Input:
Find x and y such that
4x + 2y = -50/3
9x + 6y = -83/2

Output:
4x + 2y = -50/3
9x + 6y = -83/2

Using elimination
9*(4x + 2y = -50/3)
4*(9x + 6y = -83/2)
36x + 18y = -150
36x + 24y = -166
Subtract equations
-6y = 16
y = 16/-6
y = -8/3

Substitute y
4x + 2(-8/3) = -50/3
4x = -34/3
x = -34/3/4
x = -17/6


Input: Compute the solution of x^2 + 13/40x - 187/80 = 0

Output:
x^2 + 13/40x - 187/80 = 0
(x - -17/10)(x - 11/8) = 0
x - -17/10 = 0  or  x - 11/8 = 0
x = -17/10
x = 11/8


Input: Find x for x^2 + 45/8x - 225/16 = 0

Output:
x^2 + 45/8x - 225/16 = 0
(x - 15/8)(x - -15/2) = 0
x - 15/8 = 0  or  x - -15/2 = 0
x = 15/8
x = -15/2


Input: Find x for 7x - 7/4 = 0

Output:
7x - 7/4 = 0
7x = 7/4
x = 7/4 / 7
x = 1/4


Input: Find the solution to x^3 + 89/56x^2 + 1/2x - 5/56 = 0

Output:
x^3 + 89/56x^2 + 1/2x - 5/56 = 0
(x - -1)(x - -5/7)(x - 1/8) = 0
x - -1 = 0
x - -5/7 = 0
x - 1/8 = 0
x = -1
x = -5/7
x = 1/8


Input: Find x in x^2 + 196/45x + 196/45 = 0

Output:
x^2 + 196/45x + 196/45 = 0
(x - -14/9)(x - -14/5) = 0
x - -14/9 = 0  or  x - -14/5 = 0
x = -14/9
x = -14/5


Input:
Solve simultaneously:
5x + 9y = -35/4
9x + 10y = 15/2

Output:
5x + 9y = -35/4
9x + 10y = 15/2

Using elimination
9*(5x + 9y = -35/4)
5*(9x + 10y = 15/2)
45x + 81y = -315/4
45x + 50y = 75/2
Subtract equations
31y = -465/4
y = -465/4/31
y = -15/4

Substitute y
5x + 9(-15/4) = -35/4
5x = 25
x = 25/5
x = 5


Input: Solve quickly: x^2 + 103/7x + 10 = 0

Output:
x^2 + 103/7x + 10 = 0
(x - -14)(x - -5/7) = 0
x - -14 = 0  or  x - -5/7 = 0
x = -14
x = -5/7


Input: What value of x satisfies 9x - 51 = 0

Output:
9x - 51 = 0
9x = 51
x = 51 / 9
x = 17/3


Input: Determine x in x^2 - 163/21x + 190/21 = 0

Output:
x^2 - 163/21x + 190/21 = 0
(x - 19/3)(x - 10/7) = 0
x - 19/3 = 0  or  x - 10/7 = 0
x = 19/3
x = 10/7


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

Output:
2x + 9/4 = 0
2x = -9/4
x = -9/4 / 2
x = -9/8


Input: What value of x satisfies x^2 - 11/7x + 4/7 = 0

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


Input: Determine x in 10x - 20 = 0

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


Input:
Find x and y such that
10x + 5y = -50
8x + 1y = -31

Output:
10x + 5y = -50
8x + 1y = -31

Using elimination
8*(10x + 5y = -50)
10*(8x + 1y = -31)
80x + 40y = -400
80x + 10y = -310
Subtract equations
30y = -90
y = -90/30
y = -3

Substitute y
10x + 5(-3) = -50
10x = -35
x = -35/10
x = -7/2


Input:
Solve the system:
10x + 5y = 1085/6
9x + 9y = 309/2

Output:
10x + 5y = 1085/6
9x + 9y = 309/2

Using elimination
9*(10x + 5y = 1085/6)
10*(9x + 9y = 309/2)
90x + 45y = 3255/2
90x + 90y = 1545
Subtract equations
-45y = 165/2
y = 165/2/-45
y = -11/6

Substitute y
10x + 5(-11/6) = 1085/6
10x = 190
x = 190/10
x = 19


Input: Determine x in x^3 + 81/7x^2 + 240/7x + 16 = 0

Output:
x^3 + 81/7x^2 + 240/7x + 16 = 0
(x - -7)(x - -4)(x - -4/7) = 0
x - -7 = 0
x - -4 = 0
x - -4/7 = 0
x = -7
x = -4
x = -4/7


Input:
Solve the system:
3x + 9y = 51/7
1x + 8y = 57/7

Output:
3x + 9y = 51/7
1x + 8y = 57/7

Using elimination
1*(3x + 9y = 51/7)
3*(1x + 8y = 57/7)
3x + 9y = 51/7
3x + 24y = 171/7
Subtract equations
-15y = -120/7
y = -120/7/-15
y = 8/7

Substitute y
3x + 9(8/7) = 51/7
3x = -3
x = -3/3
x = -1


Input:
Solve the system:
6x + 10y = -69
3x + 6y = -33

Output:
6x + 10y = -69
3x + 6y = -33

Using elimination
3*(6x + 10y = -69)
6*(3x + 6y = -33)
18x + 30y = -207
18x + 36y = -198
Subtract equations
-6y = -9
y = -9/-6
y = 3/2

Substitute y
6x + 10(3/2) = -69
6x = -84
x = -84/6
x = -14


Input: Solve the equation 7x - 35/8 = 0

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


Input:
Find x and y such that
5x + 5y = 75/4
8x + 5y = 39/2

Output:
5x + 5y = 75/4
8x + 5y = 39/2

Using elimination
8*(5x + 5y = 75/4)
5*(8x + 5y = 39/2)
40x + 40y = 150
40x + 25y = 195/2
Subtract equations
15y = 105/2
y = 105/2/15
y = 7/2

Substitute y
5x + 5(7/2) = 75/4
5x = 5/4
x = 5/4/5
x = 1/4


Input: What value of x satisfies x^3 - 94/35x^2 + 3/5x + 54/35 = 0

Output:
x^3 - 94/35x^2 + 3/5x + 54/35 = 0
(x - 2)(x - 9/7)(x - -3/5) = 0
x - 2 = 0
x - 9/7 = 0
x - -3/5 = 0
x = 2
x = 9/7
x = -3/5


Input: Solve x^3 + 113/45x^2 + 16/15x + 4/45 = 0

Output:
x^3 + 113/45x^2 + 16/15x + 4/45 = 0
(x - -2)(x - -2/5)(x - -1/9) = 0
x - -2 = 0
x - -2/5 = 0
x - -1/9 = 0
x = -2
x = -2/5
x = -1/9


Input:
Solve simultaneously:
2x + 5y = -62/3
10x + 5y = -290/3

Output:
2x + 5y = -62/3
10x + 5y = -290/3

Using elimination
10*(2x + 5y = -62/3)
2*(10x + 5y = -290/3)
20x + 50y = -620/3
20x + 10y = -580/3
Subtract equations
40y = -40/3
y = -40/3/40
y = -1/3

Substitute y
2x + 5(-1/3) = -62/3
2x = -19
x = -19/2
x = -19/2


Input: Solve the equation x^3 + 43/6x^2 + 97/6x + 35/3 = 0

Output:
x^3 + 43/6x^2 + 97/6x + 35/3 = 0
(x - -2)(x - -7/2)(x - -5/3) = 0
x - -2 = 0
x - -7/2 = 0
x - -5/3 = 0
x = -2
x = -7/2
x = -5/3


Input: Solve 2x - 24 = 0

Output:
2x - 24 = 0
2x = 24
x = 24 / 2
x = 12


Input: Find the solution to 5x + 75/8 = 0

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


Input:
Find x and y such that
6x + 9y = 205/24
6x + 5y = 121/24

Output:
6x + 9y = 205/24
6x + 5y = 121/24

Using elimination
6*(6x + 9y = 205/24)
6*(6x + 5y = 121/24)
36x + 54y = 205/4
36x + 30y = 121/4
Subtract equations
24y = 21
y = 21/24
y = 7/8

Substitute y
6x + 9(7/8) = 205/24
6x = 2/3
x = 2/3/6
x = 1/9


Input:
Find x and y such that
7x + 4y = -302/9
9x + 4y = -386/9

Output:
7x + 4y = -302/9
9x + 4y = -386/9

Using elimination
9*(7x + 4y = -302/9)
7*(9x + 4y = -386/9)
63x + 36y = -302
63x + 28y = -2702/9
Subtract equations
8y = -16/9
y = -16/9/8
y = -2/9

Substitute y
7x + 4(-2/9) = -302/9
7x = -98/3
x = -98/3/7
x = -14/3


Input: Solve the equation x^3 + 19/20x^2 - 251/20x - 209/10 = 0

Output:
x^3 + 19/20x^2 - 251/20x - 209/10 = 0
(x - -2)(x - -11/4)(x - 19/5) = 0
x - -2 = 0
x - -11/4 = 0
x - 19/5 = 0
x = -2
x = -11/4
x = 19/5


Input:
Find x and y such that
7x + 9y = 79/4
10x + 10y = 485/18

Output:
7x + 9y = 79/4
10x + 10y = 485/18

Using elimination
10*(7x + 9y = 79/4)
7*(10x + 10y = 485/18)
70x + 90y = 395/2
70x + 70y = 3395/18
Subtract equations
20y = 80/9
y = 80/9/20
y = 4/9

Substitute y
7x + 9(4/9) = 79/4
7x = 63/4
x = 63/4/7
x = 9/4


Input: Find x in 4x + 8 = 0

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


Input: Solve quickly: 9x + 36 = 0

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


Input: Find x for x^3 + 31/6x^2 - 73/18x - 110/9 = 0

Output:
x^3 + 31/6x^2 - 73/18x - 110/9 = 0
(x - -4/3)(x - -11/2)(x - 5/3) = 0
x - -4/3 = 0
x - -11/2 = 0
x - 5/3 = 0
x = -4/3
x = -11/2
x = 5/3


Input: Find x in x^3 + 205/24x^2 - 53x + 1547/24 = 0

Output:
x^3 + 205/24x^2 - 53x + 1547/24 = 0
(x - 7/3)(x - -13)(x - 17/8) = 0
x - 7/3 = 0
x - -13 = 0
x - 17/8 = 0
x = 7/3
x = -13
x = 17/8


Input: Solve 9x - 54/7 = 0

Output:
9x - 54/7 = 0
9x = 54/7
x = 54/7 / 9
x = 6/7


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

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


Input: Compute the solution of x^3 - 5x^2 - 12x + 36 = 0

Output:
x^3 - 5x^2 - 12x + 36 = 0
(x - 6)(x - 2)(x - -3) = 0
x - 6 = 0
x - 2 = 0
x - -3 = 0
x = 6
x = 2
x = -3


Input:
Solve the equations:
7x + 8y = 38/3
8x + 7y = 22/3

Output:
7x + 8y = 38/3
8x + 7y = 22/3

Using elimination
8*(7x + 8y = 38/3)
7*(8x + 7y = 22/3)
56x + 64y = 304/3
56x + 49y = 154/3
Subtract equations
15y = 50
y = 50/15
y = 10/3

Substitute y
7x + 8(10/3) = 38/3
7x = -14
x = -14/7
x = -2


Input: Determine x in 7x - 28/3 = 0

Output:
7x - 28/3 = 0
7x = 28/3
x = 28/3 / 7
x = 4/3


Input: What value of x satisfies 8x + 28/3 = 0

Output:
8x + 28/3 = 0
8x = -28/3
x = -28/3 / 8
x = -7/6


Input: What value of x satisfies x^2 + 47/6x - 17/3 = 0

Output:
x^2 + 47/6x - 17/3 = 0
(x - -17/2)(x - 2/3) = 0
x - -17/2 = 0  or  x - 2/3 = 0
x = -17/2
x = 2/3


