Input:
Solve the system:
4x + 5y = 61/6
10x + 2y = 271/15

Output:
4x + 5y = 61/6
10x + 2y = 271/15

Using elimination
10*(4x + 5y = 61/6)
4*(10x + 2y = 271/15)
40x + 50y = 305/3
40x + 8y = 1084/15
Subtract equations
42y = 147/5
y = 147/5/42
y = 7/10

Substitute y
4x + 5(7/10) = 61/6
4x = 20/3
x = 20/3/4
x = 5/3


Input: What value of x satisfies x^3 - 181/12x^2 - 29/2x - 8/3 = 0

Output:
x^3 - 181/12x^2 - 29/2x - 8/3 = 0
(x - 16)(x - -2/3)(x - -1/4) = 0
x - 16 = 0
x - -2/3 = 0
x - -1/4 = 0
x = 16
x = -2/3
x = -1/4


Input:
Find x and y such that
1x + 8y = -331/8
2x + 6y = -131/4

Output:
1x + 8y = -331/8
2x + 6y = -131/4

Using elimination
2*(1x + 8y = -331/8)
1*(2x + 6y = -131/4)
2x + 16y = -331/4
2x + 6y = -131/4
Subtract equations
10y = -50
y = -50/10
y = -5

Substitute y
1x + 8(-5) = -331/8
1x = -11/8
x = -11/8/1
x = -11/8


Input: Find x in 6x + 12 = 0

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


Input: Compute the solution of x^3 - 1579/315x^2 + 526/63x - 208/45 = 0

Output:
x^3 - 1579/315x^2 + 526/63x - 208/45 = 0
(x - 8/5)(x - 14/9)(x - 13/7) = 0
x - 8/5 = 0
x - 14/9 = 0
x - 13/7 = 0
x = 8/5
x = 14/9
x = 13/7


Input: What value of x satisfies 6x  = 0

Output:
6x  = 0
6x = 0
x = 0 / 6
x = 0


Input: Find x in 3x - 27/5 = 0

Output:
3x - 27/5 = 0
3x = 27/5
x = 27/5 / 3
x = 9/5


Input: Solve 5x - 75/7 = 0

Output:
5x - 75/7 = 0
5x = 75/7
x = 75/7 / 5
x = 15/7


Input: Determine x in 4x - 2 = 0

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


Input: Compute the solution of 4x + 1 = 0

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


Input: What value of x satisfies x^2 - 71/18x + 65/18 = 0

Output:
x^2 - 71/18x + 65/18 = 0
(x - 5/2)(x - 13/9) = 0
x - 5/2 = 0  or  x - 13/9 = 0
x = 5/2
x = 13/9


Input: Find x in 5x + 5 = 0

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


Input: Find x in x^2 - 9/5x + 4/5 = 0

Output:
x^2 - 9/5x + 4/5 = 0
(x - 1)(x - 4/5) = 0
x - 1 = 0  or  x - 4/5 = 0
x = 1
x = 4/5


Input: Solve x^2 - 21/8x + 19/32 = 0

Output:
x^2 - 21/8x + 19/32 = 0
(x - 19/8)(x - 1/4) = 0
x - 19/8 = 0  or  x - 1/4 = 0
x = 19/8
x = 1/4


Input: Determine x in x^3 + 49/5x^2 + 132/5x + 108/5 = 0

Output:
x^3 + 49/5x^2 + 132/5x + 108/5 = 0
(x - -2)(x - -6)(x - -9/5) = 0
x - -2 = 0
x - -6 = 0
x - -9/5 = 0
x = -2
x = -6
x = -9/5


Input: Solve quickly: 9x + 27 = 0

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


Input:
Solve the equations:
4x + 7y = 117/8
2x + 5y = 63/8

Output:
4x + 7y = 117/8
2x + 5y = 63/8

Using elimination
2*(4x + 7y = 117/8)
4*(2x + 5y = 63/8)
8x + 14y = 117/4
8x + 20y = 63/2
Subtract equations
-6y = -9/4
y = -9/4/-6
y = 3/8

Substitute y
4x + 7(3/8) = 117/8
4x = 12
x = 12/4
x = 3


Input: Find x in x^2 - 50/3x + 200/3 = 0

Output:
x^2 - 50/3x + 200/3 = 0
(x - 20/3)(x - 10) = 0
x - 20/3 = 0  or  x - 10 = 0
x = 20/3
x = 10


Input: Compute the solution of x^2 + 73/15x + 22/5 = 0

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


Input:
Solve the equations:
9x + 6y = -145/7
2x + 8y = -830/63

Output:
9x + 6y = -145/7
2x + 8y = -830/63

Using elimination
2*(9x + 6y = -145/7)
9*(2x + 8y = -830/63)
18x + 12y = -290/7
18x + 72y = -830/7
Subtract equations
-60y = 540/7
y = 540/7/-60
y = -9/7

Substitute y
9x + 6(-9/7) = -145/7
9x = -13
x = -13/9
x = -13/9


Input: Find the solution to x^2 - 23/6x - 55/6 = 0

Output:
x^2 - 23/6x - 55/6 = 0
(x - 11/2)(x - -5/3) = 0
x - 11/2 = 0  or  x - -5/3 = 0
x = 11/2
x = -5/3


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

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


Input: What value of x satisfies x^3 + 253/40x^2 - 109/8x - 9/5 = 0

Output:
x^3 + 253/40x^2 - 109/8x - 9/5 = 0
(x - -8)(x - -1/8)(x - 9/5) = 0
x - -8 = 0
x - -1/8 = 0
x - 9/5 = 0
x = -8
x = -1/8
x = 9/5


Input: What value of x satisfies 6x - 48 = 0

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


Input:
Solve simultaneously:
10x + 6y = -262/3
3x + 10y = -59

Output:
10x + 6y = -262/3
3x + 10y = -59

Using elimination
3*(10x + 6y = -262/3)
10*(3x + 10y = -59)
30x + 18y = -262
30x + 100y = -590
Subtract equations
-82y = 328
y = 328/-82
y = -4

Substitute y
10x + 6(-4) = -262/3
10x = -190/3
x = -190/3/10
x = -19/3


Input: Find x for x^3 + 89/30x^2 - 68/15x - 8/5 = 0

Output:
x^3 + 89/30x^2 - 68/15x - 8/5 = 0
(x - -3/10)(x - 4/3)(x - -4) = 0
x - -3/10 = 0
x - 4/3 = 0
x - -4 = 0
x = -3/10
x = 4/3
x = -4


Input: Compute the solution of x^3 - 169/12x^2 + 205/6x + 200/3 = 0

Output:
x^3 - 169/12x^2 + 205/6x + 200/3 = 0
(x - 10)(x - -5/4)(x - 16/3) = 0
x - 10 = 0
x - -5/4 = 0
x - 16/3 = 0
x = 10
x = -5/4
x = 16/3


Input:
Solve the equations:
6x + 3y = -27/10
5x + 3y = -49/20

Output:
6x + 3y = -27/10
5x + 3y = -49/20

Using elimination
5*(6x + 3y = -27/10)
6*(5x + 3y = -49/20)
30x + 15y = -27/2
30x + 18y = -147/10
Subtract equations
-3y = 6/5
y = 6/5/-3
y = -2/5

Substitute y
6x + 3(-2/5) = -27/10
6x = -3/2
x = -3/2/6
x = -1/4


Input:
Solve simultaneously:
1x + 9y = 576/7
7x + 6y = 63

Output:
1x + 9y = 576/7
7x + 6y = 63

Using elimination
7*(1x + 9y = 576/7)
1*(7x + 6y = 63)
7x + 63y = 576
7x + 6y = 63
Subtract equations
57y = 513
y = 513/57
y = 9

Substitute y
1x + 9(9) = 576/7
1x = 9/7
x = 9/7/1
x = 9/7


Input: Compute the solution of x^3 - 155/18x^2 + 233/27x - 20/9 = 0

Output:
x^3 - 155/18x^2 + 233/27x - 20/9 = 0
(x - 2/3)(x - 15/2)(x - 4/9) = 0
x - 2/3 = 0
x - 15/2 = 0
x - 4/9 = 0
x = 2/3
x = 15/2
x = 4/9


Input: Determine x in x^3 + 167/30x^2 - 31x - 1547/30 = 0

Output:
x^3 + 167/30x^2 - 31x - 1547/30 = 0
(x - 13/3)(x - -7/5)(x - -17/2) = 0
x - 13/3 = 0
x - -7/5 = 0
x - -17/2 = 0
x = 13/3
x = -7/5
x = -17/2


Input: Solve 10x - 65 = 0

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


Input: Solve the equation x^2 - 49/4x + 55/4 = 0

Output:
x^2 - 49/4x + 55/4 = 0
(x - 11)(x - 5/4) = 0
x - 11 = 0  or  x - 5/4 = 0
x = 11
x = 5/4


Input: Solve x^2 + 25/8x + 57/32 = 0

Output:
x^2 + 25/8x + 57/32 = 0
(x - -19/8)(x - -3/4) = 0
x - -19/8 = 0  or  x - -3/4 = 0
x = -19/8
x = -3/4


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

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


Input: Solve x^3 - 19/3x^2 - 170/3x + 200 = 0

Output:
x^3 - 19/3x^2 - 170/3x + 200 = 0
(x - 3)(x - 10)(x - -20/3) = 0
x - 3 = 0
x - 10 = 0
x - -20/3 = 0
x = 3
x = 10
x = -20/3


Input: Solve quickly: x^2 - 35/2x + 153/2 = 0

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


Input: What value of x satisfies 1x + 1/3 = 0

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


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

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


Input:
Solve the equations:
4x + 2y = -1
8x + 3y = 1/2

Output:
4x + 2y = -1
8x + 3y = 1/2

Using elimination
8*(4x + 2y = -1)
4*(8x + 3y = 1/2)
32x + 16y = -8
32x + 12y = 2
Subtract equations
4y = -10
y = -10/4
y = -5/2

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


Input: Solve quickly: x^2 - 99/20x + 28/5 = 0

Output:
x^2 - 99/20x + 28/5 = 0
(x - 16/5)(x - 7/4) = 0
x - 16/5 = 0  or  x - 7/4 = 0
x = 16/5
x = 7/4


Input: Solve x^3 - 4/5x^2 - 367/80x + 819/160 = 0

Output:
x^3 - 4/5x^2 - 367/80x + 819/160 = 0
(x - -9/4)(x - 7/4)(x - 13/10) = 0
x - -9/4 = 0
x - 7/4 = 0
x - 13/10 = 0
x = -9/4
x = 7/4
x = 13/10


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

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


Input: Find the solution to x^2 - 28/15x + 1/3 = 0

Output:
x^2 - 28/15x + 1/3 = 0
(x - 5/3)(x - 1/5) = 0
x - 5/3 = 0  or  x - 1/5 = 0
x = 5/3
x = 1/5


Input: Solve quickly: 3x + 2 = 0

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


Input: Solve the equation x^3 + 73/21x^2 + 67/21x + 5/7 = 0

Output:
x^3 + 73/21x^2 + 67/21x + 5/7 = 0
(x - -1/3)(x - -15/7)(x - -1) = 0
x - -1/3 = 0
x - -15/7 = 0
x - -1 = 0
x = -1/3
x = -15/7
x = -1


Input: What value of x satisfies x^3 + 257/210x^2 - 898/105x - 38/5 = 0

Output:
x^3 + 257/210x^2 - 898/105x - 38/5 = 0
(x - 14/5)(x - -6/7)(x - -19/6) = 0
x - 14/5 = 0
x - -6/7 = 0
x - -19/6 = 0
x = 14/5
x = -6/7
x = -19/6


Input: Solve x^3 + 75/14x^2 + 103/14x + 3 = 0

Output:
x^3 + 75/14x^2 + 103/14x + 3 = 0
(x - -7/2)(x - -6/7)(x - -1) = 0
x - -7/2 = 0
x - -6/7 = 0
x - -1 = 0
x = -7/2
x = -6/7
x = -1


Input: Solve x^2 - 104/5x + 171/5 = 0

Output:
x^2 - 104/5x + 171/5 = 0
(x - 9/5)(x - 19) = 0
x - 9/5 = 0  or  x - 19 = 0
x = 9/5
x = 19


Input:
Solve the equations:
8x + 7y = -21/10
4x + 7y = -21/10

Output:
8x + 7y = -21/10
4x + 7y = -21/10

Using elimination
4*(8x + 7y = -21/10)
8*(4x + 7y = -21/10)
32x + 28y = -42/5
32x + 56y = -84/5
Subtract equations
-28y = 42/5
y = 42/5/-28
y = -3/10

Substitute y
8x + 7(-3/10) = -21/10
8x = 0
x = 0/8
x = 0


Input: Compute the solution of x^2 - 14/3x  = 0

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


Input: Find x in x^2 + 19/5x + 13/4 = 0

Output:
x^2 + 19/5x + 13/4 = 0
(x - -5/2)(x - -13/10) = 0
x - -5/2 = 0  or  x - -13/10 = 0
x = -5/2
x = -13/10


Input: Solve the equation x^2 + 83/20x + 117/40 = 0

Output:
x^2 + 83/20x + 117/40 = 0
(x - -9/10)(x - -13/4) = 0
x - -9/10 = 0  or  x - -13/4 = 0
x = -9/10
x = -13/4


Input:
Solve the system:
8x + 4y = 328/15
6x + 10y = 43

Output:
8x + 4y = 328/15
6x + 10y = 43

Using elimination
6*(8x + 4y = 328/15)
8*(6x + 10y = 43)
48x + 24y = 656/5
48x + 80y = 344
Subtract equations
-56y = -1064/5
y = -1064/5/-56
y = 19/5

Substitute y
8x + 4(19/5) = 328/15
8x = 20/3
x = 20/3/8
x = 5/6


Input: Find the solution to x^2 - 97/56x + 3/4 = 0

Output:
x^2 - 97/56x + 3/4 = 0
(x - 7/8)(x - 6/7) = 0
x - 7/8 = 0  or  x - 6/7 = 0
x = 7/8
x = 6/7


Input:
Solve simultaneously:
4x + 4y = -7/2
4x + 5y = -43/8

Output:
4x + 4y = -7/2
4x + 5y = -43/8

Using elimination
4*(4x + 4y = -7/2)
4*(4x + 5y = -43/8)
16x + 16y = -14
16x + 20y = -43/2
Subtract equations
-4y = 15/2
y = 15/2/-4
y = -15/8

Substitute y
4x + 4(-15/8) = -7/2
4x = 4
x = 4/4
x = 1


Input: Compute the solution of x^3 + 17/3x^2 + 4x - 32/3 = 0

Output:
x^3 + 17/3x^2 + 4x - 32/3 = 0
(x - 1)(x - -4)(x - -8/3) = 0
x - 1 = 0
x - -4 = 0
x - -8/3 = 0
x = 1
x = -4
x = -8/3


Input: Solve quickly: x^3 + 77/4x^2 + 109/2x + 40 = 0

Output:
x^3 + 77/4x^2 + 109/2x + 40 = 0
(x - -5/4)(x - -16)(x - -2) = 0
x - -5/4 = 0
x - -16 = 0
x - -2 = 0
x = -5/4
x = -16
x = -2


Input: Determine x in x^2 - 11/30x - 1/5 = 0

Output:
x^2 - 11/30x - 1/5 = 0
(x - -3/10)(x - 2/3) = 0
x - -3/10 = 0  or  x - 2/3 = 0
x = -3/10
x = 2/3


Input:
Solve the system:
9x + 10y = 521/7
1x + 3y = 124/7

Output:
9x + 10y = 521/7
1x + 3y = 124/7

Using elimination
1*(9x + 10y = 521/7)
9*(1x + 3y = 124/7)
9x + 10y = 521/7
9x + 27y = 1116/7
Subtract equations
-17y = -85
y = -85/-17
y = 5

Substitute y
9x + 10(5) = 521/7
9x = 171/7
x = 171/7/9
x = 19/7


Input:
Solve the system:
3x + 7y = -597/7
2x + 1y = -90/7

Output:
3x + 7y = -597/7
2x + 1y = -90/7

Using elimination
2*(3x + 7y = -597/7)
3*(2x + 1y = -90/7)
6x + 14y = -1194/7
6x + 3y = -270/7
Subtract equations
11y = -132
y = -132/11
y = -12

Substitute y
3x + 7(-12) = -597/7
3x = -9/7
x = -9/7/3
x = -3/7


Input:
Solve the equations:
4x + 10y = 66/7
4x + 8y = 40/7

Output:
4x + 10y = 66/7
4x + 8y = 40/7

Using elimination
4*(4x + 10y = 66/7)
4*(4x + 8y = 40/7)
16x + 40y = 264/7
16x + 32y = 160/7
Subtract equations
8y = 104/7
y = 104/7/8
y = 13/7

Substitute y
4x + 10(13/7) = 66/7
4x = -64/7
x = -64/7/4
x = -16/7


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

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

Using elimination
3*(5x + 5y = 5/3)
5*(3x + 1y = 3)
15x + 15y = 5
15x + 5y = 15
Subtract equations
10y = -10
y = -10/10
y = -1

Substitute y
5x + 5(-1) = 5/3
5x = 20/3
x = 20/3/5
x = 4/3


Input: Find the solution to x^2 + 3/5x + 1/20 = 0

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


Input:
Solve simultaneously:
5x + 6y = -283/12
2x + 7y = -323/24

Output:
5x + 6y = -283/12
2x + 7y = -323/24

Using elimination
2*(5x + 6y = -283/12)
5*(2x + 7y = -323/24)
10x + 12y = -283/6
10x + 35y = -1615/24
Subtract equations
-23y = 161/8
y = 161/8/-23
y = -7/8

Substitute y
5x + 6(-7/8) = -283/12
5x = -55/3
x = -55/3/5
x = -11/3


Input: Solve the equation x^2 - 25/3x + 28/3 = 0

Output:
x^2 - 25/3x + 28/3 = 0
(x - 7)(x - 4/3) = 0
x - 7 = 0  or  x - 4/3 = 0
x = 7
x = 4/3


