6)(x - -7) = 0
x - 7/6 = 0  or  x - -7 = 0
x = 7/6
x = -7


Input: Find the solution to 2x + 6 = 0

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


Input: Find x in 6x - 4/3 = 0

Output:
6x - 4/3 = 0
6x = 4/3
x = 4/3 / 6
x = 2/9


Input:
Solve simultaneously:
4x + 10y = 14/3
7x + 5y = 37/3

Output:
4x + 10y = 14/3
7x + 5y = 37/3

Using elimination
7*(4x + 10y = 14/3)
4*(7x + 5y = 37/3)
28x + 70y = 98/3
28x + 20y = 148/3
Subtract equations
50y = -50/3
y = -50/3/50
y = -1/3

Substitute y
4x + 10(-1/3) = 14/3
4x = 8
x = 8/4
x = 2


Input: Solve quickly: x^2 - 26/7x + 19/7 = 0

Output:
x^2 - 26/7x + 19/7 = 0
(x - 19/7)(x - 1) = 0
x - 19/7 = 0  or  x - 1 = 0
x = 19/7
x = 1


Input: Find x in 10x - 40 = 0

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


Input: Find x for 7x + 70/3 = 0

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


Input: Find x in x^3 - 7/120x^2 - 77/8x - 45/4 = 0

Output:
x^3 - 7/120x^2 - 77/8x - 45/4 = 0
(x - 18/5)(x - -15/8)(x - -5/3) = 0
x - 18/5 = 0
x - -15/8 = 0
x - -5/3 = 0
x = 18/5
x = -15/8
x = -5/3


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

Output:
x^2 + 2/21x - 55/21 = 0
(x - 11/7)(x - -5/3) = 0
x - 11/7 = 0  or  x - -5/3 = 0
x = 11/7
x = -5/3


Input:
Solve the equations:
4x + 5y = -46/3
5x + 5y = -50/3

Output:
4x + 5y = -46/3
5x + 5y = -50/3

Using elimination
5*(4x + 5y = -46/3)
4*(5x + 5y = -50/3)
20x + 25y = -230/3
20x + 20y = -200/3
Subtract equations
5y = -10
y = -10/5
y = -2

Substitute y
4x + 5(-2) = -46/3
4x = -16/3
x = -16/3/4
x = -4/3


Input: Find x for x^3 - 53/40x^2 - 41/10x + 51/10 = 0

Output:
x^3 - 53/40x^2 - 41/10x + 51/10 = 0
(x - -2)(x - 6/5)(x - 17/8) = 0
x - -2 = 0
x - 6/5 = 0
x - 17/8 = 0
x = -2
x = 6/5
x = 17/8


Input: Find x in x^3 - 17/12x^2 - 479/24x + 133/3 = 0

Output:
x^3 - 17/12x^2 - 479/24x + 133/3 = 0
(x - 8/3)(x - 7/2)(x - -19/4) = 0
x - 8/3 = 0
x - 7/2 = 0
x - -19/4 = 0
x = 8/3
x = 7/2
x = -19/4


Input: Solve the equation x^2 + 7/5x + 2/5 = 0

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


Input: What value of x satisfies 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 + 25/8x - 75/8 = 0

Output:
x^2 + 25/8x - 75/8 = 0
(x - 15/8)(x - -5) = 0
x - 15/8 = 0  or  x - -5 = 0
x = 15/8
x = -5


Input:
Solve the equations:
7x + 9y = 891/5
9x + 7y = 757/5

Output:
7x + 9y = 891/5
9x + 7y = 757/5

Using elimination
9*(7x + 9y = 891/5)
7*(9x + 7y = 757/5)
63x + 81y = 8019/5
63x + 49y = 5299/5
Subtract equations
32y = 544
y = 544/32
y = 17

Substitute y
7x + 9(17) = 891/5
7x = 126/5
x = 126/5/7
x = 18/5


Input: Find the solution to x^3 + 793/40x^2 + 168/5x + 27/2 = 0

Output:
x^3 + 793/40x^2 + 168/5x + 27/2 = 0
(x - -6/5)(x - -18)(x - -5/8) = 0
x - -6/5 = 0
x - -18 = 0
x - -5/8 = 0
x = -6/5
x = -18
x = -5/8


Input:
Find x and y such that
4x + 10y = -310/9
7x + 6y = -232/9

Output:
4x + 10y = -310/9
7x + 6y = -232/9

Using elimination
7*(4x + 10y = -310/9)
4*(7x + 6y = -232/9)
28x + 70y = -2170/9
28x + 24y = -928/9
Subtract equations
46y = -138
y = -138/46
y = -3

Substitute y
4x + 10(-3) = -310/9
4x = -40/9
x = -40/9/4
x = -10/9


Input: What value of x satisfies 8x + 32/5 = 0

Output:
8x + 32/5 = 0
8x = -32/5
x = -32/5 / 8
x = -4/5


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

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


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

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


Input: Find x for 4x - 15 = 0

Output:
4x - 15 = 0
4x = 15
x = 15 / 4
x = 15/4


Input:
Solve the system:
6x + 1y = -47/10
4x + 6y = 19/5

Output:
6x + 1y = -47/10
4x + 6y = 19/5

Using elimination
4*(6x + 1y = -47/10)
6*(4x + 6y = 19/5)
24x + 4y = -94/5
24x + 36y = 114/5
Subtract equations
-32y = -208/5
y = -208/5/-32
y = 13/10