Input: Find x for x^3 - 29/6x^2 - 19/6x + 21 = 0

Output:
x^3 - 29/6x^2 - 19/6x + 21 = 0
(x - 9/2)(x - 7/3)(x - -2) = 0
x - 9/2 = 0
x - 7/3 = 0
x - -2 = 0
x = 9/2
x = 7/3
x = -2


Input:
Solve simultaneously:
7x + 8y = 79/9
10x + 8y = 106/9

Output:
7x + 8y = 79/9
10x + 8y = 106/9

Using elimination
10*(7x + 8y = 79/9)
7*(10x + 8y = 106/9)
70x + 80y = 790/9
70x + 56y = 742/9
Subtract equations
24y = 16/3
y = 16/3/24
y = 2/9

Substitute y
7x + 8(2/9) = 79/9
7x = 7
x = 7/7
x = 1


Input: Solve 1x + 2 = 0

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


Input: Determine x in x^3 + 29/2x^2 - 41x + 51/2 = 0

Output:
x^3 + 29/2x^2 - 41x + 51/2 = 0
(x - -17)(x - 1)(x - 3/2) = 0
x - -17 = 0
x - 1 = 0
x - 3/2 = 0
x = -17
x = 1
x = 3/2


Input: Solve quickly: x^3 - 25/3x^2 + 14/3x + 152/3 = 0

Output:
x^3 - 25/3x^2 + 14/3x + 152/3 = 0
(x - 19/3)(x - 4)(x - -2) = 0
x - 19/3 = 0
x - 4 = 0
x - -2 = 0
x = 19/3
x = 4
x = -2


Input: What value of x satisfies x^3 - 41/24x^2 - 13/48x + 7/8 = 0

Output:
x^3 - 41/24x^2 - 13/48x + 7/8 = 0
(x - 7/8)(x - 3/2)(x - -2/3) = 0
x - 7/8 = 0
x - 3/2 = 0
x - -2/3 = 0
x = 7/8
x = 3/2
x = -2/3


Input: Solve quickly: x^2 - 13/8x + 9/16 = 0

Output:
x^2 - 13/8x + 9/16 = 0
(x - 1/2)(x - 9/8) = 0
x - 1/2 = 0  or  x - 9/8 = 0
x = 1/2
x = 9/8


Input:
Solve the equations:
2x + 9y = 12
9x + 4y = 559/9

Output:
2x + 9y = 12
9x + 4y = 559/9

Using elimination
9*(2x + 9y = 12)
2*(9x + 4y = 559/9)
18x + 81y = 108
18x + 8y = 1118/9
Subtract equations
73y = -146/9
y = -146/9/73
y = -2/9

Substitute y
2x + 9(-2/9) = 12
2x = 14
x = 14/2
x = 7


Input: Solve 1x + 5/9 = 0

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


Input: Find x in x^3 - 5/168x^2 - 911/168x + 33/7 = 0

Output:
x^3 - 5/168x^2 - 911/168x + 33/7 = 0
(x - 11/7)(x - 9/8)(x - -8/3) = 0
x - 11/7 = 0
x - 9/8 = 0
x - -8/3 = 0
x = 11/7
x = 9/8
x = -8/3


Input:
Find x and y such that
6x + 2y = -200/9
6x + 1y = -190/9

Output:
6x + 2y = -200/9
6x + 1y = -190/9

Using elimination
6*(6x + 2y = -200/9)
6*(6x + 1y = -190/9)
36x + 12y = -400/3
36x + 6y = -380/3
Subtract equations
6y = -20/3
y = -20/3/6
y = -10/9

Substitute y
6x + 2(-10/9) = -200/9
6x = -20
x = -20/6
x = -10/3


Input: Find x for x^2 + 37/6x + 19/2 = 0

Output:
x^2 + 37/6x + 19/2 = 0
(x - -19/6)(x - -3) = 0
x - -19/6 = 0  or  x - -3 = 0
x = -19/6
x = -3


Input:
Solve the equations:
10x + 5y = 5
7x + 6y = 1

Output:
10x + 5y = 5
7x + 6y = 1

Using elimination
7*(10x + 5y = 5)
10*(7x + 6y = 1)
70x + 35y = 35
70x + 60y = 10
Subtract equations
-25y = 25
y = 25/-25
y = -1

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


Input: What value of x satisfies x^2 - 6x + 8 = 0

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


Input: Find the solution to x^2 + 85/36x + 25/18 = 0

Output:
x^2 + 85/36x + 25/18 = 0
(x - -5/4)(x - -10/9) = 0
x - -5/4 = 0  or  x - -10/9 = 0
x = -5/4
x = -10/9


Input:
Solve simultaneously:
1x + 4y = 16/7
1x + 8y = 44/7

Output:
1x + 4y = 16/7
1x + 8y = 44/7

Using elimination
1*(1x + 4y = 16/7)
1*(1x + 8y = 44/7)
1x + 4y = 16/7
1x + 8y = 44/7
Subtract equations
-4y = -4
y = -4/-4
y = 1

Substitute y
1x + 4(1) = 16/7
1x = -12/7
x = -12/7/1
x = -12/7


Input:
Solve the system:
7x + 8y = 112/5
4x + 4y = 66/5

Output:
7x + 8y = 112/5
4x + 4y = 66/5

Using elimination
4*(7x + 8y = 112/5)
7*(4x + 4y = 66/5)
28x + 32y = 448/5
28x + 28y = 462/5
Subtract equations
4y = -14/5
y = -14/5/4
y = -7/10

Substitute y
7x + 8(-7/10) = 112/5
7x = 28
x = 28/7
x = 4


Input: Find x for x^3 - 37/8x^2 - 3/2x + 297/32 = 0

Output:
x^3 - 37/8x^2 - 3/2x + 297/32 = 0
(x - 3/2)(x - 9/2)(x - -11/8) = 0
x - 3/2 = 0
x - 9/2 = 0
x - -11/8 = 0
x = 3/2
x = 9/2
x = -11/8


Input: Find x in 5x - 80/9 = 0

Output:
5x - 80/9 = 0
5x = 80/9
x = 80/9 / 5
x = 16/9


Input: Determine x in x^2 - 3x - 27/4 = 0

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


Input: Find x for 10x + 100 = 0

Output:
10x + 100 = 0
10x = -100
x = -100 / 10
x = -10


Input: Find x for x^2 + 3/4x - 27/4 = 0

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


Input:
Solve simultaneously:
10x + 9y = -1473/10
2x + 9y = -273/10

Output:
10x + 9y = -1473/10
2x + 9y = -273/10

Using elimination
2*(10x + 9y = -1473/10)
10*(2x + 9y = -273/10)
20x + 18y = -1473/5
20x + 90y = -273
Subtract equations
-72y = -108/5
y = -108/5/-72
y = 3/10

Substitute y
10x + 9(3/10) = -1473/10
10x = -150
x = -150/10
x = -15


Input: Find x for x^2 + 43/40x - 3/20 = 0

Output:
x^2 + 43/40x - 3/20 = 0
(x - 1/8)(x - -6/5) = 0
x - 1/8 = 0  or  x - -6/5 = 0
x = 1/8
x = -6/5


Input:
Solve simultaneously:
1x + 9y = 86/5
8x + 10y = 26

Output:
1x + 9y = 86/5
8x + 10y = 26

Using elimination
8*(1x + 9y = 86/5)
1*(8x + 10y = 26)
8x + 72y = 688/5
8x + 10y = 26
Subtract equations
62y = 558/5
y = 558/5/62
y = 9/5

Substitute y
1x + 9(9/5) = 86/5
1x = 1
x = 1/1
x = 1


Input: Solve x^3 - 293/20x^2 - 111/20x + 9/2 = 0

Output:
x^3 - 293/20x^2 - 111/20x + 9/2 = 0
(x - -3/4)(x - 15)(x - 2/5) = 0
x - -3/4 = 0
x - 15 = 0
x - 2/5 = 0
x = -3/4
x = 15
x = 2/5


Input:
Solve the equations:
1x + 5y = -251/8
7x + 10y = -557/8

Output:
1x + 5y = -251/8
7x + 10y = -557/8

Using elimination
7*(1x + 5y = -251/8)
1*(7x + 10y = -557/8)
7x + 35y = -1757/8
7x + 10y = -557/8
Subtract equations
25y = -150
y = -150/25
y = -6

Substitute y
1x + 5(-6) = -251/8
1x = -11/8
x = -11/8/1
x = -11/8


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

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


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

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


Input: What value of x satisfies x^2 + 43/28x - 12/7 = 0

Output:
x^2 + 43/28x - 12/7 = 0
(x - -16/7)(x - 3/4) = 0
x - -16/7 = 0  or  x - 3/4 = 0
x = -16/7
x = 3/4


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

Output:
2x + 8/3 = 0
2x = -8/3
x = -8/3 / 2
x = -4/3


Input: Compute the solution of x^3 - 7/3x^2 + 5/3x - 1/3 = 0

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


Input: Solve 5x + 65/6 = 0

Output:
5x + 65/6 = 0
5x = -65/6
x = -65/6 / 5
x = -13/6


Input: Find x in x^3 - 131/10x^2 + 723/20x + 351/8 = 0

Output:
x^3 - 131/10x^2 + 723/20x + 351/8 = 0
(x - 15/2)(x - -9/10)(x - 13/2) = 0
x - 15/2 = 0
x - -9/10 = 0
x - 13/2 = 0
x = 15/2
x = -9/10
x = 13/2


Input: Solve x^3 - 26/63x^2 - 275/63x + 50/21 = 0

Output:
x^3 - 26/63x^2 - 275/63x + 50/21 = 0
(x - -15/7)(x - 5/9)(x - 2) = 0
x - -15/7 = 0
x - 5/9 = 0
x - 2 = 0
x = -15/7
x = 5/9
x = 2


Input:
Find x and y such that
2x + 6y = -8
8x + 1y = 37

Output:
2x + 6y = -8
8x + 1y = 37

Using elimination
8*(2x + 6y = -8)
2*(8x + 1y = 37)
16x + 48y = -64
16x + 2y = 74
Subtract equations
46y = -138
y = -138/46
y = -3

Substitute y
2x + 6(-3) = -8
2x = 10
x = 10/2
x = 5


Input: Compute the solution of x^3 + 1313/315x^2 + 1222/315x + 8/21 = 0

Output:
x^3 + 1313/315x^2 + 1222/315x + 8/21 = 0
(x - -1/9)(x - -6/5)(x - -20/7) = 0
x - -1/9 = 0
x - -6/5 = 0
x - -20/7 = 0
x = -1/9
x = -6/5
x = -20/7


Input: Compute the solution of x^2 - 43/18x - 35/9 = 0

Output:
x^2 - 43/18x - 35/9 = 0
(x - 7/2)(x - -10/9) = 0
x - 7/2 = 0  or  x - -10/9 = 0
x = 7/2
x = -10/9


Input: Solve x^2 + 31/9x + 4/3 = 0

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


Input: Find x in x^3 + 35/2x^2 + 596/25x - 64/25 = 0

Output:
x^3 + 35/2x^2 + 596/25x - 64/25 = 0
(x - 1/10)(x - -16)(x - -8/5) = 0
x - 1/10 = 0
x - -16 = 0
x - -8/5 = 0
x = 1/10
x = -16
x = -8/5


Input: What value of x satisfies x^2 - 17/2x - 15 = 0

Output:
x^2 - 17/2x - 15 = 0
(x - 10)(x - -3/2) = 0
x - 10 = 0  or  x - -3/2 = 0
x = 10
x = -3/2


Input: Find x in x^3 - 247/90x^2 - 559/135x + 133/270 = 0

Output:
x^3 - 247/90x^2 - 559/135x + 133/270 = 0
(x - 19/5)(x - 1/9)(x - -7/6) = 0
x - 19/5 = 0
x - 1/9 = 0
x - -7/6 = 0
x = 19/5
x = 1/9
x = -7/6