Input: Solve the equation 7x + 7/3 = 0

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


Input: What value of x satisfies x^3 - 123/10x^2 + 593/25x + 684/25 = 0

Output:
x^3 - 123/10x^2 + 593/25x + 684/25 = 0
(x - -4/5)(x - 19/2)(x - 18/5) = 0
x - -4/5 = 0
x - 19/2 = 0
x - 18/5 = 0
x = -4/5
x = 19/2
x = 18/5


Input: Find x in x^3 + 79/84x^2 - 233/168x - 5/4 = 0

Output:
x^3 + 79/84x^2 - 233/168x - 5/4 = 0
(x - -5/4)(x - -6/7)(x - 7/6) = 0
x - -5/4 = 0
x - -6/7 = 0
x - 7/6 = 0
x = -5/4
x = -6/7
x = 7/6


Input: Solve the equation x^3 - 67/20x^2 - 117/10x + 153/4 = 0

Output:
x^3 - 67/20x^2 - 117/10x + 153/4 = 0
(x - -17/5)(x - 15/4)(x - 3) = 0
x - -17/5 = 0
x - 15/4 = 0
x - 3 = 0
x = -17/5
x = 15/4
x = 3


Input: Compute the solution of 4x + 28/9 = 0

Output:
4x + 28/9 = 0
4x = -28/9
x = -28/9 / 4
x = -7/9


Input:
Solve simultaneously:
2x + 2y = -3/10
8x + 5y = -99/20

Output:
2x + 2y = -3/10
8x + 5y = -99/20

Using elimination
8*(2x + 2y = -3/10)
2*(8x + 5y = -99/20)
16x + 16y = -12/5
16x + 10y = -99/10
Subtract equations
6y = 15/2
y = 15/2/6
y = 5/4

Substitute y
2x + 2(5/4) = -3/10
2x = -14/5
x = -14/5/2
x = -7/5


Input:
Solve the equations:
1x + 9y = -193/12
10x + 2y = -41/6

Output:
1x + 9y = -193/12
10x + 2y = -41/6

Using elimination
10*(1x + 9y = -193/12)
1*(10x + 2y = -41/6)
10x + 90y = -965/6
10x + 2y = -41/6
Subtract equations
88y = -154
y = -154/88
y = -7/4

Substitute y
1x + 9(-7/4) = -193/12
1x = -1/3
x = -1/3/1
x = -1/3


Input: Determine x in x^3 + 39/2x^2 + 205/2x + 150 = 0

Output:
x^3 + 39/2x^2 + 205/2x + 150 = 0
(x - -5/2)(x - -12)(x - -5) = 0
x - -5/2 = 0
x - -12 = 0
x - -5 = 0
x = -5/2
x = -12
x = -5


Input: Find x for x^3 - 153/35x^2 + 148/35x + 36/35 = 0

Output:
x^3 - 153/35x^2 + 148/35x + 36/35 = 0
(x - 2)(x - 18/7)(x - -1/5) = 0
x - 2 = 0
x - 18/7 = 0
x - -1/5 = 0
x = 2
x = 18/7
x = -1/5


Input:
Solve simultaneously:
6x + 3y = 27
7x + 5y = 27

Output:
6x + 3y = 27
7x + 5y = 27

Using elimination
7*(6x + 3y = 27)
6*(7x + 5y = 27)
42x + 21y = 189
42x + 30y = 162
Subtract equations
-9y = 27
y = 27/-9
y = -3

Substitute y
6x + 3(-3) = 27
6x = 36
x = 36/6
x = 6


Input: Solve the equation x^2 + 127/35x + 22/7 = 0

Output:
x^2 + 127/35x + 22/7 = 0
(x - -11/5)(x - -10/7) = 0
x - -11/5 = 0  or  x - -10/7 = 0
x = -11/5
x = -10/7


Input:
Solve the equations:
4x + 4y = 128/9
3x + 4y = 41/3

Output:
4x + 4y = 128/9
3x + 4y = 41/3

Using elimination
3*(4x + 4y = 128/9)
4*(3x + 4y = 41/3)
12x + 12y = 128/3
12x + 16y = 164/3
Subtract equations
-4y = -12
y = -12/-4
y = 3

Substitute y
4x + 4(3) = 128/9
4x = 20/9
x = 20/9/4
x = 5/9


Input: Find the solution to 4x - 52/9 = 0

Output:
4x - 52/9 = 0
4x = 52/9
x = 52/9 / 4
x = 13/9


Input: Compute the solution of 8x + 80/9 = 0

Output:
8x + 80/9 = 0
8x = -80/9
x = -80/9 / 8
x = -10/9


Input: What value of x satisfies x^3 + 91/9x^2 + 18x + 80/9 = 0

Output:
x^3 + 91/9x^2 + 18x + 80/9 = 0
(x - -8)(x - -10/9)(x - -1) = 0
x - -8 = 0
x - -10/9 = 0
x - -1 = 0
x = -8
x = -10/9
x = -1


Input: Compute the solution of x^2 + 53/42x - 22/21 = 0

Output:
x^2 + 53/42x - 22/21 = 0
(x - 4/7)(x - -11/6) = 0
x - 4/7 = 0  or  x - -11/6 = 0
x = 4/7
x = -11/6


Input:
Solve simultaneously:
9x + 9y = -18
3x + 8y = -23/3

Output:
9x + 9y = -18
3x + 8y = -23/3

Using elimination
3*(9x + 9y = -18)
9*(3x + 8y = -23/3)
27x + 27y = -54
27x + 72y = -69
Subtract equations
-45y = 15
y = 15/-45
y = -1/3

Substitute y
9x + 9(-1/3) = -18
9x = -15
x = -15/9
x = -5/3


Input: Find the solution to x^2 - 181/28x + 285/28 = 0

Output:
x^2 - 181/28x + 285/28 = 0
(x - 15/4)(x - 19/7) = 0
x - 15/4 = 0  or  x - 19/7 = 0
x = 15/4
x = 19/7


Input:
Solve the equations:
3x + 10y = -19/3
8x + 1y = -25/3

Output:
3x + 10y = -19/3
8x + 1y = -25/3

Using elimination
8*(3x + 10y = -19/3)
3*(8x + 1y = -25/3)
24x + 80y = -152/3
24x + 3y = -25
Subtract equations
77y = -77/3
y = -77/3/77
y = -1/3

Substitute y
3x + 10(-1/3) = -19/3
3x = -3
x = -3/3
x = -1


Input: Solve x^3 + 4/5x^2 - 1473/20x + 171/2 = 0

Output:
x^3 + 4/5x^2 - 1473/20x + 171/2 = 0
(x - -19/2)(x - 6/5)(x - 15/2) = 0
x - -19/2 = 0
x - 6/5 = 0
x - 15/2 = 0
x = -19/2
x = 6/5
x = 15/2


Input: Solve quickly: x^2 + 1/3x - 10/3 = 0

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


Input: Find x in x^2 - 17/8x - 15/2 = 0

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


Input: What value of x satisfies 1x + 5/2 = 0

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


Input: Find x in x^3 - 23/2x^2 + 611/16x - 1183/32 = 0

Output:
x^3 - 23/2x^2 + 611/16x - 1183/32 = 0
(x - 7/4)(x - 13/4)(x - 13/2) = 0
x - 7/4 = 0
x - 13/4 = 0
x - 13/2 = 0
x = 7/4
x = 13/4
x = 13/2


Input:
Solve the system:
2x + 2y = 62/3
4x + 10y = 304/3

Output:
2x + 2y = 62/3
4x + 10y = 304/3

Using elimination
4*(2x + 2y = 62/3)
2*(4x + 10y = 304/3)
8x + 8y = 248/3
8x + 20y = 608/3
Subtract equations
-12y = -120
y = -120/-12
y = 10

Substitute y
2x + 2(10) = 62/3
2x = 2/3
x = 2/3/2
x = 1/3


Input:
Find x and y such that
5x + 3y = -57/20
2x + 4y = -3/10

Output:
5x + 3y = -57/20
2x + 4y = -3/10

Using elimination
2*(5x + 3y = -57/20)
5*(2x + 4y = -3/10)
10x + 6y = -57/10
10x + 20y = -3/2
Subtract equations
-14y = -21/5
y = -21/5/-14
y = 3/10

Substitute y
5x + 3(3/10) = -57/20
5x = -15/4
x = -15/4/5
x = -3/4


Input: Compute the solution of 6x + 28 = 0

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


Input: Determine x in x^2 + 86/45x + 8/9 = 0

Output:
x^2 + 86/45x + 8/9 = 0
(x - -4/5)(x - -10/9) = 0
x - -4/5 = 0  or  x - -10/9 = 0
x = -4/5
x = -10/9


Input: Solve x^3 + 29/45x^2 - 91/15x + 3 = 0

Output:
x^3 + 29/45x^2 - 91/15x + 3 = 0
(x - 9/5)(x - 5/9)(x - -3) = 0
x - 9/5 = 0
x - 5/9 = 0
x - -3 = 0
x = 9/5
x = 5/9
x = -3


Input: Find x for 10x + 34 = 0

Output:
10x + 34 = 0
10x = -34
x = -34 / 10
x = -17/5


Input:
Solve the equations:
5x + 7y = 31/2
5x + 8y = 20

Output:
5x + 7y = 31/2
5x + 8y = 20

Using elimination
5*(5x + 7y = 31/2)
5*(5x + 8y = 20)
25x + 35y = 155/2
25x + 40y = 100
Subtract equations
-5y = -45/2
y = -45/2/-5
y = 9/2

Substitute y
5x + 7(9/2) = 31/2
5x = -16
x = -16/5
x = -16/5


Input:
Find x and y such that
5x + 10y = 0
6x + 1y = 110/3

Output:
5x + 10y = 0
6x + 1y = 110/3

Using elimination
6*(5x + 10y = 0)
5*(6x + 1y = 110/3)
30x + 60y = 0
30x + 5y = 550/3
Subtract equations
55y = -550/3
y = -550/3/55
y = -10/3

Substitute y
5x + 10(-10/3) = 0
5x = 100/3
x = 100/3/5
x = 20/3


Input:
Find x and y such that
4x + 7y = -5/3
10x + 1y = -29/3

Output:
4x + 7y = -5/3
10x + 1y = -29/3

Using elimination
10*(4x + 7y = -5/3)
4*(10x + 1y = -29/3)
40x + 70y = -50/3
40x + 4y = -116/3
Subtract equations
66y = 22
y = 22/66
y = 1/3

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


Input:
Solve simultaneously:
3x + 7y = 259/4
10x + 8y = 166

Output:
3x + 7y = 259/4
10x + 8y = 166

Using elimination
10*(3x + 7y = 259/4)
3*(10x + 8y = 166)
30x + 70y = 1295/2
30x + 24y = 498
Subtract equations
46y = 299/2
y = 299/2/46
y = 13/4

Substitute y
3x + 7(13/4) = 259/4
3x = 42
x = 42/3
x = 14


Input: Compute the solution of 5x - 16 = 0

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


Input:
Solve the equations:
2x + 3y = 1
7x + 1y = 45/2

Output:
2x + 3y = 1
7x + 1y = 45/2

Using elimination
7*(2x + 3y = 1)
2*(7x + 1y = 45/2)
14x + 21y = 7
14x + 2y = 45
Subtract equations
19y = -38
y = -38/19
y = -2

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


Input:
Solve the system:
3x + 10y = -17/4
7x + 6y = -5/4

Output:
3x + 10y = -17/4
7x + 6y = -5/4

Using elimination
7*(3x + 10y = -17/4)
3*(7x + 6y = -5/4)
21x + 70y = -119/4
21x + 18y = -15/4
Subtract equations
52y = -26
y = -26/52
y = -1/2

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


Input:
Solve the system:
4x + 3y = -313/5
6x + 9y = -429/5

Output:
4x + 3y = -313/5
6x + 9y = -429/5

Using elimination
6*(4x + 3y = -313/5)
4*(6x + 9y = -429/5)
24x + 18y = -1878/5
24x + 36y = -1716/5
Subtract equations
-18y = -162/5
y = -162/5/-18
y = 9/5

Substitute y
4x + 3(9/5) = -313/5
4x = -68
x = -68/4
x = -17


Input:
Find x and y such that
5x + 7y = 389/12
7x + 10y = 275/6

Output:
5x + 7y = 389/12
7x + 10y = 275/6

Using elimination
7*(5x + 7y = 389/12)
5*(7x + 10y = 275/6)
35x + 49y = 2723/12
35x + 50y = 1375/6
Subtract equations
-1y = -9/4
y = -9/4/-1
y = 9/4

Substitute y
5x + 7(9/4) = 389/12
5x = 50/3
x = 50/3/5
x = 10/3


Input: Find the solution to x^3 - 31/10x^2 + 3/2x  = 0

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


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

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


Input: Determine x in 6x - 17 = 0

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


Input:
Find x and y such that
5x + 1y = 48
10x + 7y = 197/2

Output:
5x + 1y = 48
10x + 7y = 197/2

Using elimination
10*(5x + 1y = 48)
5*(10x + 7y = 197/2)
50x + 10y = 480
50x + 35y = 985/2
Subtract equations
-25y = -25/2
y = -25/2/-25
y = 1/2

Substitute y
5x + 1(1/2) = 48
5x = 95/2
x = 95/2/5
x = 19/2


Input: Solve quickly: x^3 + 20/3x^2 + 13/3x - 20 = 0

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


Input:
Find x and y such that
8x + 2y = -19/15
8x + 7y = -13/30

Output:
8x + 2y = -19/15
8x + 7y = -13/30

Using elimination
8*(8x + 2y = -19/15)
8*(8x + 7y = -13/30)
64x + 16y = -152/15
64x + 56y = -52/15
Subtract equations
-40y = -20/3
y = -20/3/-40
y = 1/6

Substitute y
8x + 2(1/6) = -19/15
8x = -8/5
x = -8/5/8
x = -1/5


Input: Find x for x^3 - 5/6x^2 - 8/3x + 5/2 = 0

Output:
x^3 - 5/6x^2 - 8/3x + 5/2 = 0
(x - 3/2)(x - -5/3)(x - 1) = 0
x - 3/2 = 0
x - -5/3 = 0
x - 1 = 0
x = 3/2
x = -5/3
x = 1


Input:
Find x and y such that
9x + 10y = -34/9
5x + 6y = -2

Output:
9x + 10y = -34/9
5x + 6y = -2

Using elimination
5*(9x + 10y = -34/9)
9*(5x + 6y = -2)
45x + 50y = -170/9
45x + 54y = -18
Subtract equations
-4y = -8/9
y = -8/9/-4
y = 2/9

Substitute y
9x + 10(2/9) = -34/9
9x = -6
x = -6/9
x = -2/3


Input: Solve x^2 + 26/3x + 16/3 = 0

Output:
x^2 + 26/3x + 16/3 = 0
(x - -8)(x - -2/3) = 0
x - -8 = 0  or  x - -2/3 = 0
x = -8
x = -2/3


Input:
Solve simultaneously:
2x + 6y = -266/15
7x + 6y = -616/15

Output:
2x + 6y = -266/15
7x + 6y = -616/15

Using elimination
7*(2x + 6y = -266/15)
2*(7x + 6y = -616/15)
14x + 42y = -1862/15
14x + 12y = -1232/15
Subtract equations
30y = -42
y = -42/30
y = -7/5

Substitute y
2x + 6(-7/5) = -266/15
2x = -28/3
x = -28/3/2
x = -14/3


Input: Solve x^2 + 10x + 16 = 0

Output:
x^2 + 10x + 16 = 0
(x - -2)(x - -8) = 0
x - -2 = 0  or  x - -8 = 0
x = -2
x = -8


Input:
Find x and y such that
2x + 5y = -75/7
3x + 4y = -88/7

Output:
2x + 5y = -75/7
3x + 4y = -88/7

Using elimination
3*(2x + 5y = -75/7)
2*(3x + 4y = -88/7)
6x + 15y = -225/7
6x + 8y = -176/7
Subtract equations
7y = -7
y = -7/7
y = -1

Substitute y
2x + 5(-1) = -75/7
2x = -40/7
x = -40/7/2
x = -20/7


Input: Solve quickly: x^3 - 93/10x^2 + 1367/100x - 51/40 = 0

Output:
x^3 - 93/10x^2 + 1367/100x - 51/40 = 0
(x - 15/2)(x - 17/10)(x - 1/10) = 0
x - 15/2 = 0
x - 17/10 = 0
x - 1/10 = 0
x = 15/2
x = 17/10
x = 1/10


Input: Solve the equation 7x + 56/5 = 0

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


Input: Solve the equation 10x - 10/3 = 0

Output:
10x - 10/3 = 0
10x = 10/3
x = 10/3 / 10
x = 1/3


Input:
Find x and y such that
8x + 3y = -127/7
7x + 8y = -52/7

Output:
8x + 3y = -127/7
7x + 8y = -52/7

Using elimination
7*(8x + 3y = -127/7)
8*(7x + 8y = -52/7)
56x + 21y = -127
56x + 64y = -416/7
Subtract equations
-43y = -473/7
y = -473/7/-43
y = 11/7

Substitute y
8x + 3(11/7) = -127/7
8x = -160/7
x = -160/7/8
x = -20/7


Input: Solve x^2 + 13/4x - 35/4 = 0

Output:
x^2 + 13/4x - 35/4 = 0
(x - -5)(x - 7/4) = 0
x - -5 = 0  or  x - 7/4 = 0
x = -5
x = 7/4


Input:
Solve simultaneously:
9x + 8y = -66
10x + 1y = -97

Output:
9x + 8y = -66
10x + 1y = -97

Using elimination
10*(9x + 8y = -66)
9*(10x + 1y = -97)
90x + 80y = -660
90x + 9y = -873
Subtract equations
71y = 213
y = 213/71
y = 3

Substitute y
9x + 8(3) = -66
9x = -90
x = -90/9
x = -10


Input: Find the solution to x^3 - 1229/56x^2 + 4187/56x - 1881/28 = 0

Output:
x^3 - 1229/56x^2 + 4187/56x - 1881/28 = 0
(x - 18)(x - 11/7)(x - 19/8) = 0
x - 18 = 0
x - 11/7 = 0
x - 19/8 = 0
x = 18
x = 11/7
x = 19/8