Substitute y
6x + 1(13/10) = -47/10
6x = -6
x = -6/6
x = -1


Input: Find the solution to 6x + 48 = 0

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


Input: What value of x satisfies 9x + 99 = 0

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


Input: Find x for 9x + 18 = 0

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


Input:
Solve the equations:
6x + 4y = -20
10x + 8y = -92/3

Output:
6x + 4y = -20
10x + 8y = -92/3

Using elimination
10*(6x + 4y = -20)
6*(10x + 8y = -92/3)
60x + 40y = -200
60x + 48y = -184
Subtract equations
-8y = -16
y = -16/-8
y = 2

Substitute y
6x + 4(2) = -20
6x = -28
x = -28/6
x = -14/3


Input: Find x for x^3 + 154/15x^2 + 161/15x - 6 = 0

Output:
x^3 + 154/15x^2 + 161/15x - 6 = 0
(x - -5/3)(x - -9)(x - 2/5) = 0
x - -5/3 = 0
x - -9 = 0
x - 2/5 = 0
x = -5/3
x = -9
x = 2/5


Input: Find the solution to 8x + 72/5 = 0

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


Input: Find x for x^3 - 59/24x^2 - 533/48x - 385/48 = 0

Output:
x^3 - 59/24x^2 - 533/48x - 385/48 = 0
(x - -7/6)(x - -11/8)(x - 5) = 0
x - -7/6 = 0
x - -11/8 = 0
x - 5 = 0
x = -7/6
x = -11/8
x = 5


Input: Solve quickly: 10x - 150/7 = 0

Output:
10x - 150/7 = 0
10x = 150/7
x = 150/7 / 10
x = 15/7


Input:
Solve the system:
3x + 7y = 159/10
1x + 1y = 29/10

Output:
3x + 7y = 159/10
1x + 1y = 29/10

Using elimination
1*(3x + 7y = 159/10)
3*(1x + 1y = 29/10)
3x + 7y = 159/10
3x + 3y = 87/10
Subtract equations
4y = 36/5
y = 36/5/4
y = 9/5

Substitute y
3x + 7(9/5) = 159/10
3x = 33/10
x = 33/10/3
x = 11/10


Input: What value of x satisfies x^2 + 36/35x - 32/35 = 0

Output:
x^2 + 36/35x - 32/35 = 0
(x - 4/7)(x - -8/5) = 0
x - 4/7 = 0  or  x - -8/5 = 0
x = 4/7
x = -8/5


Input: Find the solution to x^3 - 151/14x^2 + 2288/63x - 2432/63 = 0

Output:
x^3 - 151/14x^2 + 2288/63x - 2432/63 = 0
(x - 16/7)(x - 19/6)(x - 16/3) = 0
x - 16/7 = 0
x - 19/6 = 0
x - 16/3 = 0
x = 16/7
x = 19/6
x = 16/3


Input: Solve the equation x^3 - 53/5x^2 - 179/4x - 399/10 = 0

Output:
x^3 - 53/5x^2 - 179/4x - 399/10 = 0
(x - -19/10)(x - -3/2)(x - 14) = 0
x - -19/10 = 0
x - -3/2 = 0
x - 14 = 0
x = -19/10
x = -3/2
x = 14


Input: What value of x satisfies x^3 - 11/9x^2 - 580/27x - 64/27 = 0

Output:
x^3 - 11/9x^2 - 580/27x - 64/27 = 0
(x - -4)(x - -1/9)(x - 16/3) = 0
x - -4 = 0
x - -1/9 = 0
x - 16/3 = 0
x = -4
x = -1/9
x = 16/3


Input: Find x in 7x + 112/5 = 0

Output:
7x + 112/5 = 0
7x = -112/5
x = -112/5 / 7
x = -16/5


Input: Solve 9x - 36/5 = 0

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


Input: Find x for x^2 - 8/5x - 4/5 = 0

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


Input: What value of x satisfies x^3 + 317/84x^2 + 181/56x - 13/24 = 0

Output:
x^3 + 317/84x^2 + 181/56x - 13/24 = 0
(x - 1/7)(x - -7/4)(x - -13/6) = 0
x - 1/7 = 0
x - -7/4 = 0
x - -13/6 = 0
x = 1/7
x = -7/4
x = -13/6


Input: Compute the solution of 10x - 55/3 = 0

Output:
10x - 55/3 = 0
10x = 55/3
x = 55/3 / 10
x = 11/6


Input: Solve the equation x^3 + 65/28x^2 + 1x  = 0

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


Input: Find x in x^3 - 64/9x^2 - 121/9x + 152/3 = 0

Output:
x^3 - 64/9x^2 - 121/9x + 152/3 = 0
(x - 8)(x - 19/9)(x - -3) = 0
x - 8 = 0
x - 19/9 = 0
x - -3 = 0
x = 8
x = 19/9
x = -3


Input:
Find x and y such that
1x + 1y = 3
10x + 6y = 32

Output:
1x + 1y = 3
10x + 6y = 32

Using elimination
10*(1x + 1y = 3)
1*(10x + 6y = 32)
10x + 10y = 30
10x + 6y = 32
Subtract equations
4y = -2
y = -2/4
y = -1/2

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


Input: Find the solution to x^3 - 311/70x^2 + 239/70x - 2/5 = 0

Output:
x^3 - 311/70x^2 + 239/70x - 2/5 = 0
(x - 1/7)(x - 4/5)(x - 7/2) = 0
x - 1/7 = 0
x - 4/5 = 0
x - 7/2 = 0
x = 1/7
x = 4/5
x = 7/2