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

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


Input: Determine x in x^3 + 226/45x^2 + 1832/225x + 64/15 = 0

Output:
x^3 + 226/45x^2 + 1832/225x + 64/15 = 0
(x - -8/5)(x - -6/5)(x - -20/9) = 0
x - -8/5 = 0
x - -6/5 = 0
x - -20/9 = 0
x = -8/5
x = -6/5
x = -20/9


Input: Find x in 3x - 57/4 = 0

Output:
3x - 57/4 = 0
3x = 57/4
x = 57/4 / 3
x = 19/4


Input:
Solve the equations:
9x + 3y = 129/4
3x + 3y = 63/4

Output:
9x + 3y = 129/4
3x + 3y = 63/4

Using elimination
3*(9x + 3y = 129/4)
9*(3x + 3y = 63/4)
27x + 9y = 387/4
27x + 27y = 567/4
Subtract equations
-18y = -45
y = -45/-18
y = 5/2

Substitute y
9x + 3(5/2) = 129/4
9x = 99/4
x = 99/4/9
x = 11/4


Input:
Solve the equations:
1x + 1y = -2
8x + 6y = -34/3

Output:
1x + 1y = -2
8x + 6y = -34/3

Using elimination
8*(1x + 1y = -2)
1*(8x + 6y = -34/3)
8x + 8y = -16
8x + 6y = -34/3
Subtract equations
2y = -14/3
y = -14/3/2
y = -7/3

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


Input: Solve 7x + 28 = 0

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


Input: Solve 5x - 85/4 = 0

Output:
5x - 85/4 = 0
5x = 85/4
x = 85/4 / 5
x = 17/4


Input: Find x in x^2 + 33/5x + 54/5 = 0

Output:
x^2 + 33/5x + 54/5 = 0
(x - -3)(x - -18/5) = 0
x - -3 = 0  or  x - -18/5 = 0
x = -3
x = -18/5


Input: What value of x satisfies 6x - 12 = 0

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


Input: Solve quickly: x^2 - 184/63x + 5/3 = 0

Output:
x^2 - 184/63x + 5/3 = 0
(x - 7/9)(x - 15/7) = 0
x - 7/9 = 0  or  x - 15/7 = 0
x = 7/9
x = 15/7


Input: What value of x satisfies 8x + 16/3 = 0

Output:
8x + 16/3 = 0
8x = -16/3
x = -16/3 / 8
x = -2/3


Input: Solve the equation x^2 + 17/3x - 2 = 0

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


Input: Find x for 7x + 105/2 = 0

Output:
7x + 105/2 = 0
7x = -105/2
x = -105/2 / 7
x = -15/2


Input: Determine x in x^3 - 211/14x^2 + 400/7x - 450/7 = 0

Output:
x^3 - 211/14x^2 + 400/7x - 450/7 = 0
(x - 5/2)(x - 10)(x - 18/7) = 0
x - 5/2 = 0
x - 10 = 0
x - 18/7 = 0
x = 5/2
x = 10
x = 18/7


Input:
Solve simultaneously:
5x + 6y = 75/4
6x + 10y = 73/2

Output:
5x + 6y = 75/4
6x + 10y = 73/2

Using elimination
6*(5x + 6y = 75/4)
5*(6x + 10y = 73/2)
30x + 36y = 225/2
30x + 50y = 365/2
Subtract equations
-14y = -70
y = -70/-14
y = 5

Substitute y
5x + 6(5) = 75/4
5x = -45/4
x = -45/4/5
x = -9/4


Input: Find the solution to x^2 - 10/3x + 17/12 = 0

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


Input: What value of x satisfies 6x + 8 = 0

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


Input:
Solve simultaneously:
6x + 6y = -21
3x + 5y = -39/2

Output:
6x + 6y = -21
3x + 5y = -39/2

Using elimination
3*(6x + 6y = -21)
6*(3x + 5y = -39/2)
18x + 18y = -63
18x + 30y = -117
Subtract equations
-12y = 54
y = 54/-12
y = -9/2

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


Input: Compute the solution of 2x + 16/3 = 0

Output:
2x + 16/3 = 0
2x = -16/3
x = -16/3 / 2
x = -8/3


Input: Solve 7x + 2 = 0

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


Input: Solve x^3 + 65/9x^2 + 100/9x  = 0

Output:
x^3 + 65/9x^2 + 100/9x  = 0
(x - -20/9)(x - 0)(x - -5) = 0
x - -20/9 = 0
x - 0 = 0
x - -5 = 0
x = -20/9
x = 0
x = -5


Input: Find x for x^3 - 1/4x^2 - 35/72x + 1/12 = 0

Output:
x^3 - 1/4x^2 - 35/72x + 1/12 = 0
(x - -2/3)(x - 3/4)(x - 1/6) = 0
x - -2/3 = 0
x - 3/4 = 0
x - 1/6 = 0
x = -2/3
x = 3/4
x = 1/6


Input: Solve the equation 2x + 16/5 = 0

Output:
2x + 16/5 = 0
2x = -16/5
x = -16/5 / 2
x = -8/5


Input:
Find x and y such that
3x + 9y = 99/28
8x + 6y = 69/14

Output:
3x + 9y = 99/28
8x + 6y = 69/14

Using elimination
8*(3x + 9y = 99/28)
3*(8x + 6y = 69/14)
24x + 72y = 198/7
24x + 18y = 207/14
Subtract equations
54y = 27/2
y = 27/2/54
y = 1/4

Substitute y
3x + 9(1/4) = 99/28
3x = 9/7
x = 9/7/3
x = 3/7


Input:
Find x and y such that
10x + 10y = -45/4
3x + 5y = -15/8

Output:
10x + 10y = -45/4
3x + 5y = -15/8

Using elimination
3*(10x + 10y = -45/4)
10*(3x + 5y = -15/8)
30x + 30y = -135/4
30x + 50y = -75/4
Subtract equations
-20y = -15
y = -15/-20
y = 3/4

Substitute y
10x + 10(3/4) = -45/4
10x = -75/4
x = -75/4/10
x = -15/8


Input: Solve quickly: x^3 + 13/2x^2 - 109/4x + 95/8 = 0

Output:
x^3 + 13/2x^2 - 109/4x + 95/8 = 0
(x - 1/2)(x - -19/2)(x - 5/2) = 0
x - 1/2 = 0
x - -19/2 = 0
x - 5/2 = 0
x = 1/2
x = -19/2
x = 5/2


Input: Solve the equation x^3 - 163/35x^2 - 276/35x - 36/35 = 0

Output:
x^3 - 163/35x^2 - 276/35x - 36/35 = 0
(x - -6/5)(x - -1/7)(x - 6) = 0
x - -6/5 = 0
x - -1/7 = 0
x - 6 = 0
x = -6/5
x = -1/7
x = 6


Input:
Find x and y such that
9x + 3y = -144
9x + 4y = -138

Output:
9x + 3y = -144
9x + 4y = -138

Using elimination
9*(9x + 3y = -144)
9*(9x + 4y = -138)
81x + 27y = -1296
81x + 36y = -1242
Subtract equations
-9y = -54
y = -54/-9
y = 6

Substitute y
9x + 3(6) = -144
9x = -162
x = -162/9
x = -18


Input:
Find x and y such that
6x + 3y = 3/2
1x + 3y = 3/2

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

Using elimination
1*(6x + 3y = 3/2)
6*(1x + 3y = 3/2)
6x + 3y = 3/2
6x + 18y = 9
Subtract equations
-15y = -15/2
y = -15/2/-15
y = 1/2

Substitute y
6x + 3(1/2) = 3/2
6x = 0
x = 0/6
x = 0


Input: Solve the equation 2x + 12/5 = 0

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


Input: Find x for x^3 - 388/45x^2 - 167/45x + 14/5 = 0

Output:
x^3 - 388/45x^2 - 167/45x + 14/5 = 0
(x - -7/9)(x - 9)(x - 2/5) = 0
x - -7/9 = 0
x - 9 = 0
x - 2/5 = 0
x = -7/9
x = 9
x = 2/5


Input:
Solve the system:
8x + 9y = 32/3
6x + 8y = 13

Output:
8x + 9y = 32/3
6x + 8y = 13

Using elimination
6*(8x + 9y = 32/3)
8*(6x + 8y = 13)
48x + 54y = 64
48x + 64y = 104
Subtract equations
-10y = -40
y = -40/-10
y = 4

Substitute y
8x + 9(4) = 32/3
8x = -76/3
x = -76/3/8
x = -19/6


Input: Solve quickly: x^2 + 1/8x - 9/8 = 0

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


Input: Solve the equation x^2 + 16/3x + 7 = 0

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


Input: Find x in x^2 - 7/9x - 20/3 = 0

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


Input: Solve quickly: 8x - 19 = 0

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


Input: What value of x satisfies 10x + 85 = 0

Output:
10x + 85 = 0
10x = -85
x = -85 / 10
x = -17/2


Input:
Solve the system:
8x + 9y = 49/15
9x + 5y = -7/2

Output:
8x + 9y = 49/15
9x + 5y = -7/2

Using elimination
9*(8x + 9y = 49/15)
8*(9x + 5y = -7/2)
72x + 81y = 147/5
72x + 40y = -28
Subtract equations
41y = 287/5
y = 287/5/41
y = 7/5

Substitute y
8x + 9(7/5) = 49/15
8x = -28/3
x = -28/3/8
x = -7/6


Input: Compute the solution of x^2 + 59/3x + 38/3 = 0

Output:
x^2 + 59/3x + 38/3 = 0
(x - -2/3)(x - -19) = 0
x - -2/3 = 0  or  x - -19 = 0
x = -2/3
x = -19


Input: Find x in x^2 - 217/36x + 68/9 = 0

Output:
x^2 - 217/36x + 68/9 = 0
(x - 17/4)(x - 16/9) = 0
x - 17/4 = 0  or  x - 16/9 = 0
x = 17/4
x = 16/9


Input: Find x in x^2 + 39/4x + 27/4 = 0

Output:
x^2 + 39/4x + 27/4 = 0
(x - -3/4)(x - -9) = 0
x - -3/4 = 0  or  x - -9 = 0
x = -3/4
x = -9


Input:
Solve the equations:
4x + 9y = 38/7
7x + 4y = 90/7

Output:
4x + 9y = 38/7
7x + 4y = 90/7

Using elimination
7*(4x + 9y = 38/7)
4*(7x + 4y = 90/7)
28x + 63y = 38
28x + 16y = 360/7
Subtract equations
47y = -94/7
y = -94/7/47
y = -2/7

Substitute y
4x + 9(-2/7) = 38/7
4x = 8
x = 8/4
x = 2


Input:
Solve the system:
4x + 9y = -163/2
9x + 6y = -162

Output:
4x + 9y = -163/2
9x + 6y = -162

Using elimination
9*(4x + 9y = -163/2)
4*(9x + 6y = -162)
36x + 81y = -1467/2
36x + 24y = -648
Subtract equations
57y = -171/2
y = -171/2/57
y = -3/2

Substitute y
4x + 9(-3/2) = -163/2
4x = -68
x = -68/4
x = -17


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

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


Input:
Solve the system:
6x + 4y = -104
7x + 2y = -104

Output:
6x + 4y = -104
7x + 2y = -104

Using elimination
7*(6x + 4y = -104)
6*(7x + 2y = -104)
42x + 28y = -728
42x + 12y = -624
Subtract equations
16y = -104
y = -104/16
y = -13/2

Substitute y
6x + 4(-13/2) = -104
6x = -78
x = -78/6
x = -13


Input:
Solve the equations:
10x + 5y = -170
10x + 8y = -164

Output:
10x + 5y = -170
10x + 8y = -164

Using elimination
10*(10x + 5y = -170)
10*(10x + 8y = -164)
100x + 50y = -1700
100x + 80y = -1640
Subtract equations
-30y = -60
y = -60/-30
y = 2