Input:
Find x and y such that
5x + 10y = -13/3
3x + 5y = -2

Output:
5x + 10y = -13/3
3x + 5y = -2

Using elimination
3*(5x + 10y = -13/3)
5*(3x + 5y = -2)
15x + 30y = -13
15x + 25y = -10
Subtract equations
5y = -3
y = -3/5
y = -3/5

Substitute y
5x + 10(-3/5) = -13/3
5x = 5/3
x = 5/3/5
x = 1/3


Input: Solve x^3 - 29/14x^2 - 9/7x  = 0

Output:
x^3 - 29/14x^2 - 9/7x  = 0
(x - 18/7)(x - 0)(x - -1/2) = 0
x - 18/7 = 0
x - 0 = 0
x - -1/2 = 0
x = 18/7
x = 0
x = -1/2


Input:
Solve the system:
7x + 7y = -119/4
1x + 5y = -21/4

Output:
7x + 7y = -119/4
1x + 5y = -21/4

Using elimination
1*(7x + 7y = -119/4)
7*(1x + 5y = -21/4)
7x + 7y = -119/4
7x + 35y = -147/4
Subtract equations
-28y = 7
y = 7/-28
y = -1/4

Substitute y
7x + 7(-1/4) = -119/4
7x = -28
x = -28/7
x = -4


Input: Solve the equation x^2 + 19/5x - 6 = 0

Output:
x^2 + 19/5x - 6 = 0
(x - 6/5)(x - -5) = 0
x - 6/5 = 0  or  x - -5 = 0
x = 6/5
x = -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: Compute the solution of x^2 + 3/5x - 8/5 = 0

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


Input: Find x for x^3 + 11/2x^2 - 6x - 18 = 0

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


Input: Solve 4x + 11 = 0

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


Input:
Find x and y such that
6x + 7y = -29/10
6x + 10y = -7/2

Output:
6x + 7y = -29/10
6x + 10y = -7/2

Using elimination
6*(6x + 7y = -29/10)
6*(6x + 10y = -7/2)
36x + 42y = -87/5
36x + 60y = -21
Subtract equations
-18y = 18/5
y = 18/5/-18
y = -1/5

Substitute y
6x + 7(-1/5) = -29/10
6x = -3/2
x = -3/2/6
x = -1/4


Input: Find the solution to 5x + 20 = 0

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


Input:
Solve simultaneously:
7x + 1y = 15
1x + 3y = -85/7

Output:
7x + 1y = 15
1x + 3y = -85/7

Using elimination
1*(7x + 1y = 15)
7*(1x + 3y = -85/7)
7x + 1y = 15
7x + 21y = -85
Subtract equations
-20y = 100
y = 100/-20
y = -5

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


Input:
Find x and y such that
8x + 10y = -72
5x + 3y = -199/5

Output:
8x + 10y = -72
5x + 3y = -199/5

Using elimination
5*(8x + 10y = -72)
8*(5x + 3y = -199/5)
40x + 50y = -360
40x + 24y = -1592/5
Subtract equations
26y = -208/5
y = -208/5/26
y = -8/5

Substitute y
8x + 10(-8/5) = -72
8x = -56
x = -56/8
x = -7


Input:
Solve simultaneously:
8x + 9y = 33
3x + 6y = 95/4

Output:
8x + 9y = 33
3x + 6y = 95/4

Using elimination
3*(8x + 9y = 33)
8*(3x + 6y = 95/4)
24x + 27y = 99
24x + 48y = 190
Subtract equations
-21y = -91
y = -91/-21
y = 13/3

Substitute y
8x + 9(13/3) = 33
8x = -6
x = -6/8
x = -3/4


Input: What value of x satisfies x^3 - 16/3x^2 - 121/12x + 95/4 = 0

Output:
x^3 - 16/3x^2 - 121/12x + 95/4 = 0
(x - -5/2)(x - 19/3)(x - 3/2) = 0
x - -5/2 = 0
x - 19/3 = 0
x - 3/2 = 0
x = -5/2
x = 19/3
x = 3/2


Input: Find x in x^2 - 31/8x - 45/8 = 0

Output:
x^2 - 31/8x - 45/8 = 0
(x - -9/8)(x - 5) = 0
x - -9/8 = 0  or  x - 5 = 0
x = -9/8
x = 5


Input: Determine x in 10x - 90 = 0

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


Input: What value of x satisfies x^3 - 397/42x^2 + 313/21x + 95/6 = 0

Output:
x^3 - 397/42x^2 + 313/21x + 95/6 = 0
(x - -5/7)(x - 19/6)(x - 7) = 0
x - -5/7 = 0
x - 19/6 = 0
x - 7 = 0
x = -5/7
x = 19/6
x = 7


Input: Determine x in x^3 + 13/6x^2 - 3/2x - 5/3 = 0

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


Input:
Find x and y such that
2x + 5y = -1
6x + 9y = -27/5

Output:
2x + 5y = -1
6x + 9y = -27/5

Using elimination
6*(2x + 5y = -1)
2*(6x + 9y = -27/5)
12x + 30y = -6
12x + 18y = -54/5
Subtract equations
12y = 24/5
y = 24/5/12
y = 2/5

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


Input: Find the solution to x^3 - 37/40x^2 - 31/40x + 7/10 = 0

Output:
x^3 - 37/40x^2 - 31/40x + 7/10 = 0
(x - 1)(x - -7/8)(x - 4/5) = 0
x - 1 = 0
x - -7/8 = 0
x - 4/5 = 0
x = 1
x = -7/8
x = 4/5


Input: Solve quickly: 6x - 54/5 = 0

Output:
6x - 54/5 = 0
6x = 54/5
x = 54/5 / 6
x = 9/5


Input: Solve the equation x^3 - 53/28x^2 - 95/7x  = 0

Output:
x^3 - 53/28x^2 - 95/7x  = 0
(x - 0)(x - -20/7)(x - 19/4) = 0
x - 0 = 0
x - -20/7 = 0
x - 19/4 = 0
x = 0
x = -20/7
x = 19/4


Input: Compute the solution of x^3 - 23/10x^2 - 427/80x + 441/40 = 0

Output:
x^3 - 23/10x^2 - 427/80x + 441/40 = 0
(x - 14/5)(x - -9/4)(x - 7/4) = 0
x - 14/5 = 0
x - -9/4 = 0
x - 7/4 = 0
x = 14/5
x = -9/4
x = 7/4


Input:
Solve the equations:
3x + 4y = 97/7
9x + 1y = 163/28

Output:
3x + 4y = 97/7
9x + 1y = 163/28

Using elimination
9*(3x + 4y = 97/7)
3*(9x + 1y = 163/28)
27x + 36y = 873/7
27x + 3y = 489/28
Subtract equations
33y = 429/4
y = 429/4/33
y = 13/4

Substitute y
3x + 4(13/4) = 97/7
3x = 6/7
x = 6/7/3
x = 2/7


Input: Solve x^2 - 3x - 10 = 0

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


Input:
Solve the equations:
7x + 7y = 47
10x + 3y = 127/7

Output:
7x + 7y = 47
10x + 3y = 127/7

Using elimination
10*(7x + 7y = 47)
7*(10x + 3y = 127/7)
70x + 70y = 470
70x + 21y = 127
Subtract equations
49y = 343
y = 343/49
y = 7

Substitute y
7x + 7(7) = 47
7x = -2
x = -2/7
x = -2/7


Input: Find the solution to 7x + 21/2 = 0

Output:
7x + 21/2 = 0
7x = -21/2
x = -21/2 / 7
x = -3/2


Input:
Solve simultaneously:
2x + 8y = 8/3
7x + 9y = 22

Output:
2x + 8y = 8/3
7x + 9y = 22

Using elimination
7*(2x + 8y = 8/3)
2*(7x + 9y = 22)
14x + 56y = 56/3
14x + 18y = 44
Subtract equations
38y = -76/3
y = -76/3/38
y = -2/3

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


Input: Solve 5x - 25/8 = 0

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


Input: Find x for 1x - 5/2 = 0

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


Input:
Solve the equations:
7x + 9y = -101/6
6x + 3y = -5

Output:
7x + 9y = -101/6
6x + 3y = -5

Using elimination
6*(7x + 9y = -101/6)
7*(6x + 3y = -5)
42x + 54y = -101
42x + 21y = -35
Subtract equations
33y = -66
y = -66/33
y = -2

Substitute y
7x + 9(-2) = -101/6
7x = 7/6
x = 7/6/7
x = 1/6


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

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


Input: Solve 9x - 27/2 = 0

Output:
9x - 27/2 = 0
9x = 27/2
x = 27/2 / 9
x = 3/2


Input: Solve the equation 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 2x - 12 = 0

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


Input: Solve quickly: x^3 - 143/28x^2 + 309/56x - 45/28 = 0

Output:
x^3 - 143/28x^2 + 309/56x - 45/28 = 0
(x - 1/2)(x - 15/4)(x - 6/7) = 0
x - 1/2 = 0
x - 15/4 = 0
x - 6/7 = 0
x = 1/2
x = 15/4
x = 6/7


Input: What value of x satisfies x^3 + 61/5x^2 + 111/4x - 189/20 = 0

Output:
x^3 + 61/5x^2 + 111/4x - 189/20 = 0
(x - -7/2)(x - -9)(x - 3/10) = 0
x - -7/2 = 0
x - -9 = 0
x - 3/10 = 0
x = -7/2
x = -9
x = 3/10


Input: Find the solution to x^3 + 53/6x^2 + 24x + 56/3 = 0

Output:
x^3 + 53/6x^2 + 24x + 56/3 = 0
(x - -4)(x - -4/3)(x - -7/2) = 0
x - -4 = 0
x - -4/3 = 0
x - -7/2 = 0
x = -4
x = -4/3
x = -7/2


Input:
Solve simultaneously:
5x + 7y = 29/6
4x + 7y = 47/6

Output:
5x + 7y = 29/6
4x + 7y = 47/6

Using elimination
4*(5x + 7y = 29/6)
5*(4x + 7y = 47/6)
20x + 28y = 58/3
20x + 35y = 235/6
Subtract equations
-7y = -119/6
y = -119/6/-7
y = 17/6

Substitute y
5x + 7(17/6) = 29/6
5x = -15
x = -15/5
x = -3


Input: Find the solution to x^3 - 19/30x^2 - 271/25x + 396/25 = 0

Output:
x^3 - 19/30x^2 - 271/25x + 396/25 = 0
(x - 11/6)(x - -18/5)(x - 12/5) = 0
x - 11/6 = 0
x - -18/5 = 0
x - 12/5 = 0
x = 11/6
x = -18/5
x = 12/5


Input: Solve the equation x^3 - 10/9x^2 - 272/81x + 256/81 = 0

Output:
x^3 - 10/9x^2 - 272/81x + 256/81 = 0
(x - 8/9)(x - -16/9)(x - 2) = 0
x - 8/9 = 0
x - -16/9 = 0
x - 2 = 0
x = 8/9
x = -16/9
x = 2


Input:
Solve the system:
4x + 2y = 88
6x + 8y = 162

Output:
4x + 2y = 88
6x + 8y = 162

Using elimination
6*(4x + 2y = 88)
4*(6x + 8y = 162)
24x + 12y = 528
24x + 32y = 648
Subtract equations
-20y = -120
y = -120/-20
y = 6

Substitute y
4x + 2(6) = 88
4x = 76
x = 76/4
x = 19


Input: Solve quickly: x^2 - 4x - 153/4 = 0

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


Input: Solve the equation x^3 + 22/15x^2 - 28/15x - 8/5 = 0

Output:
x^3 + 22/15x^2 - 28/15x - 8/5 = 0
(x - -2)(x - -2/3)(x - 6/5) = 0
x - -2 = 0
x - -2/3 = 0
x - 6/5 = 0
x = -2
x = -2/3
x = 6/5


Input: Solve quickly: x^2 - 11/24x - 7/6 = 0

Output:
x^2 - 11/24x - 7/6 = 0
(x - 4/3)(x - -7/8) = 0
x - 4/3 = 0  or  x - -7/8 = 0
x = 4/3
x = -7/8


Input: Find x in x^2 - 87/5x + 112/5 = 0

Output:
x^2 - 87/5x + 112/5 = 0
(x - 16)(x - 7/5) = 0
x - 16 = 0  or  x - 7/5 = 0
x = 16
x = 7/5


Input: Compute the solution of 10x + 14 = 0

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


Input: Find the solution to 6x - 22 = 0

Output:
6x - 22 = 0
6x = 22
x = 22 / 6
x = 11/3


Input:
Solve the system:
9x + 4y = 53
1x + 6y = 43/4

Output:
9x + 4y = 53
1x + 6y = 43/4

Using elimination
1*(9x + 4y = 53)
9*(1x + 6y = 43/4)
9x + 4y = 53
9x + 54y = 387/4
Subtract equations
-50y = -175/4
y = -175/4/-50
y = 7/8

Substitute y
9x + 4(7/8) = 53
9x = 99/2
x = 99/2/9
x = 11/2


Input:
Find x and y such that
2x + 6y = -4
4x + 10y = -8

Output:
2x + 6y = -4
4x + 10y = -8

Using elimination
4*(2x + 6y = -4)
2*(4x + 10y = -8)
8x + 24y = -16
8x + 20y = -16
Subtract equations
4y = 0
y = 0/4
y = 0

Substitute y
2x + 6(0) = -4
2x = -4
x = -4/2
x = -2


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

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


Input: Find x for 4x - 11 = 0

Output:
4x - 11 = 0
4x = 11
x = 11 / 4
x = 11/4


Input: Solve quickly: x^3 + 277/36x^2 + 275/18x + 325/36 = 0

Output:
x^3 + 277/36x^2 + 275/18x + 325/36 = 0
(x - -5/4)(x - -13/9)(x - -5) = 0
x - -5/4 = 0
x - -13/9 = 0
x - -5 = 0
x = -5/4
x = -13/9
x = -5


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

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

Using elimination
4*(1x + 4y = 11/3)
1*(4x + 4y = 8/3)
4x + 16y = 44/3
4x + 4y = 8/3
Subtract equations
12y = 12
y = 12/12
y = 1

Substitute y
1x + 4(1) = 11/3
1x = -1/3
x = -1/3/1
x = -1/3


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

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


Input:
Find x and y such that
6x + 1y = 47/14
3x + 2y = -1/28

Output:
6x + 1y = 47/14
3x + 2y = -1/28

Using elimination
3*(6x + 1y = 47/14)
6*(3x + 2y = -1/28)
18x + 3y = 141/14
18x + 12y = -3/14
Subtract equations
-9y = 72/7
y = 72/7/-9
y = -8/7

Substitute y
6x + 1(-8/7) = 47/14
6x = 9/2
x = 9/2/6
x = 3/4


Input: Determine x in x^2 - 11/6x + 1/2 = 0

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


Input:
Solve the system:
8x + 8y = -776/5
5x + 3y = -451/5

Output:
8x + 8y = -776/5
5x + 3y = -451/5

Using elimination
5*(8x + 8y = -776/5)
8*(5x + 3y = -451/5)
40x + 40y = -776
40x + 24y = -3608/5
Subtract equations
16y = -272/5
y = -272/5/16
y = -17/5

Substitute y
8x + 8(-17/5) = -776/5
8x = -128
x = -128/8
x = -16


Input: Solve quickly: 10x + 70/3 = 0

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


Input:
Find x and y such that
6x + 5y = -17/4
5x + 1y = 27/4

Output:
6x + 5y = -17/4
5x + 1y = 27/4

Using elimination
5*(6x + 5y = -17/4)
6*(5x + 1y = 27/4)
30x + 25y = -85/4
30x + 6y = 81/2
Subtract equations
19y = -247/4
y = -247/4/19
y = -13/4

Substitute y
6x + 5(-13/4) = -17/4
6x = 12
x = 12/6
x = 2


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

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


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

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


Input:
Solve the system:
10x + 3y = 29
6x + 7y = 20

Output:
10x + 3y = 29
6x + 7y = 20

Using elimination
6*(10x + 3y = 29)
10*(6x + 7y = 20)
60x + 18y = 174
60x + 70y = 200
Subtract equations
-52y = -26
y = -26/-52
y = 1/2

Substitute y
10x + 3(1/2) = 29
10x = 55/2
x = 55/2/10
x = 11/4


Input: Compute the solution of x^3 + 27/20x^2 - 2/5x  = 0

Output:
x^3 + 27/20x^2 - 2/5x  = 0
(x - 1/4)(x - -8/5)(x - 0) = 0
x - 1/4 = 0
x - -8/5 = 0
x - 0 = 0
x = 1/4
x = -8/5
x = 0


Input: Find the solution to x^3 - 44/9x^2 + 211/27x - 110/27 = 0

Output:
x^3 - 44/9x^2 + 211/27x - 110/27 = 0
(x - 2)(x - 5/3)(x - 11/9) = 0
x - 2 = 0
x - 5/3 = 0
x - 11/9 = 0
x = 2
x = 5/3
x = 11/9


Input: Solve 4x  = 0

Output:
4x  = 0
4x = 0
x = 0 / 4
x = 0


Input: Solve quickly: x^3 + 13/4x^2 - 81/16x - 1053/64 = 0

Output:
x^3 + 13/4x^2 - 81/16x - 1053/64 = 0
(x - 9/4)(x - -9/4)(x - -13/4) = 0
x - 9/4 = 0
x - -9/4 = 0
x - -13/4 = 0
x = 9/4
x = -9/4
x = -13/4


Input: Solve 6x + 36 = 0

Output:
6x + 36 = 0
6x = -36
x = -36 / 6
x = -6


Input:
Solve simultaneously:
9x + 7y = 133/8
9x + 8y = 18

Output:
9x + 7y = 133/8
9x + 8y = 18

Using elimination
9*(9x + 7y = 133/8)
9*(9x + 8y = 18)
81x + 63y = 1197/8
81x + 72y = 162
Subtract equations
-9y = -99/8
y = -99/8/-9
y = 11/8