Substitute y
10x + 5(2) = -170
10x = -180
x = -180/10
x = -18


Input: Find x for x^2 + 29/10x + 9/5 = 0

Output:
x^2 + 29/10x + 9/5 = 0
(x - -2)(x - -9/10) = 0
x - -2 = 0  or  x - -9/10 = 0
x = -2
x = -9/10


Input: Compute the solution of x^3 + 187/21x^2 + 515/21x + 143/7 = 0

Output:
x^3 + 187/21x^2 + 515/21x + 143/7 = 0
(x - -3)(x - -13/3)(x - -11/7) = 0
x - -3 = 0
x - -13/3 = 0
x - -11/7 = 0
x = -3
x = -13/3
x = -11/7


Input: Solve quickly: x^3 - 53/36x^2 - 115/36x + 77/18 = 0

Output:
x^3 - 53/36x^2 - 115/36x + 77/18 = 0
(x - 2)(x - 11/9)(x - -7/4) = 0
x - 2 = 0
x - 11/9 = 0
x - -7/4 = 0
x = 2
x = 11/9
x = -7/4


Input: Solve the equation x^2 + 85/28x - 75/28 = 0

Output:
x^2 + 85/28x - 75/28 = 0
(x - 5/7)(x - -15/4) = 0
x - 5/7 = 0  or  x - -15/4 = 0
x = 5/7
x = -15/4


Input: Find x for x^3 + 233/56x^2 + 347/112x - 19/7 = 0

Output:
x^3 + 233/56x^2 + 347/112x - 19/7 = 0
(x - -19/8)(x - 1/2)(x - -16/7) = 0
x - -19/8 = 0
x - 1/2 = 0
x - -16/7 = 0
x = -19/8
x = 1/2
x = -16/7


Input:
Find x and y such that
6x + 9y = -303/35
1x + 4y = -351/70

Output:
6x + 9y = -303/35
1x + 4y = -351/70

Using elimination
1*(6x + 9y = -303/35)
6*(1x + 4y = -351/70)
6x + 9y = -303/35
6x + 24y = -1053/35
Subtract equations
-15y = 150/7
y = 150/7/-15
y = -10/7

Substitute y
6x + 9(-10/7) = -303/35
6x = 21/5
x = 21/5/6
x = 7/10


Input: Find the solution to 1x + 7/4 = 0

Output:
1x + 7/4 = 0
1x = -7/4
x = -7/4 / 1
x = -7/4


Input:
Find x and y such that
2x + 1y = -27/20
8x + 1y = -243/20

Output:
2x + 1y = -27/20
8x + 1y = -243/20

Using elimination
8*(2x + 1y = -27/20)
2*(8x + 1y = -243/20)
16x + 8y = -54/5
16x + 2y = -243/10
Subtract equations
6y = 27/2
y = 27/2/6
y = 9/4

Substitute y
2x + 1(9/4) = -27/20
2x = -18/5
x = -18/5/2
x = -9/5


Input: Solve the equation 5x - 80 = 0

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


Input: Solve x^3 - 253/84x^2 + 73/84x + 5/3 = 0

Output:
x^3 - 253/84x^2 + 73/84x + 5/3 = 0
(x - -4/7)(x - 7/3)(x - 5/4) = 0
x - -4/7 = 0
x - 7/3 = 0
x - 5/4 = 0
x = -4/7
x = 7/3
x = 5/4


Input: Compute the solution of x^2 + 34/35x - 33/35 = 0

Output:
x^2 + 34/35x - 33/35 = 0
(x - -11/7)(x - 3/5) = 0
x - -11/7 = 0  or  x - 3/5 = 0
x = -11/7
x = 3/5


Input: Determine x in x^2 + 34/15x - 16/15 = 0

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


Input: Solve x^2 - 21/40x - 143/80 = 0

Output:
x^2 - 21/40x - 143/80 = 0
(x - -11/10)(x - 13/8) = 0
x - -11/10 = 0  or  x - 13/8 = 0
x = -11/10
x = 13/8


Input: What value of x satisfies x^3 + 13/2x^2 + 213/16x + 135/16 = 0

Output:
x^3 + 13/2x^2 + 213/16x + 135/16 = 0
(x - -5/4)(x - -3)(x - -9/4) = 0
x - -5/4 = 0
x - -3 = 0
x - -9/4 = 0
x = -5/4
x = -3
x = -9/4


Input: Solve quickly: x^3 - 29/6x^2 - 21/2x + 19/3 = 0

Output:
x^3 - 29/6x^2 - 21/2x + 19/3 = 0
(x - 1/2)(x - 19/3)(x - -2) = 0
x - 1/2 = 0
x - 19/3 = 0
x - -2 = 0
x = 1/2
x = 19/3
x = -2


Input: Solve quickly: 1x - 1 = 0

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


Input: Find x in x^2 + 89/10x + 133/10 = 0

Output:
x^2 + 89/10x + 133/10 = 0
(x - -7)(x - -19/10) = 0
x - -7 = 0  or  x - -19/10 = 0
x = -7
x = -19/10


Input:
Solve the system:
4x + 5y = -114/7
1x + 5y = -207/14

Output:
4x + 5y = -114/7
1x + 5y = -207/14

Using elimination
1*(4x + 5y = -114/7)
4*(1x + 5y = -207/14)
4x + 5y = -114/7
4x + 20y = -414/7
Subtract equations
-15y = 300/7
y = 300/7/-15
y = -20/7

Substitute y
4x + 5(-20/7) = -114/7
4x = -2
x = -2/4
x = -1/2


Input: Find the solution to 10x - 40 = 0

Output:
10x - 40 = 0
10x = 40
x = 40 / 10
x = 4


Input:
Solve the system:
3x + 6y = -175/6
6x + 1y = -205/12

Output:
3x + 6y = -175/6
6x + 1y = -205/12

Using elimination
6*(3x + 6y = -175/6)
3*(6x + 1y = -205/12)
18x + 36y = -175
18x + 3y = -205/4
Subtract equations
33y = -495/4
y = -495/4/33
y = -15/4

Substitute y
3x + 6(-15/4) = -175/6
3x = -20/3
x = -20/3/3
x = -20/9


Input: Compute the solution of x^2 + 23/4x - 85/2 = 0

Output:
x^2 + 23/4x - 85/2 = 0
(x - -10)(x - 17/4) = 0
x - -10 = 0  or  x - 17/4 = 0
x = -10
x = 17/4


Input:
Solve simultaneously:
9x + 8y = -571/20
10x + 7y = -287/10

Output:
9x + 8y = -571/20
10x + 7y = -287/10

Using elimination
10*(9x + 8y = -571/20)
9*(10x + 7y = -287/10)
90x + 80y = -571/2
90x + 63y = -2583/10
Subtract equations
17y = -136/5
y = -136/5/17
y = -8/5

Substitute y
9x + 8(-8/5) = -571/20
9x = -63/4
x = -63/4/9
x = -7/4


Input: Find x for 3x - 45/2 = 0

Output:
3x - 45/2 = 0
3x = 45/2
x = 45/2 / 3
x = 15/2


Input: What value of x satisfies x^2 - 123/10x + 133/5 = 0

Output:
x^2 - 123/10x + 133/5 = 0
(x - 19/2)(x - 14/5) = 0
x - 19/2 = 0  or  x - 14/5 = 0
x = 19/2
x = 14/5


Input: Solve the equation 4x + 64/7 = 0

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


Input: Determine x in 2x - 36/5 = 0

Output:
2x - 36/5 = 0
2x = 36/5
x = 36/5 / 2
x = 18/5


Input: Compute the solution of x^2 + 20/3x + 4 = 0

Output:
x^2 + 20/3x + 4 = 0
(x - -6)(x - -2/3) = 0
x - -6 = 0  or  x - -2/3 = 0
x = -6
x = -2/3


Input:
Solve the system:
2x + 5y = -126
5x + 8y = -225

Output:
2x + 5y = -126
5x + 8y = -225

Using elimination
5*(2x + 5y = -126)
2*(5x + 8y = -225)
10x + 25y = -630
10x + 16y = -450
Subtract equations
9y = -180
y = -180/9
y = -20

Substitute y
2x + 5(-20) = -126
2x = -26
x = -26/2
x = -13


Input: Determine x in x^2 + 23/3x + 14 = 0

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


Input:
Solve the equations:
7x + 5y = -17/2
7x + 8y = -25

Output:
7x + 5y = -17/2
7x + 8y = -25

Using elimination
7*(7x + 5y = -17/2)
7*(7x + 8y = -25)
49x + 35y = -119/2
49x + 56y = -175
Subtract equations
-21y = 231/2
y = 231/2/-21
y = -11/2

Substitute y
7x + 5(-11/2) = -17/2
7x = 19
x = 19/7
x = 19/7


Input: Find x for x^2 + 19/5x + 18/5 = 0

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


Input:
Solve the equations:
6x + 4y = -110/9
5x + 8y = -115/9

Output:
6x + 4y = -110/9
5x + 8y = -115/9

Using elimination
5*(6x + 4y = -110/9)
6*(5x + 8y = -115/9)
30x + 20y = -550/9
30x + 48y = -230/3
Subtract equations
-28y = 140/9
y = 140/9/-28
y = -5/9

Substitute y
6x + 4(-5/9) = -110/9
6x = -10
x = -10/6
x = -5/3


Input:
Solve the system:
6x + 10y = -242/7
5x + 4y = -527/21

Output:
6x + 10y = -242/7
5x + 4y = -527/21

Using elimination
5*(6x + 10y = -242/7)
6*(5x + 4y = -527/21)
30x + 50y = -1210/7
30x + 24y = -1054/7
Subtract equations
26y = -156/7
y = -156/7/26
y = -6/7

Substitute y
6x + 10(-6/7) = -242/7
6x = -26
x = -26/6
x = -13/3


Input: Find x in x^2 + 108/35x + 81/35 = 0

Output:
x^2 + 108/35x + 81/35 = 0
(x - -9/7)(x - -9/5) = 0
x - -9/7 = 0  or  x - -9/5 = 0
x = -9/7
x = -9/5


Input: Find the solution to 5x - 65/6 = 0

Output:
5x - 65/6 = 0
5x = 65/6
x = 65/6 / 5
x = 13/6


Input: Compute the solution of x^2 + 3/7x - 40/49 = 0

Output:
x^2 + 3/7x - 40/49 = 0
(x - -8/7)(x - 5/7) = 0
x - -8/7 = 0  or  x - 5/7 = 0
x = -8/7
x = 5/7


Input:
Solve simultaneously:
3x + 10y = 512/15
2x + 9y = 141/5

Output:
3x + 10y = 512/15
2x + 9y = 141/5

Using elimination
2*(3x + 10y = 512/15)
3*(2x + 9y = 141/5)
6x + 20y = 1024/15
6x + 27y = 423/5
Subtract equations
-7y = -49/3
y = -49/3/-7
y = 7/3

Substitute y
3x + 10(7/3) = 512/15
3x = 54/5
x = 54/5/3
x = 18/5


Input: Find the solution to x^2 + 4x - 32 = 0

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


Input:
Find x and y such that
4x + 5y = 21/4
5x + 4y = 15/4

Output:
4x + 5y = 21/4
5x + 4y = 15/4

Using elimination
5*(4x + 5y = 21/4)
4*(5x + 4y = 15/4)
20x + 25y = 105/4
20x + 16y = 15
Subtract equations
9y = 45/4
y = 45/4/9
y = 5/4

Substitute y
4x + 5(5/4) = 21/4
4x = -1
x = -1/4
x = -1/4


Input: Determine x in x^3 + 103/45x^2 - 44/45x - 28/9 = 0

Output:
x^3 + 103/45x^2 - 44/45x - 28/9 = 0
(x - 10/9)(x - -2)(x - -7/5) = 0
x - 10/9 = 0
x - -2 = 0
x - -7/5 = 0
x = 10/9
x = -2
x = -7/5


Input: Solve x^2 - 28/15x - 64/15 = 0

Output:
x^2 - 28/15x - 64/15 = 0
(x - -4/3)(x - 16/5) = 0
x - -4/3 = 0  or  x - 16/5 = 0
x = -4/3
x = 16/5


Input:
Find x and y such that
1x + 7y = 73/6
1x + 2y = 211/42

Output:
1x + 7y = 73/6
1x + 2y = 211/42

Using elimination
1*(1x + 7y = 73/6)
1*(1x + 2y = 211/42)
1x + 7y = 73/6
1x + 2y = 211/42
Subtract equations
5y = 50/7
y = 50/7/5
y = 10/7

Substitute y
1x + 7(10/7) = 73/6
1x = 13/6
x = 13/6/1
x = 13/6


Input: Solve the equation x^2 + 6/5x - 17/20 = 0

Output:
x^2 + 6/5x - 17/20 = 0
(x - 1/2)(x - -17/10) = 0
x - 1/2 = 0  or  x - -17/10 = 0
x = 1/2
x = -17/10


Input: Solve x^3 - 23/3x^2 - 32/3x + 64 = 0

Output:
x^3 - 23/3x^2 - 32/3x + 64 = 0
(x - 8)(x - 8/3)(x - -3) = 0
x - 8 = 0
x - 8/3 = 0
x - -3 = 0
x = 8
x = 8/3
x = -3


Input: Solve x^3 + 149/90x^2 - 67/54x - 55/27 = 0

Output:
x^3 + 149/90x^2 - 67/54x - 55/27 = 0
(x - 10/9)(x - -11/10)(x - -5/3) = 0
x - 10/9 = 0
x - -11/10 = 0
x - -5/3 = 0
x = 10/9
x = -11/10
x = -5/3


Input: Solve x^3 + 103/10x^2 - 103/10x - 143/5 = 0

Output:
x^3 + 103/10x^2 - 103/10x - 143/5 = 0
(x - -13/10)(x - 2)(x - -11) = 0
x - -13/10 = 0
x - 2 = 0
x - -11 = 0
x = -13/10
x = 2
x = -11


Input: Find x in x^2 + 13/40x - 3/16 = 0

Output:
x^2 + 13/40x - 3/16 = 0
(x - 3/10)(x - -5/8) = 0
x - 3/10 = 0  or  x - -5/8 = 0
x = 3/10
x = -5/8


Input: Find x for 7x - 35/3 = 0

Output:
7x - 35/3 = 0
7x = 35/3
x = 35/3 / 7
x = 5/3


Input: Find x for x^3 + 529/42x^2 + 272/7x + 1445/42 = 0

Output:
x^3 + 529/42x^2 + 272/7x + 1445/42 = 0
(x - -17/2)(x - -5/3)(x - -17/7) = 0
x - -17/2 = 0
x - -5/3 = 0
x - -17/7 = 0
x = -17/2
x = -5/3
x = -17/7


Input:
Solve the system:
4x + 9y = 91/18
8x + 10y = -17/9

Output:
4x + 9y = 91/18
8x + 10y = -17/9

Using elimination
8*(4x + 9y = 91/18)
4*(8x + 10y = -17/9)
32x + 72y = 364/9
32x + 40y = -68/9
Subtract equations
32y = 48
y = 48/32
y = 3/2

Substitute y
4x + 9(3/2) = 91/18
4x = -76/9
x = -76/9/4
x = -19/9


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

Output:
8x - 8/9 = 0
8x = 8/9
x = 8/9 / 8
x = 1/9


Input: Find the solution to x^2 + 18/7x  = 0

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


Input:
Solve the equations:
1x + 10y = -59/2
9x + 2y = -3/2

Output:
1x + 10y = -59/2
9x + 2y = -3/2

Using elimination
9*(1x + 10y = -59/2)
1*(9x + 2y = -3/2)
9x + 90y = -531/2
9x + 2y = -3/2
Subtract equations
88y = -264
y = -264/88
y = -3

Substitute y
1x + 10(-3) = -59/2
1x = 1/2
x = 1/2/1
x = 1/2


Input: Find the solution to x^2 + 161/30x + 104/15 = 0

Output:
x^2 + 161/30x + 104/15 = 0
(x - -13/6)(x - -16/5) = 0
x - -13/6 = 0  or  x - -16/5 = 0
x = -13/6
x = -16/5


Input: Solve quickly: 7x - 133/3 = 0

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


Input: Solve 2x  = 0

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


Input: Solve quickly: x^3 - 65/24x^2 - 647/144x + 221/18 = 0

Output:
x^3 - 65/24x^2 - 647/144x + 221/18 = 0
(x - 8/3)(x - 13/6)(x - -17/8) = 0
x - 8/3 = 0
x - 13/6 = 0
x - -17/8 = 0
x = 8/3
x = 13/6
x = -17/8


Input: Find x for 4x + 52 = 0

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


Input: Determine x in x^3 + 13/14x^2 - 13/2x - 45/7 = 0

Output:
x^3 + 13/14x^2 - 13/2x - 45/7 = 0
(x - -5/2)(x - 18/7)(x - -1) = 0
x - -5/2 = 0
x - 18/7 = 0
x - -1 = 0
x = -5/2
x = 18/7
x = -1


Input: What value of x satisfies 8x + 36 = 0

Output:
8x + 36 = 0
8x = -36
x = -36 / 8
x = -9/2


Input:
Find x and y such that
8x + 5y = -17/2
10x + 7y = -23/2

Output:
8x + 5y = -17/2
10x + 7y = -23/2

Using elimination
10*(8x + 5y = -17/2)
8*(10x + 7y = -23/2)
80x + 50y = -85
80x + 56y = -92
Subtract equations
-6y = 7
y = 7/-6
y = -7/6

Substitute y
8x + 5(-7/6) = -17/2
8x = -8/3
x = -8/3/8
x = -1/3


Input: Solve quickly: x^2 - 49/8x + 55/16 = 0

Output:
x^2 - 49/8x + 55/16 = 0
(x - 5/8)(x - 11/2) = 0
x - 5/8 = 0  or  x - 11/2 = 0
x = 5/8
x = 11/2


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

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


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

Output:
2x + 11/3 = 0
2x = -11/3
x = -11/3 / 2
x = -11/6


Input: Compute the solution of x^3 + 317/140x^2 - 979/280x - 247/40 = 0

Output:
x^3 + 317/140x^2 - 979/280x - 247/40 = 0
(x - -13/10)(x - -19/7)(x - 7/4) = 0
x - -13/10 = 0
x - -19/7 = 0
x - 7/4 = 0
x = -13/10
x = -19/7
x = 7/4


Input: Determine x in x^2 - 34/7x + 39/7 = 0

Output:
x^2 - 34/7x + 39/7 = 0
(x - 3)(x - 13/7) = 0
x - 3 = 0  or  x - 13/7 = 0
x = 3
x = 13/7


Input: Solve the equation x^3 + 25/6x^2 - 7/6x - 11 = 0

Output:
x^3 + 25/6x^2 - 7/6x - 11 = 0
(x - -11/3)(x - -2)(x - 3/2) = 0
x - -11/3 = 0
x - -2 = 0
x - 3/2 = 0
x = -11/3
x = -2
x = 3/2


Input: Determine x in x^2 + 85/21x + 50/21 = 0

Output:
x^2 + 85/21x + 50/21 = 0
(x - -10/3)(x - -5/7) = 0
x - -10/3 = 0  or  x - -5/7 = 0
x = -10/3
x = -5/7


Input: Determine x in 9x - 39 = 0

Output:
9x - 39 = 0
9x = 39
x = 39 / 9
x = 13/3


Input: Solve the equation x^3 + 97/30x^2 - 37/15x - 19/2 = 0

Output:
x^3 + 97/30x^2 - 37/15x - 19/2 = 0
(x - 5/3)(x - -19/10)(x - -3) = 0
x - 5/3 = 0
x - -19/10 = 0
x - -3 = 0
x = 5/3
x = -19/10
x = -3


Input:
Solve simultaneously:
7x + 10y = -547/28
9x + 9y = -549/28

Output:
7x + 10y = -547/28
9x + 9y = -549/28

Using elimination
9*(7x + 10y = -547/28)
7*(9x + 9y = -549/28)
63x + 90y = -4923/28
63x + 63y = -549/4
Subtract equations
27y = -270/7
y = -270/7/27
y = -10/7

Substitute y
7x + 10(-10/7) = -547/28
7x = -21/4
x = -21/4/7
x = -3/4


Input: Find x in x^2 + 16/5x  = 0

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


Input: Find the solution to x^2 - 6/5x - 8/5 = 0

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


Input: Solve quickly: x^2 + 89/5x + 266/5 = 0

Output:
x^2 + 89/5x + 266/5 = 0
(x - -19/5)(x - -14) = 0
x - -19/5 = 0  or  x - -14 = 0
x = -19/5
x = -14


Input: Solve the equation x^3 + 331/140x^2 - 463/140x + 51/70 = 0

Output:
x^3 + 331/140x^2 - 463/140x + 51/70 = 0
(x - -17/5)(x - 3/4)(x - 2/7) = 0
x - -17/5 = 0
x - 3/4 = 0
x - 2/7 = 0
x = -17/5
x = 3/4
x = 2/7


Input: Find x for x^3 + 31/12x^2 - 205/12x - 25 = 0

Output:
x^3 + 31/12x^2 - 205/12x - 25 = 0
(x - -5)(x - 15/4)(x - -4/3) = 0
x - -5 = 0
x - 15/4 = 0
x - -4/3 = 0
x = -5
x = 15/4
x = -4/3


Input: Find x in x^3 + 9/4x^2 - 317/8x + 51 = 0

Output:
x^3 + 9/4x^2 - 317/8x + 51 = 0
(x - -8)(x - 17/4)(x - 3/2) = 0
x - -8 = 0
x - 17/4 = 0
x - 3/2 = 0
x = -8
x = 17/4
x = 3/2


Input:
Solve the equations:
3x + 4y = 41/2
10x + 8y = 157/3

Output:
3x + 4y = 41/2
10x + 8y = 157/3

Using elimination
10*(3x + 4y = 41/2)
3*(10x + 8y = 157/3)
30x + 40y = 205
30x + 24y = 157
Subtract equations
16y = 48
y = 48/16
y = 3

Substitute y
3x + 4(3) = 41/2
3x = 17/2
x = 17/2/3
x = 17/6


Input: Find x for x^3 - 193/40x^2 + 38/5x - 39/10 = 0

Output:
x^3 - 193/40x^2 + 38/5x - 39/10 = 0
(x - 13/8)(x - 6/5)(x - 2) = 0
x - 13/8 = 0
x - 6/5 = 0
x - 2 = 0
x = 13/8
x = 6/5
x = 2


Input: Compute the solution of 9x - 171/8 = 0

Output:
9x - 171/8 = 0
9x = 171/8
x = 171/8 / 9
x = 19/8


Input: What value of x satisfies x^3 - 49/30x^2 - 127/30x + 91/15 = 0

Output:
x^3 - 49/30x^2 - 127/30x + 91/15 = 0
(x - -2)(x - 7/3)(x - 13/10) = 0
x - -2 = 0
x - 7/3 = 0
x - 13/10 = 0
x = -2
x = 7/3
x = 13/10


Input: Compute the solution of x^2 + 21/5x - 4 = 0

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


Input: Solve the equation x^2 - 47/5x - 6 = 0

Output:
x^2 - 47/5x - 6 = 0
(x - 10)(x - -3/5) = 0
x - 10 = 0  or  x - -3/5 = 0
x = 10
x = -3/5


Input: What value of x satisfies x^3 - 7/5x^2 - 188/25x - 36/25 = 0

Output:
x^3 - 7/5x^2 - 188/25x - 36/25 = 0
(x - -1/5)(x - 18/5)(x - -2) = 0
x - -1/5 = 0
x - 18/5 = 0
x - -2 = 0
x = -1/5
x = 18/5
x = -2