Substitute y
9x + 7(11/8) = 133/8
9x = 7
x = 7/9
x = 7/9


Input:
Solve the equations:
8x + 8y = 512/5
9x + 6y = 351/5

Output:
8x + 8y = 512/5
9x + 6y = 351/5

Using elimination
9*(8x + 8y = 512/5)
8*(9x + 6y = 351/5)
72x + 72y = 4608/5
72x + 48y = 2808/5
Subtract equations
24y = 360
y = 360/24
y = 15

Substitute y
8x + 8(15) = 512/5
8x = -88/5
x = -88/5/8
x = -11/5


Input: Solve the equation 10x - 180/7 = 0

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


Input: Solve the equation x^3 + 133/10x^2 - 1982/25x + 2394/25 = 0

Output:
x^3 + 133/10x^2 - 1982/25x + 2394/25 = 0
(x - 19/10)(x - -18)(x - 14/5) = 0
x - 19/10 = 0
x - -18 = 0
x - 14/5 = 0
x = 19/10
x = -18
x = 14/5


Input: Solve quickly: 5x + 20 = 0

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


Input: Find x in 9x - 144 = 0

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


Input: Find x in 9x - 171/4 = 0

Output:
9x - 171/4 = 0
9x = 171/4
x = 171/4 / 9
x = 19/4


Input:
Solve the equations:
8x + 5y = 20
10x + 9y = 136/5

Output:
8x + 5y = 20
10x + 9y = 136/5

Using elimination
10*(8x + 5y = 20)
8*(10x + 9y = 136/5)
80x + 50y = 200
80x + 72y = 1088/5
Subtract equations
-22y = -88/5
y = -88/5/-22
y = 4/5

Substitute y
8x + 5(4/5) = 20
8x = 16
x = 16/8
x = 2


Input: Solve quickly: x^3 + 49/24x^2 - 1/24x - 1/4 = 0

Output:
x^3 + 49/24x^2 - 1/24x - 1/4 = 0
(x - 1/3)(x - -3/8)(x - -2) = 0
x - 1/3 = 0
x - -3/8 = 0
x - -2 = 0
x = 1/3
x = -3/8
x = -2


Input: Solve quickly: 4x - 10 = 0

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


Input: Find x for 2x + 1/4 = 0

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


Input: Find x in 3x + 12 = 0

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


Input: Solve 10x - 110/3 = 0

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


Input:
Solve the system:
9x + 8y = 15
6x + 6y = 9

Output:
9x + 8y = 15
6x + 6y = 9

Using elimination
6*(9x + 8y = 15)
9*(6x + 6y = 9)
54x + 48y = 90
54x + 54y = 81
Subtract equations
-6y = 9
y = 9/-6
y = -3/2

Substitute y
9x + 8(-3/2) = 15
9x = 27
x = 27/9
x = 3


Input: Find x for 4x - 1/2 = 0

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


Input: Solve the equation x^3 - 23/21x^2 - 75/7x + 33/7 = 0

Output:
x^3 - 23/21x^2 - 75/7x + 33/7 = 0
(x - -3)(x - 3/7)(x - 11/3) = 0
x - -3 = 0
x - 3/7 = 0
x - 11/3 = 0
x = -3
x = 3/7
x = 11/3


Input:
Solve the equations:
9x + 3y = -1071/8
6x + 4y = -177/2

Output:
9x + 3y = -1071/8
6x + 4y = -177/2

Using elimination
6*(9x + 3y = -1071/8)
9*(6x + 4y = -177/2)
54x + 18y = -3213/4
54x + 36y = -1593/2
Subtract equations
-18y = -27/4
y = -27/4/-18
y = 3/8

Substitute y
9x + 3(3/8) = -1071/8
9x = -135
x = -135/9
x = -15


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

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


Input:
Solve the system:
10x + 2y = -556/21
8x + 7y = -974/21

Output:
10x + 2y = -556/21
8x + 7y = -974/21

Using elimination
8*(10x + 2y = -556/21)
10*(8x + 7y = -974/21)
80x + 16y = -4448/21
80x + 70y = -9740/21
Subtract equations
-54y = 252
y = 252/-54
y = -14/3

Substitute y
10x + 2(-14/3) = -556/21
10x = -120/7
x = -120/7/10
x = -12/7


Input:
Solve the equations:
2x + 4y = -31/3
8x + 8y = -40/3

Output:
2x + 4y = -31/3
8x + 8y = -40/3

Using elimination
8*(2x + 4y = -31/3)
2*(8x + 8y = -40/3)
16x + 32y = -248/3
16x + 16y = -80/3
Subtract equations
16y = -56
y = -56/16
y = -7/2

Substitute y
2x + 4(-7/2) = -31/3
2x = 11/3
x = 11/3/2
x = 11/6


Input: Determine x in 6x + 20 = 0

Output:
6x + 20 = 0
6x = -20
x = -20 / 6
x = -10/3


Input:
Find x and y such that
9x + 6y = -57
1x + 5y = 63

Output:
9x + 6y = -57
1x + 5y = 63

Using elimination
1*(9x + 6y = -57)
9*(1x + 5y = 63)
9x + 6y = -57
9x + 45y = 567
Subtract equations
-39y = -624
y = -624/-39
y = 16

Substitute y
9x + 6(16) = -57
9x = -153
x = -153/9
x = -17


Input:
Solve simultaneously:
7x + 7y = -427/8
10x + 7y = -233/4

Output:
7x + 7y = -427/8
10x + 7y = -233/4

Using elimination
10*(7x + 7y = -427/8)
7*(10x + 7y = -233/4)
70x + 70y = -2135/4
70x + 49y = -1631/4
Subtract equations
21y = -126
y = -126/21
y = -6

Substitute y
7x + 7(-6) = -427/8
7x = -91/8
x = -91/8/7
x = -13/8


Input: Find the solution to 8x + 76 = 0

Output:
8x + 76 = 0
8x = -76
x = -76 / 8
x = -19/2


Input: Determine x in x^2 + 35/8x + 3/2 = 0

Output:
x^2 + 35/8x + 3/2 = 0
(x - -4)(x - -3/8) = 0
x - -4 = 0  or  x - -3/8 = 0
x = -4
x = -3/8


Input: Solve x^2 - 32/3x + 80/3 = 0

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


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

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

Using elimination
8*(10x + 3y = -52/5)
10*(8x + 5y = -52/5)
80x + 24y = -416/5
80x + 50y = -104
Subtract equations
-26y = 104/5
y = 104/5/-26
y = -4/5

Substitute y
10x + 3(-4/5) = -52/5
10x = -8
x = -8/10
x = -4/5


Input: Find the solution to x^3 + 43/8x^2 - 7/36x - 20/9 = 0

Output:
x^3 + 43/8x^2 - 7/36x - 20/9 = 0
(x - -2/3)(x - 5/8)(x - -16/3) = 0
x - -2/3 = 0
x - 5/8 = 0
x - -16/3 = 0
x = -2/3
x = 5/8
x = -16/3


Input:
Solve simultaneously:
6x + 5y = 397/6
4x + 6y = 41

Output:
6x + 5y = 397/6
4x + 6y = 41

Using elimination
4*(6x + 5y = 397/6)
6*(4x + 6y = 41)
24x + 20y = 794/3
24x + 36y = 246
Subtract equations
-16y = 56/3
y = 56/3/-16
y = -7/6

Substitute y
6x + 5(-7/6) = 397/6
6x = 72
x = 72/6
x = 12


Input:
Solve the system:
2x + 2y = 37/9
1x + 8y = 23/18

Output:
2x + 2y = 37/9
1x + 8y = 23/18

Using elimination
1*(2x + 2y = 37/9)
2*(1x + 8y = 23/18)
2x + 2y = 37/9
2x + 16y = 23/9
Subtract equations
-14y = 14/9
y = 14/9/-14
y = -1/9

Substitute y
2x + 2(-1/9) = 37/9
2x = 13/3
x = 13/3/2
x = 13/6


Input: Find the solution to 4x - 28 = 0

Output:
4x - 28 = 0
4x = 28
x = 28 / 4
x = 7


Input: Solve quickly: x^2 - 7/40x - 33/20 = 0

Output:
x^2 - 7/40x - 33/20 = 0
(x - -6/5)(x - 11/8) = 0
x - -6/5 = 0  or  x - 11/8 = 0
x = -6/5
x = 11/8


Input:
Solve the system:
10x + 8y = 34/5
8x + 10y = 29/5

Output:
10x + 8y = 34/5
8x + 10y = 29/5

Using elimination
8*(10x + 8y = 34/5)
10*(8x + 10y = 29/5)
80x + 64y = 272/5
80x + 100y = 58
Subtract equations
-36y = -18/5
y = -18/5/-36
y = 1/10

Substitute y
10x + 8(1/10) = 34/5
10x = 6
x = 6/10
x = 3/5


Input: Find x for x^3 + 6/5x^2 - 1x - 6/5 = 0

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


Input: Compute the solution of x^3 - 459/140x^2 + 213/70x - 4/7 = 0

Output:
x^3 - 459/140x^2 + 213/70x - 4/7 = 0
(x - 1/4)(x - 8/5)(x - 10/7) = 0
x - 1/4 = 0
x - 8/5 = 0
x - 10/7 = 0
x = 1/4
x = 8/5
x = 10/7


Input: Determine x in x^2 + 24/35x - 128/35 = 0

Output:
x^2 + 24/35x - 128/35 = 0
(x - 8/5)(x - -16/7) = 0
x - 8/5 = 0  or  x - -16/7 = 0
x = 8/5
x = -16/7


Input: Compute the solution of 2x - 34/7 = 0

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


Input:
Solve the equations:
10x + 1y = 10
6x + 9y = 6

Output:
10x + 1y = 10
6x + 9y = 6

Using elimination
6*(10x + 1y = 10)
10*(6x + 9y = 6)
60x + 6y = 60
60x + 90y = 60
Subtract equations
-84y = 0
y = 0/-84
y = 0

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


Input: Solve x^3 - 15/2x^2 - 22x + 144 = 0

Output:
x^3 - 15/2x^2 - 22x + 144 = 0
(x - 8)(x - 4)(x - -9/2) = 0
x - 8 = 0
x - 4 = 0
x - -9/2 = 0
x = 8
x = 4
x = -9/2


Input: Determine x in x^3 + 7/10x^2 - 81/25x - 567/250 = 0

Output:
x^3 + 7/10x^2 - 81/25x - 567/250 = 0
(x - -9/5)(x - -7/10)(x - 9/5) = 0
x - -9/5 = 0
x - -7/10 = 0
x - 9/5 = 0
x = -9/5
x = -7/10
x = 9/5


Input: Find x in x^2 + 9/5x + 4/5 = 0

Output:
x^2 + 9/5x + 4/5 = 0
(x - -4/5)(x - -1) = 0
x - -4/5 = 0  or  x - -1 = 0
x = -4/5
x = -1


Input: Solve 8x + 28/5 = 0

Output:
8x + 28/5 = 0
8x = -28/5
x = -28/5 / 8
x = -7/10


Input: Solve quickly: x^2 - 19/6x - 10/3 = 0

Output:
x^2 - 19/6x - 10/3 = 0
(x - -5/6)(x - 4) = 0
x - -5/6 = 0  or  x - 4 = 0
x = -5/6
x = 4


Input:
Find x and y such that
3x + 7y = 5
10x + 2y = 38

Output:
3x + 7y = 5
10x + 2y = 38

Using elimination
10*(3x + 7y = 5)
3*(10x + 2y = 38)
30x + 70y = 50
30x + 6y = 114
Subtract equations
64y = -64
y = -64/64
y = -1

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


Input: Find x in x^2 - 17/4x + 15/4 = 0

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


Input: Find x for 6x + 9/2 = 0

Output:
6x + 9/2 = 0
6x = -9/2
x = -9/2 / 6
x = -3/4


Input: What value of x satisfies x^3 - 86/9x^2 + 595/27x + 208/81 = 0

Output:
x^3 - 86/9x^2 + 595/27x + 208/81 = 0
(x - -1/9)(x - 13/3)(x - 16/3) = 0
x - -1/9 = 0
x - 13/3 = 0
x - 16/3 = 0
x = -1/9
x = 13/3
x = 16/3


Input: Solve 7x + 49/3 = 0

Output:
7x + 49/3 = 0
7x = -49/3
x = -49/3 / 7
x = -7/3


Input: Solve x^2 + 31/36x - 95/36 = 0

Output:
x^2 + 31/36x - 95/36 = 0
(x - 5/4)(x - -19/9) = 0
x - 5/4 = 0  or  x - -19/9 = 0
x = 5/4
x = -19/9


Input:
Solve the system:
1x + 4y = 10
5x + 1y = 43/2

Output:
1x + 4y = 10
5x + 1y = 43/2

Using elimination
5*(1x + 4y = 10)
1*(5x + 1y = 43/2)
5x + 20y = 50
5x + 1y = 43/2
Subtract equations
19y = 57/2
y = 57/2/19
y = 3/2

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


Input: What value of x satisfies x^3 + 33/8x^2 + 27/8x - 243/128 = 0

Output:
x^3 + 33/8x^2 + 27/8x - 243/128 = 0
(x - 3/8)(x - -9/4)(x - -9/4) = 0
x - 3/8 = 0
x - -9/4 = 0
x - -9/4 = 0
x = 3/8
x = -9/4
x = -9/4


Input:
Solve the equations:
4x + 10y = 11/2
1x + 3y = 49/40

Output:
4x + 10y = 11/2
1x + 3y = 49/40

Using elimination
1*(4x + 10y = 11/2)
4*(1x + 3y = 49/40)
4x + 10y = 11/2
4x + 12y = 49/10
Subtract equations
-2y = 3/5
y = 3/5/-2
y = -3/10

Substitute y
4x + 10(-3/10) = 11/2
4x = 17/2
x = 17/2/4
x = 17/8


Input: Find x in 1x + 5/3 = 0

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


Input: What value of x satisfies x^3 - 193/140x^2 - 233/140x - 11/35 = 0

Output:
x^3 - 193/140x^2 - 233/140x - 11/35 = 0
(x - -1/4)(x - 11/5)(x - -4/7) = 0
x - -1/4 = 0
x - 11/5 = 0
x - -4/7 = 0
x = -1/4
x = 11/5
x = -4/7


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

Output:
9x + 5y = 3
9x + 10y = 3

Using elimination
9*(9x + 5y = 3)
9*(9x + 10y = 3)
81x + 45y = 27
81x + 90y = 27
Subtract equations
-45y = 0
y = 0/-45
y = 0

Substitute y
9x + 5(0) = 3
9x = 3
x = 3/9
x = 1/3


Input: Solve the equation 3x - 24/7 = 0

Output:
3x - 24/7 = 0
3x = 24/7
x = 24/7 / 3
x = 8/7


Input: Find x for x^2 + 53/30x + 7/10 = 0

Output:
x^2 + 53/30x + 7/10 = 0
(x - -3/5)(x - -7/6) = 0
x - -3/5 = 0  or  x - -7/6 = 0
x = -3/5
x = -7/6


Input: Compute the solution of x^3 + 113/20x^2 + 127/20x + 17/10 = 0

Output:
x^3 + 113/20x^2 + 127/20x + 17/10 = 0
(x - -2/5)(x - -1)(x - -17/4) = 0
x - -2/5 = 0
x - -1 = 0
x - -17/4 = 0
x = -2/5
x = -1
x = -17/4


Input: Determine x in 3x + 9/8 = 0

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


Input: Solve the equation 2x + 36/7 = 0

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


Input: Find x in 3x + 36/7 = 0

Output:
3x + 36/7 = 0
3x = -36/7
x = -36/7 / 3
x = -12/7


Input: Find x for x^2 + 14/5x + 9/5 = 0

Output:
x^2 + 14/5x + 9/5 = 0
(x - -9/5)(x - -1) = 0
x - -9/5 = 0  or  x - -1 = 0
x = -9/5
x = -1


Input: Solve the equation 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: Find x in x^3 + 128/35x^2 + 117/35x  = 0

Output:
x^3 + 128/35x^2 + 117/35x  = 0
(x - -13/7)(x - 0)(x - -9/5) = 0
x - -13/7 = 0
x - 0 = 0
x - -9/5 = 0
x = -13/7
x = 0
x = -9/5


Input:
Solve the equations:
6x + 7y = 161/3
3x + 1y = 113/3

Output:
6x + 7y = 161/3
3x + 1y = 113/3

Using elimination
3*(6x + 7y = 161/3)
6*(3x + 1y = 113/3)
18x + 21y = 161
18x + 6y = 226
Subtract equations
15y = -65
y = -65/15
y = -13/3

Substitute y
6x + 7(-13/3) = 161/3
6x = 84
x = 84/6
x = 14


Input: Determine x in x^2 + 15/4x - 27/2 = 0

Output:
x^2 + 15/4x - 27/2 = 0
(x - 9/4)(x - -6) = 0
x - 9/4 = 0  or  x - -6 = 0
x = 9/4
x = -6


Input:
Find x and y such that
1x + 6y = 9/2
8x + 7y = 113/2

Output:
1x + 6y = 9/2
8x + 7y = 113/2

Using elimination
8*(1x + 6y = 9/2)
1*(8x + 7y = 113/2)
8x + 48y = 36
8x + 7y = 113/2
Subtract equations
41y = -41/2
y = -41/2/41
y = -1/2

Substitute y
1x + 6(-1/2) = 9/2
1x = 15/2
x = 15/2/1
x = 15/2


Input: Solve the equation x^2 - 34/15x - 16/15 = 0

Output:
x^2 - 34/15x - 16/15 = 0
(x - -2/5)(x - 8/3) = 0
x - -2/5 = 0  or  x - 8/3 = 0
x = -2/5
x = 8/3


Input: What value of x satisfies 1x - 4 = 0

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


Input: Determine x in 10x + 9 = 0

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


Input: Find x for x^3 - 307/120x^2 + 419/240x - 3/20 = 0

Output:
x^3 - 307/120x^2 + 419/240x - 3/20 = 0
(x - 1/10)(x - 9/8)(x - 4/3) = 0
x - 1/10 = 0
x - 9/8 = 0
x - 4/3 = 0
x = 1/10
x = 9/8
x = 4/3