Input:
Find x and y such that
1x + 9y = -187/10
2x + 1y = 0

Output:
1x + 9y = -187/10
2x + 1y = 0

Using elimination
2*(1x + 9y = -187/10)
1*(2x + 1y = 0)
2x + 18y = -187/5
2x + 1y = 0
Subtract equations
17y = -187/5
y = -187/5/17
y = -11/5

Substitute y
1x + 9(-11/5) = -187/10
1x = 11/10
x = 11/10/1
x = 11/10


Input:
Solve the system:
6x + 9y = 199/2
5x + 3y = 295/6

Output:
6x + 9y = 199/2
5x + 3y = 295/6

Using elimination
5*(6x + 9y = 199/2)
6*(5x + 3y = 295/6)
30x + 45y = 995/2
30x + 18y = 295
Subtract equations
27y = 405/2
y = 405/2/27
y = 15/2

Substitute y
6x + 9(15/2) = 199/2
6x = 32
x = 32/6
x = 16/3


Input:
Solve simultaneously:
2x + 3y = 165/7
9x + 6y = 750/7

Output:
2x + 3y = 165/7
9x + 6y = 750/7

Using elimination
9*(2x + 3y = 165/7)
2*(9x + 6y = 750/7)
18x + 27y = 1485/7
18x + 12y = 1500/7
Subtract equations
15y = -15/7
y = -15/7/15
y = -1/7

Substitute y
2x + 3(-1/7) = 165/7
2x = 24
x = 24/2
x = 12


Input: Solve the equation x^3 + 3/28x^2 - 149/56x + 3/8 = 0

Output:
x^3 + 3/28x^2 - 149/56x + 3/8 = 0
(x - 3/2)(x - 1/7)(x - -7/4) = 0
x - 3/2 = 0
x - 1/7 = 0
x - -7/4 = 0
x = 3/2
x = 1/7
x = -7/4


Input: Compute the solution of x^2 + 7/6x - 51/2 = 0

Output:
x^2 + 7/6x - 51/2 = 0
(x - 9/2)(x - -17/3) = 0
x - 9/2 = 0  or  x - -17/3 = 0
x = 9/2
x = -17/3


Input: Solve quickly: 5x + 20/9 = 0

Output:
5x + 20/9 = 0
5x = -20/9
x = -20/9 / 5
x = -4/9


Input:
Solve the system:
9x + 9y = -180/7
4x + 9y = -115/7

Output:
9x + 9y = -180/7
4x + 9y = -115/7

Using elimination
4*(9x + 9y = -180/7)
9*(4x + 9y = -115/7)
36x + 36y = -720/7
36x + 81y = -1035/7
Subtract equations
-45y = 45
y = 45/-45
y = -1

Substitute y
9x + 9(-1) = -180/7
9x = -117/7
x = -117/7/9
x = -13/7


Input: Solve quickly: 2x - 38/3 = 0

Output:
2x - 38/3 = 0
2x = 38/3
x = 38/3 / 2
x = 19/3


Input: Determine x in x^3 + 5x^2 - 17x - 21 = 0

Output:
x^3 + 5x^2 - 17x - 21 = 0
(x - -1)(x - 3)(x - -7) = 0
x - -1 = 0
x - 3 = 0
x - -7 = 0
x = -1
x = 3
x = -7


Input: Solve x^2 - 58/21x + 17/21 = 0

Output:
x^2 - 58/21x + 17/21 = 0
(x - 1/3)(x - 17/7) = 0
x - 1/3 = 0  or  x - 17/7 = 0
x = 1/3
x = 17/7


Input:
Solve the system:
8x + 4y = -140/3
6x + 1y = -5

Output:
8x + 4y = -140/3
6x + 1y = -5

Using elimination
6*(8x + 4y = -140/3)
8*(6x + 1y = -5)
48x + 24y = -280
48x + 8y = -40
Subtract equations
16y = -240
y = -240/16
y = -15

Substitute y
8x + 4(-15) = -140/3
8x = 40/3
x = 40/3/8
x = 5/3


Input: Find the solution to 9x + 27 = 0

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


Input:
Find x and y such that
1x + 10y = 3/2
5x + 2y = -21/10

Output:
1x + 10y = 3/2
5x + 2y = -21/10

Using elimination
5*(1x + 10y = 3/2)
1*(5x + 2y = -21/10)
5x + 50y = 15/2
5x + 2y = -21/10
Subtract equations
48y = 48/5
y = 48/5/48
y = 1/5

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


Input: Solve 4x  = 0

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


Input: Find the solution to x^2 + 11/35x - 6/35 = 0

Output:
x^2 + 11/35x - 6/35 = 0
(x - 2/7)(x - -3/5) = 0
x - 2/7 = 0  or  x - -3/5 = 0
x = 2/7
x = -3/5


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

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


Input:
Find x and y such that
10x + 3y = -5
5x + 4y = -65/6

Output:
10x + 3y = -5
5x + 4y = -65/6

Using elimination
5*(10x + 3y = -5)
10*(5x + 4y = -65/6)
50x + 15y = -25
50x + 40y = -325/3
Subtract equations
-25y = 250/3
y = 250/3/-25
y = -10/3

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


Input: Find x in 7x - 35 = 0

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


Input: Compute the solution of x^3 - 277/56x^2 - 3043/112x - 1445/56 = 0

Output:
x^3 - 277/56x^2 - 3043/112x - 1445/56 = 0
(x - -17/8)(x - 17/2)(x - -10/7) = 0
x - -17/8 = 0
x - 17/2 = 0
x - -10/7 = 0
x = -17/8
x = 17/2
x = -10/7


Input: Find x for x^3 + 43/6x^2 + 61/6x - 7 = 0

Output:
x^3 + 43/6x^2 + 61/6x - 7 = 0
(x - -3)(x - -14/3)(x - 1/2) = 0
x - -3 = 0
x - -14/3 = 0
x - 1/2 = 0
x = -3
x = -14/3
x = 1/2


Input: Compute the solution of x^2 + 23/2x + 51/2 = 0

Output:
x^2 + 23/2x + 51/2 = 0
(x - -17/2)(x - -3) = 0
x - -17/2 = 0  or  x - -3 = 0
x = -17/2
x = -3


Input: Find x for 10x - 10/7 = 0

Output:
10x - 10/7 = 0
10x = 10/7
x = 10/7 / 10
x = 1/7


Input: Solve quickly: x^3 + 41/6x^2 + 275/48x - 475/24 = 0

Output:
x^3 + 41/6x^2 + 275/48x - 475/24 = 0
(x - -19/4)(x - -10/3)(x - 5/4) = 0
x - -19/4 = 0
x - -10/3 = 0
x - 5/4 = 0
x = -19/4
x = -10/3
x = 5/4


Input: Solve quickly: x^2 + 1x - 15/4 = 0

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


Input:
Solve the system:
8x + 10y = 221/2
4x + 8y = 62

Output:
8x + 10y = 221/2
4x + 8y = 62

Using elimination
4*(8x + 10y = 221/2)
8*(4x + 8y = 62)
32x + 40y = 442
32x + 64y = 496
Subtract equations
-24y = -54
y = -54/-24
y = 9/4

Substitute y
8x + 10(9/4) = 221/2
8x = 88
x = 88/8
x = 11


Input: Solve the equation x^2 - 79/15x + 14/5 = 0

Output:
x^2 - 79/15x + 14/5 = 0
(x - 3/5)(x - 14/3) = 0
x - 3/5 = 0  or  x - 14/3 = 0
x = 3/5
x = 14/3


Input:
Solve the equations:
3x + 5y = -5/3
3x + 8y = -8/3

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

Using elimination
3*(3x + 5y = -5/3)
3*(3x + 8y = -8/3)
9x + 15y = -5
9x + 24y = -8
Subtract equations
-9y = 3
y = 3/-9
y = -1/3

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


Input:
Solve simultaneously:
1x + 6y = -20/3
8x + 7y = -316/9

Output:
1x + 6y = -20/3
8x + 7y = -316/9

Using elimination
8*(1x + 6y = -20/3)
1*(8x + 7y = -316/9)
8x + 48y = -160/3
8x + 7y = -316/9
Subtract equations
41y = -164/9
y = -164/9/41
y = -4/9

Substitute y
1x + 6(-4/9) = -20/3
1x = -4
x = -4/1
x = -4


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

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


Input: Find the solution to x^2 - 37/10x + 21/10 = 0

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


Input:
Solve simultaneously:
2x + 4y = -42
8x + 2y = -84

Output:
2x + 4y = -42
8x + 2y = -84

Using elimination
8*(2x + 4y = -42)
2*(8x + 2y = -84)
16x + 32y = -336
16x + 4y = -168
Subtract equations
28y = -168
y = -168/28
y = -6

Substitute y
2x + 4(-6) = -42
2x = -18
x = -18/2
x = -9


Input: Find the solution to 6x - 3 = 0

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


Input:
Solve the equations:
4x + 8y = 88
3x + 7y = 78

Output:
4x + 8y = 88
3x + 7y = 78

Using elimination
3*(4x + 8y = 88)
4*(3x + 7y = 78)
12x + 24y = 264
12x + 28y = 312
Subtract equations
-4y = -48
y = -48/-4
y = 12

Substitute y
4x + 8(12) = 88
4x = -8
x = -8/4
x = -2


Input: Solve the equation 9x + 9 = 0

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


Input: What value of x satisfies x^2 - 177/35x + 44/7 = 0

Output:
x^2 - 177/35x + 44/7 = 0
(x - 20/7)(x - 11/5) = 0
x - 20/7 = 0  or  x - 11/5 = 0
x = 20/7
x = 11/5


Input: Find x in 2x + 8 = 0

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


Input: Solve the equation x^3 - 37/20x^2 - 203/320x + 17/160 = 0

Output:
x^3 - 37/20x^2 - 203/320x + 17/160 = 0
(x - -2/5)(x - 17/8)(x - 1/8) = 0
x - -2/5 = 0
x - 17/8 = 0
x - 1/8 = 0
x = -2/5
x = 17/8
x = 1/8


Input: Solve quickly: x^3 - 1077/56x^2 + 45/2x - 81/14 = 0

Output:
x^3 - 1077/56x^2 + 45/2x - 81/14 = 0
(x - 6/7)(x - 18)(x - 3/8) = 0
x - 6/7 = 0
x - 18 = 0
x - 3/8 = 0
x = 6/7
x = 18
x = 3/8


Input: Compute the solution of x^3 - 25/2x^2 - 19/2x + 39 = 0

Output:
x^3 - 25/2x^2 - 19/2x + 39 = 0
(x - 3/2)(x - 13)(x - -2) = 0
x - 3/2 = 0
x - 13 = 0
x - -2 = 0
x = 3/2
x = 13
x = -2


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

Output:
3x - 17/2 = 0
3x = 17/2
x = 17/2 / 3
x = 17/6


Input: What value of x satisfies x^3 - 32/15x^2 + 7/5x - 4/15 = 0

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


Input: Determine x in x^2 - 1/15x - 8/3 = 0

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


Input: Find x for 7x - 63/5 = 0

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


Input: Solve the equation x^3 + 293/56x^2 + 725/112x - 25/28 = 0

Output:
x^3 + 293/56x^2 + 725/112x - 25/28 = 0
(x - -5/2)(x - -20/7)(x - 1/8) = 0
x - -5/2 = 0
x - -20/7 = 0
x - 1/8 = 0
x = -5/2
x = -20/7
x = 1/8


Input: Find x for x^3 - 117/10x^2 + 6x + 187/10 = 0

Output:
x^3 - 117/10x^2 + 6x + 187/10 = 0
(x - 11)(x - 17/10)(x - -1) = 0
x - 11 = 0
x - 17/10 = 0
x - -1 = 0
x = 11
x = 17/10
x = -1


Input: Find x in x^3 - 15/4x^2 - 83/8x + 165/8 = 0

Output:
x^3 - 15/4x^2 - 83/8x + 165/8 = 0
(x - 3/2)(x - -11/4)(x - 5) = 0
x - 3/2 = 0
x - -11/4 = 0
x - 5 = 0
x = 3/2
x = -11/4
x = 5