Input: Solve x^3 - 35/6x^2 + 643/75x - 4/5 = 0

Output:
x^3 - 35/6x^2 + 643/75x - 4/5 = 0
(x - 10/3)(x - 12/5)(x - 1/10) = 0
x - 10/3 = 0
x - 12/5 = 0
x - 1/10 = 0
x = 10/3
x = 12/5
x = 1/10


Input: Solve x^2 + 23/7x + 60/49 = 0

Output:
x^2 + 23/7x + 60/49 = 0
(x - -20/7)(x - -3/7) = 0
x - -20/7 = 0  or  x - -3/7 = 0
x = -20/7
x = -3/7


Input:
Solve the equations:
2x + 6y = 91/6
7x + 1y = 1111/36

Output:
2x + 6y = 91/6
7x + 1y = 1111/36

Using elimination
7*(2x + 6y = 91/6)
2*(7x + 1y = 1111/36)
14x + 42y = 637/6
14x + 2y = 1111/18
Subtract equations
40y = 400/9
y = 400/9/40
y = 10/9

Substitute y
2x + 6(10/9) = 91/6
2x = 17/2
x = 17/2/2
x = 17/4


Input: Compute the solution of x^3 - 198/35x^2 + 373/35x - 234/35 = 0

Output:
x^3 - 198/35x^2 + 373/35x - 234/35 = 0
(x - 2)(x - 9/5)(x - 13/7) = 0
x - 2 = 0
x - 9/5 = 0
x - 13/7 = 0
x = 2
x = 9/5
x = 13/7


Input: Compute the solution of x^2 + 31/3x + 12 = 0

Output:
x^2 + 31/3x + 12 = 0
(x - -9)(x - -4/3) = 0
x - -9 = 0  or  x - -4/3 = 0
x = -9
x = -4/3


Input: Find x in x^3 + 83/12x^2 - 167/8x - 153/8 = 0

Output:
x^3 + 83/12x^2 - 167/8x - 153/8 = 0
(x - -9)(x - -3/4)(x - 17/6) = 0
x - -9 = 0
x - -3/4 = 0
x - 17/6 = 0
x = -9
x = -3/4
x = 17/6


Input:
Solve the equations:
6x + 4y = -20
4x + 5y = -47/3

Output:
6x + 4y = -20
4x + 5y = -47/3

Using elimination
4*(6x + 4y = -20)
6*(4x + 5y = -47/3)
24x + 16y = -80
24x + 30y = -94
Subtract equations
-14y = 14
y = 14/-14
y = -1

Substitute y
6x + 4(-1) = -20
6x = -16
x = -16/6
x = -8/3


Input: Solve quickly: 8x + 24 = 0

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


Input: Solve the equation x^3 - 29/10x^2 - 1/2x + 3/5 = 0

Output:
x^3 - 29/10x^2 - 1/2x + 3/5 = 0
(x - 2/5)(x - -1/2)(x - 3) = 0
x - 2/5 = 0
x - -1/2 = 0
x - 3 = 0
x = 2/5
x = -1/2
x = 3


Input:
Solve the equations:
10x + 2y = -361/12
2x + 6y = -95/4

Output:
10x + 2y = -361/12
2x + 6y = -95/4

Using elimination
2*(10x + 2y = -361/12)
10*(2x + 6y = -95/4)
20x + 4y = -361/6
20x + 60y = -475/2
Subtract equations
-56y = 532/3
y = 532/3/-56
y = -19/6

Substitute y
10x + 2(-19/6) = -361/12
10x = -95/4
x = -95/4/10
x = -19/8


Input:
Solve the system:
2x + 9y = 35
10x + 6y = 19

Output:
2x + 9y = 35
10x + 6y = 19

Using elimination
10*(2x + 9y = 35)
2*(10x + 6y = 19)
20x + 90y = 350
20x + 12y = 38
Subtract equations
78y = 312
y = 312/78
y = 4

Substitute y
2x + 9(4) = 35
2x = -1
x = -1/2
x = -1/2


Input:
Find x and y such that
1x + 2y = 29/12
2x + 3y = 89/24

Output:
1x + 2y = 29/12
2x + 3y = 89/24

Using elimination
2*(1x + 2y = 29/12)
1*(2x + 3y = 89/24)
2x + 4y = 29/6
2x + 3y = 89/24
Subtract equations
1y = 9/8
y = 9/8/1
y = 9/8

Substitute y
1x + 2(9/8) = 29/12
1x = 1/6
x = 1/6/1
x = 1/6


Input: Determine x in x^2 + 39/5x + 54/5 = 0

Output:
x^2 + 39/5x + 54/5 = 0
(x - -9/5)(x - -6) = 0
x - -9/5 = 0  or  x - -6 = 0
x = -9/5
x = -6


Input: Solve x^2 + 38/7x + 40/7 = 0

Output:
x^2 + 38/7x + 40/7 = 0
(x - -10/7)(x - -4) = 0
x - -10/7 = 0  or  x - -4 = 0
x = -10/7
x = -4


Input:
Solve the system:
1x + 2y = 164/45
3x + 4y = 292/45

Output:
1x + 2y = 164/45
3x + 4y = 292/45

Using elimination
3*(1x + 2y = 164/45)
1*(3x + 4y = 292/45)
3x + 6y = 164/15
3x + 4y = 292/45
Subtract equations
2y = 40/9
y = 40/9/2
y = 20/9

Substitute y
1x + 2(20/9) = 164/45
1x = -4/5
x = -4/5/1
x = -4/5


Input: Find x for x^3 + 71/210x^2 - 111/14x + 114/35 = 0

Output:
x^3 + 71/210x^2 - 111/14x + 114/35 = 0
(x - 12/5)(x - -19/6)(x - 3/7) = 0
x - 12/5 = 0
x - -19/6 = 0
x - 3/7 = 0
x = 12/5
x = -19/6
x = 3/7


Input: Find x in 7x - 14 = 0

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


Input: Solve quickly: x^2 - 127/8x - 153/8 = 0

Output:
x^2 - 127/8x - 153/8 = 0
(x - -9/8)(x - 17) = 0
x - -9/8 = 0  or  x - 17 = 0
x = -9/8
x = 17


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

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


Input:
Find x and y such that
1x + 7y = -5
7x + 7y = -17

Output:
1x + 7y = -5
7x + 7y = -17

Using elimination
7*(1x + 7y = -5)
1*(7x + 7y = -17)
7x + 49y = -35
7x + 7y = -17
Subtract equations
42y = -18
y = -18/42
y = -3/7

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


Input:
Solve simultaneously:
7x + 10y = 428/9
3x + 10y = 164/3

Output:
7x + 10y = 428/9
3x + 10y = 164/3

Using elimination
3*(7x + 10y = 428/9)
7*(3x + 10y = 164/3)
21x + 30y = 428/3
21x + 70y = 1148/3
Subtract equations
-40y = -240
y = -240/-40
y = 6

Substitute y
7x + 10(6) = 428/9
7x = -112/9
x = -112/9/7
x = -16/9


Input: Solve quickly: 6x - 7 = 0

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


Input: Find x in x^3 + 926/35x^2 + 976/7x + 1440/7 = 0

Output:
x^3 + 926/35x^2 + 976/7x + 1440/7 = 0
(x - -18/5)(x - -20)(x - -20/7) = 0
x - -18/5 = 0
x - -20 = 0
x - -20/7 = 0
x = -18/5
x = -20
x = -20/7


Input: Determine x in 4x + 64/7 = 0

Output:
4x + 64/7 = 0
4x = -64/7
x = -64/7 / 4
x = -16/7


Input: Solve quickly: 4x + 12 = 0

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


Input:
Solve the system:
7x + 5y = -1109/42
5x + 7y = -169/6

Output:
7x + 5y = -1109/42
5x + 7y = -169/6

Using elimination
5*(7x + 5y = -1109/42)
7*(5x + 7y = -169/6)
35x + 25y = -5545/42
35x + 49y = -1183/6
Subtract equations
-24y = 456/7
y = 456/7/-24
y = -19/7

Substitute y
7x + 5(-19/7) = -1109/42
7x = -77/6
x = -77/6/7
x = -11/6


Input: Compute the solution of 10x - 5/2 = 0

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


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

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


Input: Solve x^2 - 6/7x - 40/7 = 0

Output:
x^2 - 6/7x - 40/7 = 0
(x - -2)(x - 20/7) = 0
x - -2 = 0  or  x - 20/7 = 0
x = -2
x = 20/7


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

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


Input: Solve x^3 + 73/72x^2 - 139/216x - 7/12 = 0

Output:
x^3 + 73/72x^2 - 139/216x - 7/12 = 0
(x - -2/3)(x - -9/8)(x - 7/9) = 0
x - -2/3 = 0
x - -9/8 = 0
x - 7/9 = 0
x = -2/3
x = -9/8
x = 7/9


Input: Solve x^3 + 35/8x^2 - 539/32x + 343/32 = 0

Output:
x^3 + 35/8x^2 - 539/32x + 343/32 = 0
(x - -7)(x - 7/4)(x - 7/8) = 0
x - -7 = 0
x - 7/4 = 0
x - 7/8 = 0
x = -7
x = 7/4
x = 7/8


Input: Determine x in 9x - 27/2 = 0

Output:
9x - 27/2 = 0
9x = 27/2
x = 27/2 / 9
x = 3/2


Input: What value of x satisfies x^2 + 29/5x + 36/5 = 0

Output:
x^2 + 29/5x + 36/5 = 0
(x - -9/5)(x - -4) = 0
x - -9/5 = 0  or  x - -4 = 0
x = -9/5
x = -4


Input: Solve 6x + 12 = 0

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


Input: Find the solution to x^3 + 3/8x^2 - 523/144x + 35/16 = 0

Output:
x^3 + 3/8x^2 - 523/144x + 35/16 = 0
(x - -7/3)(x - 5/6)(x - 9/8) = 0
x - -7/3 = 0
x - 5/6 = 0
x - 9/8 = 0
x = -7/3
x = 5/6
x = 9/8


Input: Solve x^2 - 3/5x - 68/5 = 0

Output:
x^2 - 3/5x - 68/5 = 0
(x - 4)(x - -17/5) = 0
x - 4 = 0  or  x - -17/5 = 0
x = 4
x = -17/5


Input:
Find x and y such that
6x + 2y = -77/20
5x + 8y = -1091/40

Output:
6x + 2y = -77/20
5x + 8y = -1091/40

Using elimination
5*(6x + 2y = -77/20)
6*(5x + 8y = -1091/40)
30x + 10y = -77/4
30x + 48y = -3273/20
Subtract equations
-38y = 722/5
y = 722/5/-38
y = -19/5

Substitute y
6x + 2(-19/5) = -77/20
6x = 15/4
x = 15/4/6
x = 5/8


Input: Find the solution to x^2 + 17/36x - 35/36 = 0

Output:
x^2 + 17/36x - 35/36 = 0
(x - 7/9)(x - -5/4) = 0
x - 7/9 = 0  or  x - -5/4 = 0
x = 7/9
x = -5/4


Input:
Find x and y such that
9x + 8y = -89/10
8x + 1y = -9/5

Output:
9x + 8y = -89/10
8x + 1y = -9/5

Using elimination
8*(9x + 8y = -89/10)
9*(8x + 1y = -9/5)
72x + 64y = -356/5
72x + 9y = -81/5
Subtract equations
55y = -55
y = -55/55
y = -1

Substitute y
9x + 8(-1) = -89/10
9x = -9/10
x = -9/10/9
x = -1/10


Input: Determine x in 8x - 72/5 = 0

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


Input: Find x in x^2 + 59/30x - 28/15 = 0

Output:
x^2 + 59/30x - 28/15 = 0
(x - -8/3)(x - 7/10) = 0
x - -8/3 = 0  or  x - 7/10 = 0
x = -8/3
x = 7/10


Input: Find x in x^3 + 12/7x^2 - 4/7x  = 0

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


Input: What value of x satisfies x^3 + 119/72x^2 - 329/144x - 11/3 = 0

Output:
x^3 + 119/72x^2 - 329/144x - 11/3 = 0
(x - 3/2)(x - -11/8)(x - -16/9) = 0
x - 3/2 = 0
x - -11/8 = 0
x - -16/9 = 0
x = 3/2
x = -11/8
x = -16/9


Input: Find x in 5x + 65/3 = 0

Output:
5x + 65/3 = 0
5x = -65/3
x = -65/3 / 5
x = -13/3


Input: Compute the solution of x^2 + 11/4x - 51/8 = 0

Output:
x^2 + 11/4x - 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 quickly: 4x + 38 = 0

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


Input: Find x for x^2 - 5/6x - 7/3 = 0

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


Input: Solve quickly: 2x + 13/2 = 0

Output:
2x + 13/2 = 0
2x = -13/2
x = -13/2 / 2
x = -13/4


Input: Solve the equation 4x + 6 = 0

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


Input: Find the solution to x^3 - 11/24x^2 - 547/48x - 133/12 = 0

Output:
x^3 - 11/24x^2 - 547/48x - 133/12 = 0
(x - -19/8)(x - 4)(x - -7/6) = 0
x - -19/8 = 0
x - 4 = 0
x - -7/6 = 0
x = -19/8
x = 4
x = -7/6


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

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


Input:
Solve the equations:
4x + 8y = -280/9
10x + 1y = -377/9

Output:
4x + 8y = -280/9
10x + 1y = -377/9

Using elimination
10*(4x + 8y = -280/9)
4*(10x + 1y = -377/9)
40x + 80y = -2800/9
40x + 4y = -1508/9
Subtract equations
76y = -1292/9
y = -1292/9/76
y = -17/9

Substitute y
4x + 8(-17/9) = -280/9
4x = -16
x = -16/4
x = -4


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

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


Input: Find x for x^3 - 109/30x^2 - 808/45x - 136/9 = 0

Output:
x^3 - 109/30x^2 - 808/45x - 136/9 = 0
(x - -17/10)(x - 20/3)(x - -4/3) = 0
x - -17/10 = 0
x - 20/3 = 0
x - -4/3 = 0
x = -17/10
x = 20/3
x = -4/3


Input: Determine x in x^2 + 1x - 2 = 0

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


Input:
Find x and y such that
4x + 6y = 144/5
6x + 6y = 156/5

Output:
4x + 6y = 144/5
6x + 6y = 156/5

Using elimination
6*(4x + 6y = 144/5)
4*(6x + 6y = 156/5)
24x + 36y = 864/5
24x + 24y = 624/5
Subtract equations
12y = 48
y = 48/12
y = 4

Substitute y
4x + 6(4) = 144/5
4x = 24/5
x = 24/5/4
x = 6/5


Input: Find x for x^3 - 641/105x^2 + 1262/105x - 264/35 = 0

Output:
x^3 - 641/105x^2 + 1262/105x - 264/35 = 0
(x - 4/3)(x - 11/5)(x - 18/7) = 0
x - 4/3 = 0
x - 11/5 = 0
x - 18/7 = 0
x = 4/3
x = 11/5
x = 18/7


Input: Determine x in x^2 + 10/3x - 32/3 = 0

Output:
x^2 + 10/3x - 32/3 = 0
(x - 2)(x - -16/3) = 0
x - 2 = 0  or  x - -16/3 = 0
x = 2
x = -16/3


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

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


Input:
Solve the system:
2x + 7y = -7
7x + 10y = -302/7

Output:
2x + 7y = -7
7x + 10y = -302/7

Using elimination
7*(2x + 7y = -7)
2*(7x + 10y = -302/7)
14x + 49y = -49
14x + 20y = -604/7
Subtract equations
29y = 261/7
y = 261/7/29
y = 9/7

Substitute y
2x + 7(9/7) = -7
2x = -16
x = -16/2
x = -8


Input: Find x in x^2 - 18x - 40 = 0

Output:
x^2 - 18x - 40 = 0
(x - -2)(x - 20) = 0
x - -2 = 0  or  x - 20 = 0
x = -2
x = 20


Input: Solve x^3 + 41/12x^2 + 71/24x + 3/4 = 0

Output:
x^3 + 41/12x^2 + 71/24x + 3/4 = 0
(x - -9/4)(x - -2/3)(x - -1/2) = 0
x - -9/4 = 0
x - -2/3 = 0
x - -1/2 = 0
x = -9/4
x = -2/3
x = -1/2


Input: Solve quickly: 4x - 4 = 0

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


Input: What value of x satisfies 5x  = 0

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


Input: Solve quickly: x^2 + 17/6x + 2 = 0

Output:
x^2 + 17/6x + 2 = 0
(x - -3/2)(x - -4/3) = 0
x - -3/2 = 0  or  x - -4/3 = 0
x = -3/2
x = -4/3


Input:
Solve simultaneously:
5x + 3y = 113/4
10x + 8y = 119/2

Output:
5x + 3y = 113/4
10x + 8y = 119/2

Using elimination
10*(5x + 3y = 113/4)
5*(10x + 8y = 119/2)
50x + 30y = 565/2
50x + 40y = 595/2
Subtract equations
-10y = -15
y = -15/-10
y = 3/2

Substitute y
5x + 3(3/2) = 113/4
5x = 95/4
x = 95/4/5
x = 19/4


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

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


Input: Compute the solution of x^3 + 7/8x^2 - 121/16x + 91/16 = 0

Output:
x^3 + 7/8x^2 - 121/16x + 91/16 = 0
(x - -7/2)(x - 1)(x - 13/8) = 0
x - -7/2 = 0
x - 1 = 0
x - 13/8 = 0
x = -7/2
x = 1
x = 13/8


Input:
Solve the equations:
1x + 6y = -157/5
6x + 10y = -746/15

Output:
1x + 6y = -157/5
6x + 10y = -746/15

Using elimination
6*(1x + 6y = -157/5)
1*(6x + 10y = -746/15)
6x + 36y = -942/5
6x + 10y = -746/15
Subtract equations
26y = -416/3
y = -416/3/26
y = -16/3

Substitute y
1x + 6(-16/3) = -157/5
1x = 3/5
x = 3/5/1
x = 3/5


Input: What value of x satisfies x^2 + 29/40x - 39/8 = 0

Output:
x^2 + 29/40x - 39/8 = 0
(x - -13/5)(x - 15/8) = 0
x - -13/5 = 0  or  x - 15/8 = 0
x = -13/5
x = 15/8


Input:
Solve the system:
3x + 8y = -198/5
4x + 8y = -288/5

Output:
3x + 8y = -198/5
4x + 8y = -288/5

Using elimination
4*(3x + 8y = -198/5)
3*(4x + 8y = -288/5)
12x + 32y = -792/5
12x + 24y = -864/5
Subtract equations
8y = 72/5
y = 72/5/8
y = 9/5

Substitute y
3x + 8(9/5) = -198/5
3x = -54
x = -54/3
x = -18


Input:
Find x and y such that
10x + 6y = -27
10x + 10y = -35

Output:
10x + 6y = -27
10x + 10y = -35

Using elimination
10*(10x + 6y = -27)
10*(10x + 10y = -35)
100x + 60y = -270
100x + 100y = -350
Subtract equations
-40y = 80
y = 80/-40
y = -2

Substitute y
10x + 6(-2) = -27
10x = -15
x = -15/10
x = -3/2


Input: Find x in x^2 + 47/10x + 51/10 = 0

Output:
x^2 + 47/10x + 51/10 = 0
(x - -3)(x - -17/10) = 0
x - -3 = 0  or  x - -17/10 = 0
x = -3
x = -17/10


Input: Determine x in x^2 - 67/9x + 26/3 = 0

Output:
x^2 - 67/9x + 26/3 = 0
(x - 6)(x - 13/9) = 0
x - 6 = 0  or  x - 13/9 = 0
x = 6
x = 13/9


Input: Determine x in x^3 + 3/2x^2 - 71/18x + 5/3 = 0

Output:
x^3 + 3/2x^2 - 71/18x + 5/3 = 0
(x - 5/6)(x - 2/3)(x - -3) = 0
x - 5/6 = 0
x - 2/3 = 0
x - -3 = 0
x = 5/6
x = 2/3
x = -3


Input: Compute the solution of x^2 - 12x + 35 = 0

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


Input: What value of x satisfies x^3 + 14/9x^2 + 29/36x + 5/36 = 0

Output:
x^3 + 14/9x^2 + 29/36x + 5/36 = 0
(x - -1/2)(x - -5/9)(x - -1/2) = 0
x - -1/2 = 0
x - -5/9 = 0
x - -1/2 = 0
x = -1/2
x = -5/9
x = -1/2


Input:
Solve the equations:
1x + 7y = 392/5
8x + 1y = 111/5

Output:
1x + 7y = 392/5
8x + 1y = 111/5

Using elimination
8*(1x + 7y = 392/5)
1*(8x + 1y = 111/5)
8x + 56y = 3136/5
8x + 1y = 111/5
Subtract equations
55y = 605
y = 605/55
y = 11

Substitute y
1x + 7(11) = 392/5
1x = 7/5
x = 7/5/1
x = 7/5


Input: Find x in x^3 - 29/5x^2 + 219/20x - 27/4 = 0

Output:
x^3 - 29/5x^2 + 219/20x - 27/4 = 0
(x - 5/2)(x - 3/2)(x - 9/5) = 0
x - 5/2 = 0
x - 3/2 = 0
x - 9/5 = 0
x = 5/2
x = 3/2
x = 9/5


Input: Solve the equation x^3 - 71/12x^2 + 45/4x - 325/48 = 0

Output:
x^3 - 71/12x^2 + 45/4x - 325/48 = 0
(x - 13/6)(x - 5/2)(x - 5/4) = 0
x - 13/6 = 0
x - 5/2 = 0
x - 5/4 = 0
x = 13/6
x = 5/2
x = 5/4


Input: Determine x in x^2 - 4/15x - 32/5 = 0

Output:
x^2 - 4/15x - 32/5 = 0
(x - -12/5)(x - 8/3) = 0
x - -12/5 = 0  or  x - 8/3 = 0
x = -12/5
x = 8/3


Input: Compute the solution of 8x - 68 = 0

Output:
8x - 68 = 0
8x = 68
x = 68 / 8
x = 17/2


Input: Find x for x^3 + 41/24x^2 - 131/36x - 26/9 = 0

Output:
x^3 + 41/24x^2 - 131/36x - 26/9 = 0
(x - -2/3)(x - 13/8)(x - -8/3) = 0
x - -2/3 = 0
x - 13/8 = 0
x - -8/3 = 0
x = -2/3
x = 13/8
x = -8/3


Input:
Solve simultaneously:
7x + 9y = 141/10
3x + 6y = 69/10

Output:
7x + 9y = 141/10
3x + 6y = 69/10

Using elimination
3*(7x + 9y = 141/10)
7*(3x + 6y = 69/10)
21x + 27y = 423/10
21x + 42y = 483/10
Subtract equations
-15y = -6
y = -6/-15
y = 2/5

Substitute y
7x + 9(2/5) = 141/10
7x = 21/2
x = 21/2/7
x = 3/2


Input: Solve quickly: x^2 - 19/24x - 143/48 = 0

Output:
x^2 - 19/24x - 143/48 = 0
(x - -11/8)(x - 13/6) = 0
x - -11/8 = 0  or  x - 13/6 = 0
x = -11/8
x = 13/6


Input:
Solve the system:
3x + 7y = 199/18
10x + 1y = -115/9

Output:
3x + 7y = 199/18
10x + 1y = -115/9

Using elimination
10*(3x + 7y = 199/18)
3*(10x + 1y = -115/9)
30x + 70y = 995/9
30x + 3y = -115/3
Subtract equations
67y = 1340/9
y = 1340/9/67
y = 20/9

Substitute y
3x + 7(20/9) = 199/18
3x = -9/2
x = -9/2/3
x = -3/2


Input:
Solve the equations:
3x + 4y = -11/2
1x + 2y = -5/2

Output:
3x + 4y = -11/2
1x + 2y = -5/2

Using elimination
1*(3x + 4y = -11/2)
3*(1x + 2y = -5/2)
3x + 4y = -11/2
3x + 6y = -15/2
Subtract equations
-2y = 2
y = 2/-2
y = -1

Substitute y
3x + 4(-1) = -11/2
3x = -3/2
x = -3/2/3
x = -1/2


Input: Find x in x^3 - 119/40x^2 + 21/80x + 27/8 = 0

Output:
x^3 - 119/40x^2 + 21/80x + 27/8 = 0
(x - 2)(x - 15/8)(x - -9/10) = 0
x - 2 = 0
x - 15/8 = 0
x - -9/10 = 0
x = 2
x = 15/8
x = -9/10


Input: What value of x satisfies x^2 + 71/5x - 342/5 = 0

Output:
x^2 + 71/5x - 342/5 = 0
(x - 19/5)(x - -18) = 0
x - 19/5 = 0  or  x - -18 = 0
x = 19/5
x = -18


Input: Find the solution to 4x - 8/3 = 0

Output:
4x - 8/3 = 0
4x = 8/3
x = 8/3 / 4
x = 2/3


Input: Find x in x^3 + 19/8x^2 - 5/8x - 11/4 = 0

Output:
x^3 + 19/8x^2 - 5/8x - 11/4 = 0
(x - -2)(x - 1)(x - -11/8) = 0
x - -2 = 0
x - 1 = 0
x - -11/8 = 0
x = -2
x = 1
x = -11/8


Input: Solve quickly: x^2 - 43/12x + 35/12 = 0

Output:
x^2 - 43/12x + 35/12 = 0
(x - 5/4)(x - 7/3) = 0
x - 5/4 = 0  or  x - 7/3 = 0
x = 5/4
x = 7/3


Input: Find x for x^2 + 53/15x + 187/60 = 0

Output:
x^2 + 53/15x + 187/60 = 0
(x - -17/10)(x - -11/6) = 0
x - -17/10 = 0  or  x - -11/6 = 0
x = -17/10
x = -11/6


Input: What value of x satisfies 8x - 160/7 = 0

Output:
8x - 160/7 = 0
8x = 160/7
x = 160/7 / 8
x = 20/7


Input: Find the solution to 10x + 50/3 = 0

Output:
10x + 50/3 = 0
10x = -50/3
x = -50/3 / 10
x = -5/3


Input: What value of x satisfies x^2 - 29/2x + 45 = 0

Output:
x^2 - 29/2x + 45 = 0
(x - 10)(x - 9/2) = 0
x - 10 = 0  or  x - 9/2 = 0
x = 10
x = 9/2


Input:
Solve simultaneously:
4x + 10y = 10
6x + 2y = 33/10

Output:
4x + 10y = 10
6x + 2y = 33/10

Using elimination
6*(4x + 10y = 10)
4*(6x + 2y = 33/10)
24x + 60y = 60
24x + 8y = 66/5
Subtract equations
52y = 234/5
y = 234/5/52
y = 9/10

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


Input: Solve quickly: 2x - 1 = 0

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


Input: Solve x^2 + 17x + 30 = 0

Output:
x^2 + 17x + 30 = 0
(x - -2)(x - -15) = 0
x - -2 = 0  or  x - -15 = 0
x = -2
x = -15


Input: Solve quickly: x^3 - 19/5x^2 + 48/25x + 36/25 = 0

Output:
x^3 - 19/5x^2 + 48/25x + 36/25 = 0
(x - -2/5)(x - 3)(x - 6/5) = 0
x - -2/5 = 0
x - 3 = 0
x - 6/5 = 0
x = -2/5
x = 3
x = 6/5


Input: Solve x^2 + 139/36x + 55/18 = 0

Output:
x^2 + 139/36x + 55/18 = 0
(x - -11/4)(x - -10/9) = 0
x - -11/4 = 0  or  x - -10/9 = 0
x = -11/4
x = -10/9


Input: Solve quickly: x^2 + 38/5x - 63/5 = 0

Output:
x^2 + 38/5x - 63/5 = 0
(x - -9)(x - 7/5) = 0
x - -9 = 0  or  x - 7/5 = 0
x = -9
x = 7/5


Input: Solve x^3 + 23/3x^2 - 11/4x - 2/3 = 0

Output:
x^3 + 23/3x^2 - 11/4x - 2/3 = 0
(x - -1/6)(x - -8)(x - 1/2) = 0
x - -1/6 = 0
x - -8 = 0
x - 1/2 = 0
x = -1/6
x = -8
x = 1/2


Input: Solve quickly: x^3 + 181/20x^2 + 7/2x - 196/5 = 0

Output:
x^3 + 181/20x^2 + 7/2x - 196/5 = 0
(x - 7/4)(x - -8)(x - -14/5) = 0
x - 7/4 = 0
x - -8 = 0
x - -14/5 = 0
x = 7/4
x = -8
x = -14/5


Input: Compute the solution of x^2 - 13/9x - 10/27 = 0

Output:
x^2 - 13/9x - 10/27 = 0
(x - -2/9)(x - 5/3) = 0
x - -2/9 = 0  or  x - 5/3 = 0
x = -2/9
x = 5/3


Input: What value of x satisfies x^2 - 13/40x + 1/40 = 0

Output:
x^2 - 13/40x + 1/40 = 0
(x - 1/5)(x - 1/8) = 0
x - 1/5 = 0  or  x - 1/8 = 0
x = 1/5
x = 1/8


Input: Compute the solution of x^2 + 9/20x - 77/20 = 0

Output:
x^2 + 9/20x - 77/20 = 0
(x - -11/5)(x - 7/4) = 0
x - -11/5 = 0  or  x - 7/4 = 0
x = -11/5
x = 7/4


Input:
Solve the system:
7x + 6y = 77/10
5x + 9y = 11/2

Output:
7x + 6y = 77/10
5x + 9y = 11/2

Using elimination
5*(7x + 6y = 77/10)
7*(5x + 9y = 11/2)
35x + 30y = 77/2
35x + 63y = 77/2
Subtract equations
-33y = 0
y = 0/-33
y = 0

Substitute y
7x + 6(0) = 77/10
7x = 77/10
x = 77/10/7
x = 11/10


Input: Find the solution to 5x + 85/9 = 0

Output:
5x + 85/9 = 0
5x = -85/9
x = -85/9 / 5
x = -17/9


Input: Solve the equation x^3 - 58/21x^2 - 5/12x + 17/28 = 0

Output:
x^3 - 58/21x^2 - 5/12x + 17/28 = 0
(x - 3/7)(x - -1/2)(x - 17/6) = 0
x - 3/7 = 0
x - -1/2 = 0
x - 17/6 = 0
x = 3/7
x = -1/2
x = 17/6


Input: Solve quickly: x^3 + 17/2x^2 + 33/2x + 9 = 0

Output:
x^3 + 17/2x^2 + 33/2x + 9 = 0
(x - -6)(x - -3/2)(x - -1) = 0
x - -6 = 0
x - -3/2 = 0
x - -1 = 0
x = -6
x = -3/2
x = -1


Input: Find x in 2x  = 0

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


Input:
Solve the equations:
8x + 1y = -453/35
1x + 4y = -572/35

Output:
8x + 1y = -453/35
1x + 4y = -572/35

Using elimination
1*(8x + 1y = -453/35)
8*(1x + 4y = -572/35)
8x + 1y = -453/35
8x + 32y = -4576/35
Subtract equations
-31y = 589/5
y = 589/5/-31
y = -19/5

Substitute y
8x + 1(-19/5) = -453/35
8x = -64/7
x = -64/7/8
x = -8/7


Input: Find the solution to x^3 - 65/3x^2 + 296/3x - 128 = 0

Output:
x^3 - 65/3x^2 + 296/3x - 128 = 0
(x - 8/3)(x - 16)(x - 3) = 0
x - 8/3 = 0
x - 16 = 0
x - 3 = 0
x = 8/3
x = 16
x = 3


Input:
Find x and y such that
1x + 3y = -146/15
5x + 10y = -119/3

Output:
1x + 3y = -146/15
5x + 10y = -119/3

Using elimination
5*(1x + 3y = -146/15)
1*(5x + 10y = -119/3)
5x + 15y = -146/3
5x + 10y = -119/3
Subtract equations
5y = -9
y = -9/5
y = -9/5

Substitute y
1x + 3(-9/5) = -146/15
1x = -13/3
x = -13/3/1
x = -13/3


Input: Solve 1x - 8/3 = 0

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


Input:
Solve simultaneously:
5x + 8y = 216/7
5x + 5y = 465/28

Output:
5x + 8y = 216/7
5x + 5y = 465/28

Using elimination
5*(5x + 8y = 216/7)
5*(5x + 5y = 465/28)
25x + 40y = 1080/7
25x + 25y = 2325/28
Subtract equations
15y = 285/4
y = 285/4/15
y = 19/4

Substitute y
5x + 8(19/4) = 216/7
5x = -50/7
x = -50/7/5
x = -10/7


Input: Solve quickly: 7x + 13 = 0

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


Input: What value of x satisfies x^2 - 59/18x + 8/3 = 0

Output:
x^2 - 59/18x + 8/3 = 0
(x - 3/2)(x - 16/9) = 0
x - 3/2 = 0  or  x - 16/9 = 0
x = 3/2
x = 16/9


Input: Solve quickly: x^2 + 3/2x - 7/16 = 0

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


Input: Compute the solution of 10x - 100/9 = 0

Output:
10x - 100/9 = 0
10x = 100/9
x = 100/9 / 10
x = 10/9


Input: Solve quickly: x^2 - 109/9x + 4/3 = 0

Output:
x^2 - 109/9x + 4/3 = 0
(x - 12)(x - 1/9) = 0
x - 12 = 0  or  x - 1/9 = 0
x = 12
x = 1/9


Input:
Solve the equations:
8x + 7y = 208/5
6x + 7y = 191/5

Output:
8x + 7y = 208/5
6x + 7y = 191/5

Using elimination
6*(8x + 7y = 208/5)
8*(6x + 7y = 191/5)
48x + 42y = 1248/5
48x + 56y = 1528/5
Subtract equations
-14y = -56
y = -56/-14
y = 4

Substitute y
8x + 7(4) = 208/5
8x = 68/5
x = 68/5/8
x = 17/10


Input: Solve the equation x^3 + 102/35x^2 - 11/5x - 144/35 = 0

Output:
x^3 + 102/35x^2 - 11/5x - 144/35 = 0
(x - -1)(x - -16/5)(x - 9/7) = 0
x - -1 = 0
x - -16/5 = 0
x - 9/7 = 0
x = -1
x = -16/5
x = 9/7


Input: Find the solution to x^2 + 27/28x - 5/14 = 0

Output:
x^2 + 27/28x - 5/14 = 0
(x - 2/7)(x - -5/4) = 0
x - 2/7 = 0  or  x - -5/4 = 0
x = 2/7
x = -5/4


Input: Solve the equation 6x + 32/3 = 0

Output:
6x + 32/3 = 0
6x = -32/3
x = -32/3 / 6
x = -16/9


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

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


Input: Find x in 1x + 9 = 0

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


Input: Determine x in x^3 + 13x^2 - 106x + 152 = 0

Output:
x^3 + 13x^2 - 106x + 152 = 0
(x - 2)(x - 4)(x - -19) = 0
x - 2 = 0
x - 4 = 0
x - -19 = 0
x = 2
x = 4
x = -19


Input: Determine x in x^2 + 1/2x - 33/50 = 0

Output:
x^2 + 1/2x - 33/50 = 0
(x - -11/10)(x - 3/5) = 0
x - -11/10 = 0  or  x - 3/5 = 0
x = -11/10
x = 3/5


Input: Find x for x^2 + 9/8x - 9/16 = 0

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


Input:
Solve simultaneously:
9x + 7y = -48
5x + 7y = -164/3

Output:
9x + 7y = -48
5x + 7y = -164/3

Using elimination
5*(9x + 7y = -48)
9*(5x + 7y = -164/3)
45x + 35y = -240
45x + 63y = -492
Subtract equations
-28y = 252
y = 252/-28
y = -9