Input: Determine x in x^2 + 7/8x + 3/16 = 0

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


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

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


Input: What value of x satisfies x^3 - 253/70x^2 + 271/70x - 9/7 = 0

Output:
x^3 - 253/70x^2 + 271/70x - 9/7 = 0
(x - 9/10)(x - 2)(x - 5/7) = 0
x - 9/10 = 0
x - 2 = 0
x - 5/7 = 0
x = 9/10
x = 2
x = 5/7


Input: Find x for x^2 - 13/9x + 22/81 = 0

Output:
x^2 - 13/9x + 22/81 = 0
(x - 11/9)(x - 2/9) = 0
x - 11/9 = 0  or  x - 2/9 = 0
x = 11/9
x = 2/9


Input: What value of x satisfies x^3 + 47/24x^2 + 7/6x + 5/24 = 0

Output:
x^3 + 47/24x^2 + 7/6x + 5/24 = 0
(x - -1)(x - -5/8)(x - -1/3) = 0
x - -1 = 0
x - -5/8 = 0
x - -1/3 = 0
x = -1
x = -5/8
x = -1/3


Input: Determine x in x^2 + 24/7x + 143/49 = 0

Output:
x^2 + 24/7x + 143/49 = 0
(x - -13/7)(x - -11/7) = 0
x - -13/7 = 0  or  x - -11/7 = 0
x = -13/7
x = -11/7


Input: Determine x in 1x - 1 = 0

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


Input: Determine x in x^2 + 22/5x - 9/20 = 0

Output:
x^2 + 22/5x - 9/20 = 0
(x - 1/10)(x - -9/2) = 0
x - 1/10 = 0  or  x - -9/2 = 0
x = 1/10
x = -9/2


Input: Solve the equation 1x - 7/6 = 0

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


Input:
Solve simultaneously:
10x + 1y = -17
9x + 6y = -357/10

Output:
10x + 1y = -17
9x + 6y = -357/10

Using elimination
9*(10x + 1y = -17)
10*(9x + 6y = -357/10)
90x + 9y = -153
90x + 60y = -357
Subtract equations
-51y = 204
y = 204/-51
y = -4

Substitute y
10x + 1(-4) = -17
10x = -13
x = -13/10
x = -13/10


Input: Determine x in x^3 - 20x^2 - 9x + 180 = 0

Output:
x^3 - 20x^2 - 9x + 180 = 0
(x - -3)(x - 3)(x - 20) = 0
x - -3 = 0
x - 3 = 0
x - 20 = 0
x = -3
x = 3
x = 20


Input: Solve the equation 1x + 15/2 = 0

Output:
1x + 15/2 = 0
1x = -15/2
x = -15/2 / 1
x = -15/2


Input:
Solve simultaneously:
3x + 7y = -109/2
9x + 7y = -75/2

Output:
3x + 7y = -109/2
9x + 7y = -75/2

Using elimination
9*(3x + 7y = -109/2)
3*(9x + 7y = -75/2)
27x + 63y = -981/2
27x + 21y = -225/2
Subtract equations
42y = -378
y = -378/42
y = -9

Substitute y
3x + 7(-9) = -109/2
3x = 17/2
x = 17/2/3
x = 17/6


Input:
Solve simultaneously:
10x + 4y = -524/9
8x + 5y = -646/9

Output:
10x + 4y = -524/9
8x + 5y = -646/9

Using elimination
8*(10x + 4y = -524/9)
10*(8x + 5y = -646/9)
80x + 32y = -4192/9
80x + 50y = -6460/9
Subtract equations
-18y = 252
y = 252/-18
y = -14

Substitute y
10x + 4(-14) = -524/9
10x = -20/9
x = -20/9/10
x = -2/9


Input: Compute the solution of 8x + 8/5 = 0

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


Input: Find the solution to 4x + 32/3 = 0

Output:
4x + 32/3 = 0
4x = -32/3
x = -32/3 / 4
x = -8/3


Input: Find x for x^3 - 227/30x^2 + 41/10x + 38/3 = 0

Output:
x^3 - 227/30x^2 + 41/10x + 38/3 = 0
(x - 19/10)(x - 20/3)(x - -1) = 0
x - 19/10 = 0
x - 20/3 = 0
x - -1 = 0
x = 19/10
x = 20/3
x = -1


Input:
Solve simultaneously:
6x + 3y = 81/2
7x + 5y = 279/4

Output:
6x + 3y = 81/2
7x + 5y = 279/4

Using elimination
7*(6x + 3y = 81/2)
6*(7x + 5y = 279/4)
42x + 21y = 567/2
42x + 30y = 837/2
Subtract equations
-9y = -135
y = -135/-9
y = 15

Substitute y
6x + 3(15) = 81/2
6x = -9/2
x = -9/2/6
x = -3/4


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

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


Input: Find the solution to x^2  - 169 = 0

Output:
x^2  - 169 = 0
(x - -13)(x - 13) = 0
x - -13 = 0  or  x - 13 = 0
x = -13
x = 13


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

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


Input: What value of x satisfies x^3 - 157/36x^2 + 211/36x - 5/2 = 0

Output:
x^3 - 157/36x^2 + 211/36x - 5/2 = 0
(x - 1)(x - 9/4)(x - 10/9) = 0
x - 1 = 0
x - 9/4 = 0
x - 10/9 = 0
x = 1
x = 9/4
x = 10/9


Input:
Solve the equations:
6x + 3y = 102/5
3x + 8y = 246/5

Output:
6x + 3y = 102/5
3x + 8y = 246/5

Using elimination
3*(6x + 3y = 102/5)
6*(3x + 8y = 246/5)
18x + 9y = 306/5
18x + 48y = 1476/5
Subtract equations
-39y = -234
y = -234/-39
y = 6

Substitute y
6x + 3(6) = 102/5
6x = 12/5
x = 12/5/6
x = 2/5


Input: Determine x in x^2 + 5/21x - 50/21 = 0

Output:
x^2 + 5/21x - 50/21 = 0
(x - -5/3)(x - 10/7) = 0
x - -5/3 = 0  or  x - 10/7 = 0
x = -5/3
x = 10/7


Input:
Solve simultaneously:
2x + 7y = -41/8
6x + 3y = 3/8

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

Using elimination
6*(2x + 7y = -41/8)
2*(6x + 3y = 3/8)
12x + 42y = -123/4
12x + 6y = 3/4
Subtract equations
36y = -63/2
y = -63/2/36
y = -7/8

Substitute y
2x + 7(-7/8) = -41/8
2x = 1
x = 1/2
x = 1/2


Input: Find x in x^2 + 8/5x - 48/5 = 0

Output:
x^2 + 8/5x - 48/5 = 0
(x - -4)(x - 12/5) = 0
x - -4 = 0  or  x - 12/5 = 0
x = -4
x = 12/5


Input: Solve 5x - 85/4 = 0

Output:
5x - 85/4 = 0
5x = 85/4
x = 85/4 / 5
x = 17/4


Input: Find x in 7x + 56/3 = 0

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


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

Output:
2x + 11/3 = 0
2x = -11/3
x = -11/3 / 2
x = -11/6


Input: Solve quickly: x^2 + 77/30x + 49/30 = 0

Output:
x^2 + 77/30x + 49/30 = 0
(x - -7/6)(x - -7/5) = 0
x - -7/6 = 0  or  x - -7/5 = 0
x = -7/6
x = -7/5


Input:
Solve the system:
4x + 6y = -103/20
8x + 9y = -277/40

Output:
4x + 6y = -103/20
8x + 9y = -277/40

Using elimination
8*(4x + 6y = -103/20)
4*(8x + 9y = -277/40)
32x + 48y = -206/5
32x + 36y = -277/10
Subtract equations
12y = -27/2
y = -27/2/12
y = -9/8

Substitute y
4x + 6(-9/8) = -103/20
4x = 8/5
x = 8/5/4
x = 2/5


Input: Find x for 7x - 14 = 0

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


Input: Find the solution to 5x + 10 = 0

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


Input: Find x for 2x - 4 = 0

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


Input: Compute the solution of 1x + 17/3 = 0

Output:
1x + 17/3 = 0
1x = -17/3
x = -17/3 / 1
x = -17/3


Input:
Solve the system:
1x + 6y = 1
7x + 3y = 67/4

Output:
1x + 6y = 1
7x + 3y = 67/4

Using elimination
7*(1x + 6y = 1)
1*(7x + 3y = 67/4)
7x + 42y = 7
7x + 3y = 67/4
Subtract equations
39y = -39/4
y = -39/4/39
y = -1/4

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


Input: Determine x in x^3 + 65/8x^2 + 337/16x + 273/16 = 0

Output:
x^3 + 65/8x^2 + 337/16x + 273/16 = 0
(x - -13/8)(x - -3)(x - -7/2) = 0
x - -13/8 = 0
x - -3 = 0
x - -7/2 = 0
x = -13/8
x = -3
x = -7/2


Input: Solve the equation x^3 + 29/7x^2 - 247/63x - 845/63 = 0

Output:
x^3 + 29/7x^2 - 247/63x - 845/63 = 0
(x - -13/3)(x - -5/3)(x - 13/7) = 0
x - -13/3 = 0
x - -5/3 = 0
x - 13/7 = 0
x = -13/3
x = -5/3
x = 13/7


Input: Find the solution to 1x - 16 = 0

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


Input: What value of x satisfies x^3 + 29/8x^2 - 271/32x - 255/32 = 0

Output:
x^3 + 29/8x^2 - 271/32x - 255/32 = 0
(x - -3/4)(x - 17/8)(x - -5) = 0
x - -3/4 = 0
x - 17/8 = 0
x - -5 = 0
x = -3/4
x = 17/8
x = -5


Input: Find the solution to 8x - 19 = 0

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


Input:
Find x and y such that
5x + 7y = -53/8
1x + 8y = -37/8

Output:
5x + 7y = -53/8
1x + 8y = -37/8

Using elimination
1*(5x + 7y = -53/8)
5*(1x + 8y = -37/8)
5x + 7y = -53/8
5x + 40y = -185/8
Subtract equations
-33y = 33/2
y = 33/2/-33
y = -1/2

Substitute y
5x + 7(-1/2) = -53/8
5x = -25/8
x = -25/8/5
x = -5/8


Input:
Find x and y such that
6x + 8y = 47/3
10x + 5y = 115/6

Output:
6x + 8y = 47/3
10x + 5y = 115/6

Using elimination
10*(6x + 8y = 47/3)
6*(10x + 5y = 115/6)
60x + 80y = 470/3
60x + 30y = 115
Subtract equations
50y = 125/3
y = 125/3/50
y = 5/6

Substitute y
6x + 8(5/6) = 47/3
6x = 9
x = 9/6
x = 3/2


Input: Determine x in 9x - 12 = 0

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


Input: Find x for x^3 - 28/3x^2 + 32/3x  = 0

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


Input:
Find x and y such that
8x + 10y = 47/2
8x + 6y = 41/2

Output:
8x + 10y = 47/2
8x + 6y = 41/2

Using elimination
8*(8x + 10y = 47/2)
8*(8x + 6y = 41/2)
64x + 80y = 188
64x + 48y = 164
Subtract equations
32y = 24
y = 24/32
y = 3/4

Substitute y
8x + 10(3/4) = 47/2
8x = 16
x = 16/8
x = 2


Input:
Solve the system:
5x + 7y = 91/12
10x + 3y = 17

Output:
5x + 7y = 91/12
10x + 3y = 17

Using elimination
10*(5x + 7y = 91/12)
5*(10x + 3y = 17)
50x + 70y = 455/6
50x + 15y = 85
Subtract equations
55y = -55/6
y = -55/6/55
y = -1/6