Substitute y
9x + 7(-9) = -48
9x = 15
x = 15/9
x = 5/3


Input:
Solve the system:
5x + 10y = 5
7x + 5y = 11/2

Output:
5x + 10y = 5
7x + 5y = 11/2

Using elimination
7*(5x + 10y = 5)
5*(7x + 5y = 11/2)
35x + 70y = 35
35x + 25y = 55/2
Subtract equations
45y = 15/2
y = 15/2/45
y = 1/6

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


Input: Determine x in 9x - 7 = 0

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


Input: Find x in x^2 + 23/9x + 14/9 = 0

Output:
x^2 + 23/9x + 14/9 = 0
(x - -14/9)(x - -1) = 0
x - -14/9 = 0  or  x - -1 = 0
x = -14/9
x = -1


Input: Solve x^2 + 59/9x - 28/9 = 0

Output:
x^2 + 59/9x - 28/9 = 0
(x - -7)(x - 4/9) = 0
x - -7 = 0  or  x - 4/9 = 0
x = -7
x = 4/9


Input: Find the solution to x^2 - 33/2x + 8 = 0

Output:
x^2 - 33/2x + 8 = 0
(x - 16)(x - 1/2) = 0
x - 16 = 0  or  x - 1/2 = 0
x = 16
x = 1/2


Input: Solve quickly: 9x - 90/7 = 0

Output:
9x - 90/7 = 0
9x = 90/7
x = 90/7 / 9
x = 10/7


Input: Find x in x^2 + 13/5x - 28/5 = 0

Output:
x^2 + 13/5x - 28/5 = 0
(x - 7/5)(x - -4) = 0
x - 7/5 = 0  or  x - -4 = 0
x = 7/5
x = -4


Input: Find x for 10x - 15 = 0

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


Input:
Solve the system:
2x + 2y = -14/3
7x + 10y = -79/3

Output:
2x + 2y = -14/3
7x + 10y = -79/3

Using elimination
7*(2x + 2y = -14/3)
2*(7x + 10y = -79/3)
14x + 14y = -98/3
14x + 20y = -158/3
Subtract equations
-6y = 20
y = 20/-6
y = -10/3

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


Input: Compute the solution of x^2 + 67/4x + 12 = 0

Output:
x^2 + 67/4x + 12 = 0
(x - -3/4)(x - -16) = 0
x - -3/4 = 0  or  x - -16 = 0
x = -3/4
x = -16


Input:
Solve the system:
8x + 3y = 31/24
5x + 3y = 43/24

Output:
8x + 3y = 31/24
5x + 3y = 43/24

Using elimination
5*(8x + 3y = 31/24)
8*(5x + 3y = 43/24)
40x + 15y = 155/24
40x + 24y = 43/3
Subtract equations
-9y = -63/8
y = -63/8/-9
y = 7/8

Substitute y
8x + 3(7/8) = 31/24
8x = -4/3
x = -4/3/8
x = -1/6


Input:
Solve simultaneously:
7x + 9y = 2/15
1x + 10y = 89/6

Output:
7x + 9y = 2/15
1x + 10y = 89/6

Using elimination
1*(7x + 9y = 2/15)
7*(1x + 10y = 89/6)
7x + 9y = 2/15
7x + 70y = 623/6
Subtract equations
-61y = -1037/10
y = -1037/10/-61
y = 17/10

Substitute y
7x + 9(17/10) = 2/15
7x = -91/6
x = -91/6/7
x = -13/6


Input: Find the solution to x^2 + 35/24x - 49/24 = 0

Output:
x^2 + 35/24x - 49/24 = 0
(x - -7/3)(x - 7/8) = 0
x - -7/3 = 0  or  x - 7/8 = 0
x = -7/3
x = 7/8


Input: Compute the solution of 5x - 25 = 0

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


Input:
Solve simultaneously:
6x + 2y = -178/5
8x + 5y = -40

Output:
6x + 2y = -178/5
8x + 5y = -40

Using elimination
8*(6x + 2y = -178/5)
6*(8x + 5y = -40)
48x + 16y = -1424/5
48x + 30y = -240
Subtract equations
-14y = -224/5
y = -224/5/-14
y = 16/5

Substitute y
6x + 2(16/5) = -178/5
6x = -42
x = -42/6
x = -7


Input: Find x in x^3 - 47/10x^2 + 113/25x - 28/25 = 0

Output:
x^3 - 47/10x^2 + 113/25x - 28/25 = 0
(x - 7/2)(x - 2/5)(x - 4/5) = 0
x - 7/2 = 0
x - 2/5 = 0
x - 4/5 = 0
x = 7/2
x = 2/5
x = 4/5


Input: Solve the equation 8x + 8/7 = 0

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


Input: What value of x satisfies x^2 - 196/45x + 19/9 = 0

Output:
x^2 - 196/45x + 19/9 = 0
(x - 19/5)(x - 5/9) = 0
x - 19/5 = 0  or  x - 5/9 = 0
x = 19/5
x = 5/9


Input: Solve the equation x^2 - 10/3x - 16 = 0

Output:
x^2 - 10/3x - 16 = 0
(x - 6)(x - -8/3) = 0
x - 6 = 0  or  x - -8/3 = 0
x = 6
x = -8/3


Input: Find x for x^3 - 33/40x^2 - 26/5x + 57/10 = 0

Output:
x^3 - 33/40x^2 - 26/5x + 57/10 = 0
(x - 2)(x - -19/8)(x - 6/5) = 0
x - 2 = 0
x - -19/8 = 0
x - 6/5 = 0
x = 2
x = -19/8
x = 6/5


Input: Find the solution to x^2 - 1/10x - 3/50 = 0

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


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

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


Input: Find the solution to x^3 + 3/4x^2 - 107/8x - 45/2 = 0

Output:
x^3 + 3/4x^2 - 107/8x - 45/2 = 0
(x - 4)(x - -5/2)(x - -9/4) = 0
x - 4 = 0
x - -5/2 = 0
x - -9/4 = 0
x = 4
x = -5/2
x = -9/4


Input: Find x for x^3 - 235/36x^2 + 493/36x - 28/3 = 0

Output:
x^3 - 235/36x^2 + 493/36x - 28/3 = 0
(x - 16/9)(x - 7/4)(x - 3) = 0
x - 16/9 = 0
x - 7/4 = 0
x - 3 = 0
x = 16/9
x = 7/4
x = 3


Input: Find x in 10x - 16 = 0

Output:
10x - 16 = 0
10x = 16
x = 16 / 10
x = 8/5


Input: Compute the solution of x^2 - 5/4x - 25/8 = 0

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


Input: Solve the equation 1x + 2 = 0

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


Input:
Solve the system:
9x + 1y = 43
10x + 4y = -4/3

Output:
9x + 1y = 43
10x + 4y = -4/3

Using elimination
10*(9x + 1y = 43)
9*(10x + 4y = -4/3)
90x + 10y = 430
90x + 36y = -12
Subtract equations
-26y = 442
y = 442/-26
y = -17

Substitute y
9x + 1(-17) = 43
9x = 60
x = 60/9
x = 20/3


Input: Determine x in x^3 + 59/15x^2 - 14x - 48/5 = 0

Output:
x^3 + 59/15x^2 - 14x - 48/5 = 0
(x - 8/3)(x - -6)(x - -3/5) = 0
x - 8/3 = 0
x - -6 = 0
x - -3/5 = 0
x = 8/3
x = -6
x = -3/5


Input: Find the solution to x^3 + 67/24x^2 + 23/72x - 7/4 = 0

Output:
x^3 + 67/24x^2 + 23/72x - 7/4 = 0
(x - 2/3)(x - -9/8)(x - -7/3) = 0
x - 2/3 = 0
x - -9/8 = 0
x - -7/3 = 0
x = 2/3
x = -9/8
x = -7/3


Input: Solve the equation 4x - 4 = 0

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


Input:
Solve the system:
3x + 4y = -69/7
10x + 1y = -505/21

Output:
3x + 4y = -69/7
10x + 1y = -505/21

Using elimination
10*(3x + 4y = -69/7)
3*(10x + 1y = -505/21)
30x + 40y = -690/7
30x + 3y = -505/7
Subtract equations
37y = -185/7
y = -185/7/37
y = -5/7

Substitute y
3x + 4(-5/7) = -69/7
3x = -7
x = -7/3
x = -7/3


Input: What value of x satisfies 1x + 3/4 = 0

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


Input: Find the solution to 3x - 18 = 0

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


Input: Solve quickly: x^3 + 191/84x^2 - 29/14x - 44/21 = 0

Output:
x^3 + 191/84x^2 - 29/14x - 44/21 = 0
(x - -2/3)(x - 8/7)(x - -11/4) = 0
x - -2/3 = 0
x - 8/7 = 0
x - -11/4 = 0
x = -2/3
x = 8/7
x = -11/4


Input: Find x for 4x - 34 = 0

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


Input:
Solve simultaneously:
7x + 9y = 6
2x + 6y = -12

Output:
7x + 9y = 6
2x + 6y = -12

Using elimination
2*(7x + 9y = 6)
7*(2x + 6y = -12)
14x + 18y = 12
14x + 42y = -84
Subtract equations
-24y = 96
y = 96/-24
y = -4

Substitute y
7x + 9(-4) = 6
7x = 42
x = 42/7
x = 6


Input: Find x in x^2 + 31/30x - 91/30 = 0

Output:
x^2 + 31/30x - 91/30 = 0
(x - 13/10)(x - -7/3) = 0
x - 13/10 = 0  or  x - -7/3 = 0
x = 13/10
x = -7/3


Input:
Solve simultaneously:
2x + 6y = 69/7
1x + 1y = 9/14

Output:
2x + 6y = 69/7
1x + 1y = 9/14

Using elimination
1*(2x + 6y = 69/7)
2*(1x + 1y = 9/14)
2x + 6y = 69/7
2x + 2y = 9/7
Subtract equations
4y = 60/7
y = 60/7/4
y = 15/7

Substitute y
2x + 6(15/7) = 69/7
2x = -3
x = -3/2
x = -3/2


Input: Find x for x^2 - 8/3x + 7/9 = 0

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


Input:
Find x and y such that
6x + 9y = 279/7
2x + 8y = 108/7

Output:
6x + 9y = 279/7
2x + 8y = 108/7

Using elimination
2*(6x + 9y = 279/7)
6*(2x + 8y = 108/7)
12x + 18y = 558/7
12x + 48y = 648/7
Subtract equations
-30y = -90/7
y = -90/7/-30
y = 3/7

Substitute y
6x + 9(3/7) = 279/7
6x = 36
x = 36/6
x = 6


Input: What value of x satisfies x^2 + 13/6x - 119/6 = 0

Output:
x^2 + 13/6x - 119/6 = 0
(x - 7/2)(x - -17/3) = 0
x - 7/2 = 0  or  x - -17/3 = 0
x = 7/2
x = -17/3


Input: Find x for x^3 - 22/5x^2 - 29/5x + 14 = 0

Output:
x^3 - 22/5x^2 - 29/5x + 14 = 0
(x - 5)(x - -2)(x - 7/5) = 0
x - 5 = 0
x - -2 = 0
x - 7/5 = 0
x = 5
x = -2
x = 7/5


Input: Solve the equation x^3 - 107/8x^2 - 201/8x + 45/4 = 0

Output:
x^3 - 107/8x^2 - 201/8x + 45/4 = 0
(x - 15)(x - 3/8)(x - -2) = 0
x - 15 = 0
x - 3/8 = 0
x - -2 = 0
x = 15
x = 3/8
x = -2


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

Output:
x^2 + 3/2x - 22 = 0
(x - 4)(x - -11/2) = 0
x - 4 = 0  or  x - -11/2 = 0
x = 4
x = -11/2


Input: Solve 2x + 3 = 0

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


Input: Solve x^2 + 31/15x + 14/15 = 0

Output:
x^2 + 31/15x + 14/15 = 0
(x - -2/3)(x - -7/5) = 0
x - -2/3 = 0  or  x - -7/5 = 0
x = -2/3
x = -7/5


Input: Find x for x^3 - 217/24x^2 - 3043/48x - 2023/24 = 0

Output:
x^3 - 217/24x^2 - 3043/48x - 2023/24 = 0
(x - 14)(x - -17/8)(x - -17/6) = 0
x - 14 = 0
x - -17/8 = 0
x - -17/6 = 0
x = 14
x = -17/8
x = -17/6


Input: Solve the equation x^3 + 229/72x^2 + 65/24x + 25/36 = 0

Output:
x^3 + 229/72x^2 + 65/24x + 25/36 = 0
(x - -5/9)(x - -2)(x - -5/8) = 0
x - -5/9 = 0
x - -2 = 0
x - -5/8 = 0
x = -5/9
x = -2
x = -5/8


Input: Find the solution to 1x - 5/7 = 0

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


Input:
Solve the system:
6x + 6y = -35
7x + 4y = -127/3

Output:
6x + 6y = -35
7x + 4y = -127/3

Using elimination
7*(6x + 6y = -35)
6*(7x + 4y = -127/3)
42x + 42y = -245
42x + 24y = -254
Subtract equations
18y = 9
y = 9/18
y = 1/2

Substitute y
6x + 6(1/2) = -35
6x = -38
x = -38/6
x = -19/3


Input: Find x for x^2 - 28/5x + 36/5 = 0

Output:
x^2 - 28/5x + 36/5 = 0
(x - 18/5)(x - 2) = 0
x - 18/5 = 0  or  x - 2 = 0
x = 18/5
x = 2


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

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


Input: Find x in x^2 - 149/20x + 68/5 = 0

Output:
x^2 - 149/20x + 68/5 = 0
(x - 16/5)(x - 17/4) = 0
x - 16/5 = 0  or  x - 17/4 = 0
x = 16/5
x = 17/4


Input: Solve the equation x^3 + 736/45x^2 + 2033/45x + 182/9 = 0

Output:
x^3 + 736/45x^2 + 2033/45x + 182/9 = 0
(x - -14/5)(x - -13)(x - -5/9) = 0
x - -14/5 = 0
x - -13 = 0
x - -5/9 = 0
x = -14/5
x = -13
x = -5/9


Input: Determine x in x^3 - 9/5x^2 - 129/100x + 209/100 = 0

Output:
x^3 - 9/5x^2 - 129/100x + 209/100 = 0
(x - -11/10)(x - 19/10)(x - 1) = 0
x - -11/10 = 0
x - 19/10 = 0
x - 1 = 0
x = -11/10
x = 19/10
x = 1


Input:
Solve the equations:
3x + 4y = 578/21
2x + 6y = 284/7

Output:
3x + 4y = 578/21
2x + 6y = 284/7

Using elimination
2*(3x + 4y = 578/21)
3*(2x + 6y = 284/7)
6x + 8y = 1156/21
6x + 18y = 852/7
Subtract equations
-10y = -200/3
y = -200/3/-10
y = 20/3

Substitute y
3x + 4(20/3) = 578/21
3x = 6/7
x = 6/7/3
x = 2/7


Input: Find the solution to 8x - 76 = 0

Output:
8x - 76 = 0
8x = 76
x = 76 / 8
x = 19/2


Input:
Solve the equations:
9x + 9y = 111/2
1x + 6y = 157/6

Output:
9x + 9y = 111/2
1x + 6y = 157/6

Using elimination
1*(9x + 9y = 111/2)
9*(1x + 6y = 157/6)
9x + 9y = 111/2
9x + 54y = 471/2
Subtract equations
-45y = -180
y = -180/-45
y = 4

Substitute y
9x + 9(4) = 111/2
9x = 39/2
x = 39/2/9
x = 13/6


Input: Compute the solution of x^2 + 149/21x + 34/3 = 0

Output:
x^2 + 149/21x + 34/3 = 0
(x - -14/3)(x - -17/7) = 0
x - -14/3 = 0  or  x - -17/7 = 0
x = -14/3
x = -17/7


Input:
Find x and y such that
4x + 6y = -82/5
1x + 6y = -88/5

Output:
4x + 6y = -82/5
1x + 6y = -88/5

Using elimination
1*(4x + 6y = -82/5)
4*(1x + 6y = -88/5)
4x + 6y = -82/5
4x + 24y = -352/5
Subtract equations
-18y = 54
y = 54/-18
y = -3

Substitute y
4x + 6(-3) = -82/5
4x = 8/5
x = 8/5/4
x = 2/5


Input: Find x for x^2 - 7/12x - 51/8 = 0

Output:
x^2 - 7/12x - 51/8 = 0
(x - -9/4)(x - 17/6) = 0
x - -9/4 = 0  or  x - 17/6 = 0
x = -9/4
x = 17/6


Input: Solve 4x + 16 = 0

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


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

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


Input:
Find x and y such that
6x + 1y = 24/5
10x + 2y = 8

Output:
6x + 1y = 24/5
10x + 2y = 8

Using elimination
10*(6x + 1y = 24/5)
6*(10x + 2y = 8)
60x + 10y = 48
60x + 12y = 48
Subtract equations
-2y = 0
y = 0/-2
y = 0

Substitute y
6x + 1(0) = 24/5
6x = 24/5
x = 24/5/6
x = 4/5


Input:
Solve simultaneously:
7x + 7y = 259/6
9x + 7y = 277/6

Output:
7x + 7y = 259/6
9x + 7y = 277/6

Using elimination
9*(7x + 7y = 259/6)
7*(9x + 7y = 277/6)
63x + 63y = 777/2
63x + 49y = 1939/6
Subtract equations
14y = 196/3
y = 196/3/14
y = 14/3

Substitute y
7x + 7(14/3) = 259/6
7x = 21/2
x = 21/2/7
x = 3/2


Input: Determine x in 9x - 162 = 0

Output:
9x - 162 = 0
9x = 162
x = 162 / 9
x = 18


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

Output:
x^2 + 4/5x - 57/5 = 0
(x - -19/5)(x - 3) = 0
x - -19/5 = 0  or  x - 3 = 0
x = -19/5
x = 3


Input:
Solve the system:
2x + 9y = 137
7x + 6y = 46

Output:
2x + 9y = 137
7x + 6y = 46

Using elimination
7*(2x + 9y = 137)
2*(7x + 6y = 46)
14x + 63y = 959
14x + 12y = 92
Subtract equations
51y = 867
y = 867/51
y = 17

Substitute y
2x + 9(17) = 137
2x = -16
x = -16/2
x = -8


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

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


Input: Solve quickly: x^3 + 54/7x^2 - 156/7x + 40/7 = 0

Output:
x^3 + 54/7x^2 - 156/7x + 40/7 = 0
(x - 2/7)(x - 2)(x - -10) = 0
x - 2/7 = 0
x - 2 = 0
x - -10 = 0
x = 2/7
x = 2
x = -10


Input: Find x in 8x - 16 = 0

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


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

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


Input: Solve the equation x^3 - 47/12x^2 - 5/6x + 2 = 0

Output:
x^3 - 47/12x^2 - 5/6x + 2 = 0
(x - 4)(x - -3/4)(x - 2/3) = 0
x - 4 = 0
x - -3/4 = 0
x - 2/3 = 0
x = 4
x = -3/4
x = 2/3


Input: What value of x satisfies x^2 + 13/14x - 6/7 = 0

Output:
x^2 + 13/14x - 6/7 = 0
(x - -3/2)(x - 4/7) = 0
x - -3/2 = 0  or  x - 4/7 = 0
x = -3/2
x = 4/7


Input: Solve the equation x^2 - 8x + 143/9 = 0

Output:
x^2 - 8x + 143/9 = 0
(x - 11/3)(x - 13/3) = 0
x - 11/3 = 0  or  x - 13/3 = 0
x = 11/3
x = 13/3


Input: Find x in x^2 + 56/9x + 4/3 = 0

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


Input:
Solve the equations:
8x + 9y = -16/5
6x + 6y = -33/10

Output:
8x + 9y = -16/5
6x + 6y = -33/10

Using elimination
6*(8x + 9y = -16/5)
8*(6x + 6y = -33/10)
48x + 54y = -96/5
48x + 48y = -132/5
Subtract equations
6y = 36/5
y = 36/5/6
y = 6/5

Substitute y
8x + 9(6/5) = -16/5
8x = -14
x = -14/8
x = -7/4


Input: Determine x in x^2 + 17/3x - 30 = 0

Output:
x^2 + 17/3x - 30 = 0
(x - 10/3)(x - -9) = 0
x - 10/3 = 0  or  x - -9 = 0
x = 10/3
x = -9


Input: Compute the solution of x^3 + 286/21x^2 - 167/3x + 646/21 = 0

Output:
x^3 + 286/21x^2 - 167/3x + 646/21 = 0
(x - 19/7)(x - 2/3)(x - -17) = 0
x - 19/7 = 0
x - 2/3 = 0
x - -17 = 0
x = 19/7
x = 2/3
x = -17


Input: Solve quickly: x^2 + 46/21x + 8/7 = 0

Output:
x^2 + 46/21x + 8/7 = 0
(x - -4/3)(x - -6/7) = 0
x - -4/3 = 0  or  x - -6/7 = 0
x = -4/3
x = -6/7


Input:
Solve simultaneously:
8x + 7y = -493/9
2x + 10y = -280/9

Output:
8x + 7y = -493/9
2x + 10y = -280/9

Using elimination
2*(8x + 7y = -493/9)
8*(2x + 10y = -280/9)
16x + 14y = -986/9
16x + 80y = -2240/9
Subtract equations
-66y = 418/3
y = 418/3/-66
y = -19/9

Substitute y
8x + 7(-19/9) = -493/9
8x = -40
x = -40/8
x = -5


Input: Find x for 1x - 4 = 0

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


Input: Solve the equation x^2 - 37/3x - 40 = 0

Output:
x^2 - 37/3x - 40 = 0
(x - 15)(x - -8/3) = 0
x - 15 = 0  or  x - -8/3 = 0
x = 15
x = -8/3


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

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


Input:
Find x and y such that
4x + 5y = -52/5
10x + 2y = -26

Output:
4x + 5y = -52/5
10x + 2y = -26

Using elimination
10*(4x + 5y = -52/5)
4*(10x + 2y = -26)
40x + 50y = -104
40x + 8y = -104
Subtract equations
42y = 0
y = 0/42
y = 0

Substitute y
4x + 5(0) = -52/5
4x = -52/5
x = -52/5/4
x = -13/5


Input:
Solve the equations:
5x + 2y = 277/36
4x + 6y = 479/36

Output:
5x + 2y = 277/36
4x + 6y = 479/36

Using elimination
4*(5x + 2y = 277/36)
5*(4x + 6y = 479/36)
20x + 8y = 277/9
20x + 30y = 2395/36
Subtract equations
-22y = -143/4
y = -143/4/-22
y = 13/8

Substitute y
5x + 2(13/8) = 277/36
5x = 40/9
x = 40/9/5
x = 8/9


Input:
Solve simultaneously:
1x + 6y = 9
2x + 7y = 21/2

Output:
1x + 6y = 9
2x + 7y = 21/2

Using elimination
2*(1x + 6y = 9)
1*(2x + 7y = 21/2)
2x + 12y = 18
2x + 7y = 21/2
Subtract equations
5y = 15/2
y = 15/2/5
y = 3/2

Substitute y
1x + 6(3/2) = 9
1x = 0
x = 0/1
x = 0


Input: Find x in x^2 + 59/45x - 272/45 = 0

Output:
x^2 + 59/45x - 272/45 = 0
(x - 17/9)(x - -16/5) = 0
x - 17/9 = 0  or  x - -16/5 = 0
x = 17/9
x = -16/5


Input: Solve 8x + 40/7 = 0

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


Input: Determine x in x^2 - 53/21x - 20/21 = 0

Output:
x^2 - 53/21x - 20/21 = 0
(x - -1/3)(x - 20/7) = 0
x - -1/3 = 0  or  x - 20/7 = 0
x = -1/3
x = 20/7


Input: Find the solution to x^2  - 9/16 = 0

Output:
x^2  - 9/16 = 0
(x - -3/4)(x - 3/4) = 0
x - -3/4 = 0  or  x - 3/4 = 0
x = -3/4
x = 3/4


Input: Find x for 10x + 55/4 = 0

Output:
10x + 55/4 = 0
10x = -55/4
x = -55/4 / 10
x = -11/8


Input: Compute the solution of x^3 + 29/6x^2 + 20/3x + 17/6 = 0

Output:
x^3 + 29/6x^2 + 20/3x + 17/6 = 0
(x - -1)(x - -1)(x - -17/6) = 0
x - -1 = 0
x - -1 = 0
x - -17/6 = 0
x = -1
x = -1
x = -17/6


Input:
Solve the system:
3x + 6y = 57/2
8x + 1y = -4

Output:
3x + 6y = 57/2
8x + 1y = -4

Using elimination
8*(3x + 6y = 57/2)
3*(8x + 1y = -4)
24x + 48y = 228
24x + 3y = -12
Subtract equations
45y = 240
y = 240/45
y = 16/3

Substitute y
3x + 6(16/3) = 57/2
3x = -7/2
x = -7/2/3
x = -7/6


Input: Find the solution to x^3 + 59/30x^2 + 37/75x - 21/50 = 0

Output:
x^3 + 59/30x^2 + 37/75x - 21/50 = 0
(x - -7/5)(x - -9/10)(x - 1/3) = 0
x - -7/5 = 0
x - -9/10 = 0
x - 1/3 = 0
x = -7/5
x = -9/10
x = 1/3


Input:
Find x and y such that
3x + 10y = -309/7
7x + 2y = -465/7

Output:
3x + 10y = -309/7
7x + 2y = -465/7

Using elimination
7*(3x + 10y = -309/7)
3*(7x + 2y = -465/7)
21x + 70y = -309
21x + 6y = -1395/7
Subtract equations
64y = -768/7
y = -768/7/64
y = -12/7

Substitute y
3x + 10(-12/7) = -309/7
3x = -27
x = -27/3
x = -9


Input: Compute the solution of x^3 + 35/12x^2 - 7/6x - 6 = 0

Output:
x^3 + 35/12x^2 - 7/6x - 6 = 0
(x - -9/4)(x - 4/3)(x - -2) = 0
x - -9/4 = 0
x - 4/3 = 0
x - -2 = 0
x = -9/4
x = 4/3
x = -2


Input: Determine x in 8x - 16 = 0

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


Input: Solve quickly: x^2 + 19x + 34 = 0

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


Input: Solve x^3 + 1/5x^2 - 278/45x - 176/45 = 0

Output:
x^3 + 1/5x^2 - 278/45x - 176/45 = 0
(x - -2/3)(x - -11/5)(x - 8/3) = 0
x - -2/3 = 0
x - -11/5 = 0
x - 8/3 = 0
x = -2/3
x = -11/5
x = 8/3


Input: Find x for x^2 - 5x - 24 = 0

Output:
x^2 - 5x - 24 = 0
(x - -3)(x - 8) = 0
x - -3 = 0  or  x - 8 = 0
x = -3
x = 8


Input: Find the solution to x^3 + 1088/315x^2 + 947/315x + 38/105 = 0

Output:
x^3 + 1088/315x^2 + 947/315x + 38/105 = 0
(x - -6/5)(x - -1/7)(x - -19/9) = 0
x - -6/5 = 0
x - -1/7 = 0
x - -19/9 = 0
x = -6/5
x = -1/7
x = -19/9


Input: Determine x in x^3 + 7/4x^2 - 14x + 45/4 = 0

Output:
x^3 + 7/4x^2 - 14x + 45/4 = 0
(x - -5)(x - 9/4)(x - 1) = 0
x - -5 = 0
x - 9/4 = 0
x - 1 = 0
x = -5
x = 9/4
x = 1


Input:
Solve the system:
5x + 8y = 10/3
1x + 2y = 4/3

Output:
5x + 8y = 10/3
1x + 2y = 4/3

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

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


Input:
Find x and y such that
3x + 8y = 13
1x + 8y = 25/3

Output:
3x + 8y = 13
1x + 8y = 25/3

Using elimination
1*(3x + 8y = 13)
3*(1x + 8y = 25/3)
3x + 8y = 13
3x + 24y = 25
Subtract equations
-16y = -12
y = -12/-16
y = 3/4

Substitute y
3x + 8(3/4) = 13
3x = 7
x = 7/3
x = 7/3


Input:
Find x and y such that
5x + 10y = -125/3
8x + 7y = -157/6

Output:
5x + 10y = -125/3
8x + 7y = -157/6

Using elimination
8*(5x + 10y = -125/3)
5*(8x + 7y = -157/6)
40x + 80y = -1000/3
40x + 35y = -785/6
Subtract equations
45y = -405/2
y = -405/2/45
y = -9/2

Substitute y
5x + 10(-9/2) = -125/3
5x = 10/3
x = 10/3/5
x = 2/3


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

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


Input: Compute the solution of 5x + 25/2 = 0

Output:
5x + 25/2 = 0
5x = -25/2
x = -25/2 / 5
x = -5/2


Input: Determine x in 4x + 8 = 0

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


Input: Find x for x^2 + 63/10x + 19/2 = 0

Output:
x^2 + 63/10x + 19/2 = 0
(x - -5/2)(x - -19/5) = 0
x - -5/2 = 0  or  x - -19/5 = 0
x = -5/2
x = -19/5


Input: What value of x satisfies x^3 - 209/15x^2 + 157/3x - 133/5 = 0

Output:
x^3 - 209/15x^2 + 157/3x - 133/5 = 0
(x - 7)(x - 3/5)(x - 19/3) = 0
x - 7 = 0
x - 3/5 = 0
x - 19/3 = 0
x = 7
x = 3/5
x = 19/3


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

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


Input:
Solve simultaneously:
4x + 5y = 9/2
1x + 8y = -63/10

Output:
4x + 5y = 9/2
1x + 8y = -63/10

Using elimination
1*(4x + 5y = 9/2)
4*(1x + 8y = -63/10)
4x + 5y = 9/2
4x + 32y = -126/5
Subtract equations
-27y = 297/10
y = 297/10/-27
y = -11/10

Substitute y
4x + 5(-11/10) = 9/2
4x = 10
x = 10/4
x = 5/2


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

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


Input: Solve quickly: x^2 - 19/24x + 1/12 = 0

Output:
x^2 - 19/24x + 1/12 = 0
(x - 2/3)(x - 1/8) = 0
x - 2/3 = 0  or  x - 1/8 = 0
x = 2/3
x = 1/8


Input: Solve the equation x^2 + 20/7x + 64/49 = 0

Output:
x^2 + 20/7x + 64/49 = 0
(x - -4/7)(x - -16/7) = 0
x - -4/7 = 0  or  x - -16/7 = 0
x = -4/7
x = -16/7


Input: Solve 10x + 30 = 0

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


Input:
Solve the system:
8x + 8y = -376/3
1x + 2y = -52/3

Output:
8x + 8y = -376/3
1x + 2y = -52/3

Using elimination
1*(8x + 8y = -376/3)
8*(1x + 2y = -52/3)
8x + 8y = -376/3
8x + 16y = -416/3
Subtract equations
-8y = 40/3
y = 40/3/-8
y = -5/3

Substitute y
8x + 8(-5/3) = -376/3
8x = -112
x = -112/8
x = -14


Input: Solve quickly: x^2 + 11x - 26 = 0

Output:
x^2 + 11x - 26 = 0
(x - -13)(x - 2) = 0
x - -13 = 0  or  x - 2 = 0
x = -13
x = 2


Input: Find the solution to x^2 + 25/3x - 50/3 = 0

Output:
x^2 + 25/3x - 50/3 = 0
(x - 5/3)(x - -10) = 0
x - 5/3 = 0  or  x - -10 = 0
x = 5/3
x = -10


Input: Determine x in 7x - 14/3 = 0

Output:
7x - 14/3 = 0
7x = 14/3
x = 14/3 / 7
x = 2/3


Input: Solve quickly: x^2 - 23/5x + 12/5 = 0

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


Input: Find x for x^2 + 13x + 42 = 0

Output:
x^2 + 13x + 42 = 0
(x - -7)(x - -6) = 0
x - -7 = 0  or  x - -6 = 0
x = -7
x = -6


Input: Find x for x^2 + 19/9x + 16/27 = 0

Output:
x^2 + 19/9x + 16/27 = 0
(x - -1/3)(x - -16/9) = 0
x - -1/3 = 0  or  x - -16/9 = 0
x = -1/3
x = -16/9


Input: Determine x in 10x + 120 = 0

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


Input:
Solve simultaneously:
6x + 2y = 232/7
4x + 6y = 108/7

Output:
6x + 2y = 232/7
4x + 6y = 108/7

Using elimination
4*(6x + 2y = 232/7)
6*(4x + 6y = 108/7)
24x + 8y = 928/7
24x + 36y = 648/7
Subtract equations
-28y = 40
y = 40/-28
y = -10/7

Substitute y
6x + 2(-10/7) = 232/7
6x = 36
x = 36/6
x = 6


Input: Determine x in x^2 - 17x - 38 = 0

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


Input:
Find x and y such that
6x + 5y = 50
1x + 6y = -2

Output:
6x + 5y = 50
1x + 6y = -2

Using elimination
1*(6x + 5y = 50)
6*(1x + 6y = -2)
6x + 5y = 50
6x + 36y = -12
Subtract equations
-31y = 62
y = 62/-31
y = -2

Substitute y
6x + 5(-2) = 50
6x = 60
x = 60/6
x = 10


Input: Compute the solution of x^3 - 730/63x^2 - 736/21x + 160/9 = 0

Output:
x^3 - 730/63x^2 - 736/21x + 160/9 = 0
(x - 4/9)(x - -20/7)(x - 14) = 0
x - 4/9 = 0
x - -20/7 = 0
x - 14 = 0
x = 4/9
x = -20/7
x = 14


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

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


Input: Solve the equation x^3 + 44/15x^2 - 73/20x - 9/2 = 0

Output:
x^3 + 44/15x^2 - 73/20x - 9/2 = 0
(x - -18/5)(x - 3/2)(x - -5/6) = 0
x - -18/5 = 0
x - 3/2 = 0
x - -5/6 = 0
x = -18/5
x = 3/2
x = -5/6


Input: Compute the solution of x^2 + 11/30x - 121/30 = 0

Output:
x^2 + 11/30x - 121/30 = 0
(x - -11/5)(x - 11/6) = 0
x - -11/5 = 0  or  x - 11/6 = 0
x = -11/5
x = 11/6


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

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


Input: Solve 7x - 28 = 0

Output:
7x - 28 = 0
7x = 28
x = 28 / 7
x = 4


Input: Find x for 3x + 54/5 = 0

Output:
3x + 54/5 = 0
3x = -54/5
x = -54/5 / 3
x = -18/5


Input: Compute the solution of x^2 - 37/4x + 105/8 = 0

Output:
x^2 - 37/4x + 105/8 = 0
(x - 15/2)(x - 7/4) = 0
x - 15/2 = 0  or  x - 7/4 = 0
x = 15/2
x = 7/4


Input:
Find x and y such that
3x + 10y = -39/4
9x + 1y = -411/20

Output:
3x + 10y = -39/4
9x + 1y = -411/20

Using elimination
9*(3x + 10y = -39/4)
3*(9x + 1y = -411/20)
27x + 90y = -351/4
27x + 3y = -1233/20
Subtract equations
87y = -261/10
y = -261/10/87
y = -3/10

Substitute y
3x + 10(-3/10) = -39/4
3x = -27/4
x = -27/4/3
x = -9/4


Input: Find the solution to x^3 - 59/42x^2 + 10/21x  = 0

Output:
x^3 - 59/42x^2 + 10/21x  = 0
(x - 4/7)(x - 5/6)(x - 0) = 0
x - 4/7 = 0
x - 5/6 = 0
x - 0 = 0
x = 4/7
x = 5/6
x = 0


Input: Determine x in x^3 + 1/9x^2 - 188/27x - 64/9 = 0

Output:
x^3 + 1/9x^2 - 188/27x - 64/9 = 0
(x - 3)(x - -16/9)(x - -4/3) = 0
x - 3 = 0
x - -16/9 = 0
x - -4/3 = 0
x = 3
x = -16/9
x = -4/3