Substitute y
5x + 7(-1/6) = 91/12
5x = 35/4
x = 35/4/5
x = 7/4


Input:
Solve simultaneously:
3x + 2y = 47/4
4x + 5y = 43/2

Output:
3x + 2y = 47/4
4x + 5y = 43/2

Using elimination
4*(3x + 2y = 47/4)
3*(4x + 5y = 43/2)
12x + 8y = 47
12x + 15y = 129/2
Subtract equations
-7y = -35/2
y = -35/2/-7
y = 5/2

Substitute y
3x + 2(5/2) = 47/4
3x = 27/4
x = 27/4/3
x = 9/4


Input: Find the solution to x^3 - 161/15x^2 - 1174/15x - 96 = 0

Output:
x^3 - 161/15x^2 - 1174/15x - 96 = 0
(x - -5/3)(x - 16)(x - -18/5) = 0
x - -5/3 = 0
x - 16 = 0
x - -18/5 = 0
x = -5/3
x = 16
x = -18/5


Input:
Solve simultaneously:
7x + 3y = -288/5
10x + 7y = -387/5

Output:
7x + 3y = -288/5
10x + 7y = -387/5

Using elimination
10*(7x + 3y = -288/5)
7*(10x + 7y = -387/5)
70x + 30y = -576
70x + 49y = -2709/5
Subtract equations
-19y = -171/5
y = -171/5/-19
y = 9/5

Substitute y
7x + 3(9/5) = -288/5
7x = -63
x = -63/7
x = -9


Input: Solve the equation 5x - 60/7 = 0

Output:
5x - 60/7 = 0
5x = 60/7
x = 60/7 / 5
x = 12/7


Input:
Solve the equations:
6x + 4y = 12
6x + 2y = 11

Output:
6x + 4y = 12
6x + 2y = 11

Using elimination
6*(6x + 4y = 12)
6*(6x + 2y = 11)
36x + 24y = 72
36x + 12y = 66
Subtract equations
12y = 6
y = 6/12
y = 1/2

Substitute y
6x + 4(1/2) = 12
6x = 10
x = 10/6
x = 5/3


Input:
Solve simultaneously:
7x + 2y = -134/35
8x + 9y = 384/35

Output:
7x + 2y = -134/35
8x + 9y = 384/35

Using elimination
8*(7x + 2y = -134/35)
7*(8x + 9y = 384/35)
56x + 16y = -1072/35
56x + 63y = 384/5
Subtract equations
-47y = -752/7
y = -752/7/-47
y = 16/7

Substitute y
7x + 2(16/7) = -134/35
7x = -42/5
x = -42/5/7
x = -6/5


Input: Solve the equation x^2 + 13/6x + 5/6 = 0

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


Input:
Find x and y such that
7x + 7y = 539/15
3x + 1y = 69/5

Output:
7x + 7y = 539/15
3x + 1y = 69/5

Using elimination
3*(7x + 7y = 539/15)
7*(3x + 1y = 69/5)
21x + 21y = 539/5
21x + 7y = 483/5
Subtract equations
14y = 56/5
y = 56/5/14
y = 4/5

Substitute y
7x + 7(4/5) = 539/15
7x = 91/3
x = 91/3/7
x = 13/3


Input: Compute the solution of x^3 + 61/3x^2 + 256/3x + 80 = 0

Output:
x^3 + 61/3x^2 + 256/3x + 80 = 0
(x - -15)(x - -4/3)(x - -4) = 0
x - -15 = 0
x - -4/3 = 0
x - -4 = 0
x = -15
x = -4/3
x = -4


Input: Solve quickly: x^3 - 664/63x^2 + 1297/63x - 136/63 = 0

Output:
x^3 - 664/63x^2 + 1297/63x - 136/63 = 0
(x - 17/7)(x - 8)(x - 1/9) = 0
x - 17/7 = 0
x - 8 = 0
x - 1/9 = 0
x = 17/7
x = 8
x = 1/9


Input: Solve the equation 10x + 140/3 = 0

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


Input: Find the solution to x^3 - 34/15x^2 - 113/15x + 44/5 = 0

Output:
x^3 - 34/15x^2 - 113/15x + 44/5 = 0
(x - 1)(x - 11/3)(x - -12/5) = 0
x - 1 = 0
x - 11/3 = 0
x - -12/5 = 0
x = 1
x = 11/3
x = -12/5


Input: Solve 6x + 78 = 0

Output:
6x + 78 = 0
6x = -78
x = -78 / 6
x = -13


Input:
Find x and y such that
4x + 6y = -48
10x + 2y = 10

Output:
4x + 6y = -48
10x + 2y = 10

Using elimination
10*(4x + 6y = -48)
4*(10x + 2y = 10)
40x + 60y = -480
40x + 8y = 40
Subtract equations
52y = -520
y = -520/52
y = -10

Substitute y
4x + 6(-10) = -48
4x = 12
x = 12/4
x = 3


Input: Determine x in 9x - 4 = 0

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


Input:
Solve the equations:
9x + 6y = 380/21
7x + 4y = 124/9

Output:
9x + 6y = 380/21
7x + 4y = 124/9

Using elimination
7*(9x + 6y = 380/21)
9*(7x + 4y = 124/9)
63x + 42y = 380/3
63x + 36y = 124
Subtract equations
6y = 8/3
y = 8/3/6
y = 4/9

Substitute y
9x + 6(4/9) = 380/21
9x = 108/7
x = 108/7/9
x = 12/7


Input: Solve quickly: x^3 - 57/10x^2 - 2071/10x - 1287/5 = 0

Output:
x^3 - 57/10x^2 - 2071/10x - 1287/5 = 0
(x - 18)(x - -13/10)(x - -11) = 0
x - 18 = 0
x - -13/10 = 0
x - -11 = 0
x = 18
x = -13/10
x = -11


Input: Determine x in 3x - 18 = 0

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


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

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


Input: Determine x in 2x - 34/9 = 0

Output:
2x - 34/9 = 0
2x = 34/9
x = 34/9 / 2
x = 17/9


Input:
Solve simultaneously:
5x + 1y = -119/2
7x + 9y = -311/2

Output:
5x + 1y = -119/2
7x + 9y = -311/2

Using elimination
7*(5x + 1y = -119/2)
5*(7x + 9y = -311/2)
35x + 7y = -833/2
35x + 45y = -1555/2
Subtract equations
-38y = 361
y = 361/-38
y = -19/2

Substitute y
5x + 1(-19/2) = -119/2
5x = -50
x = -50/5
x = -10


Input: Solve x^2 - 20x + 36 = 0

Output:
x^2 - 20x + 36 = 0
(x - 18)(x - 2) = 0
x - 18 = 0  or  x - 2 = 0
x = 18
x = 2


Input: Determine x in x^3 - 71/18x^2 + 253/54x - 40/27 = 0

Output:
x^3 - 71/18x^2 + 253/54x - 40/27 = 0
(x - 16/9)(x - 5/3)(x - 1/2) = 0
x - 16/9 = 0
x - 5/3 = 0
x - 1/2 = 0
x = 16/9
x = 5/3
x = 1/2


Input: Solve x^2 + 133/9x + 208/9 = 0

Output:
x^2 + 133/9x + 208/9 = 0
(x - -16/9)(x - -13) = 0
x - -16/9 = 0  or  x - -13 = 0
x = -16/9
x = -13


Input: Solve the equation 10x + 20/3 = 0

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


Input: Compute the solution of x^2 - 31/24x - 13/24 = 0

Output:
x^2 - 31/24x - 13/24 = 0
(x - 13/8)(x - -1/3) = 0
x - 13/8 = 0  or  x - -1/3 = 0
x = 13/8
x = -1/3


Input: Solve the equation 2x - 12/5 = 0

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


Input:
Solve the system:
4x + 4y = 28
1x + 6y = 32

Output:
4x + 4y = 28
1x + 6y = 32

Using elimination
1*(4x + 4y = 28)
4*(1x + 6y = 32)
4x + 4y = 28
4x + 24y = 128
Subtract equations
-20y = -100
y = -100/-20
y = 5

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


Input:
Solve simultaneously:
5x + 7y = 14
9x + 4y = -46/5

Output:
5x + 7y = 14
9x + 4y = -46/5

Using elimination
9*(5x + 7y = 14)
5*(9x + 4y = -46/5)
45x + 63y = 126
45x + 20y = -46
Subtract equations
43y = 172
y = 172/43
y = 4

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


Input: What value of x satisfies x^2 + 25/14x - 8/7 = 0

Output:
x^2 + 25/14x - 8/7 = 0
(x - -16/7)(x - 1/2) = 0
x - -16/7 = 0  or  x - 1/2 = 0
x = -16/7
x = 1/2


Input: Solve 7x - 77/9 = 0

Output:
7x - 77/9 = 0
7x = 77/9
x = 77/9 / 7
x = 11/9


Input: What value of x satisfies 9x - 21/2 = 0

Output:
9x - 21/2 = 0
9x = 21/2
x = 21/2 / 9
x = 7/6


Input: Solve the equation x^2 - 33/5x - 14/5 = 0

Output:
x^2 - 33/5x - 14/5 = 0
(x - -2/5)(x - 7) = 0
x - -2/5 = 0  or  x - 7 = 0
x = -2/5
x = 7


Input: Solve quickly: x^2 + 1/15x - 28/5 = 0

Output:
x^2 + 1/15x - 28/5 = 0
(x - 7/3)(x - -12/5) = 0
x - 7/3 = 0  or  x - -12/5 = 0
x = 7/3
x = -12/5


Input: Solve x^2 - 24/7x + 20/7 = 0

Output:
x^2 - 24/7x + 20/7 = 0
(x - 2)(x - 10/7) = 0
x - 2 = 0  or  x - 10/7 = 0
x = 2
x = 10/7


Input: Solve quickly: x^2 + 13/7x - 24/7 = 0

Output:
x^2 + 13/7x - 24/7 = 0
(x - 8/7)(x - -3) = 0
x - 8/7 = 0  or  x - -3 = 0
x = 8/7
x = -3


Input: Solve quickly: 7x + 133 = 0

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


Input:
Find x and y such that
7x + 9y = 167/2
5x + 3y = 37/2

Output:
7x + 9y = 167/2
5x + 3y = 37/2

Using elimination
5*(7x + 9y = 167/2)
7*(5x + 3y = 37/2)
35x + 45y = 835/2
35x + 21y = 259/2
Subtract equations
24y = 288
y = 288/24
y = 12

Substitute y
7x + 9(12) = 167/2
7x = -49/2
x = -49/2/7
x = -7/2


Input: Find x for x^2 + 7/10x - 13/5 = 0

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


Input: Compute the solution of 7x + 70/9 = 0

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


Input: Find x in x^2 + 104/9x - 169/9 = 0

Output:
x^2 + 104/9x - 169/9 = 0
(x - -13)(x - 13/9) = 0
x - -13 = 0  or  x - 13/9 = 0
x = -13
x = 13/9


Input: Solve quickly: 3x - 39/10 = 0

Output:
3x - 39/10 = 0
3x = 39/10
x = 39/10 / 3
x = 13/10


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

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


Input: Compute the solution of 3x - 3/10 = 0

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


Input:
Solve simultaneously:
1x + 3y = 159/14
3x + 3y = 239/14

Output:
1x + 3y = 159/14
3x + 3y = 239/14

Using elimination
3*(1x + 3y = 159/14)
1*(3x + 3y = 239/14)
3x + 9y = 477/14
3x + 3y = 239/14
Subtract equations
6y = 17
y = 17/6
y = 17/6

Substitute y
1x + 3(17/6) = 159/14
1x = 20/7
x = 20/7/1
x = 20/7


Input: Find the solution to x^3 - 43/6x^2 - 208/3x - 169/2 = 0

Output:
x^3 - 43/6x^2 - 208/3x - 169/2 = 0
(x - -3/2)(x - -13/3)(x - 13) = 0
x - -3/2 = 0
x - -13/3 = 0
x - 13 = 0
x = -3/2
x = -13/3
x = 13


Input: Compute the solution of x^3 + 175/36x^2 + 17/9x - 56/9 = 0

Output:
x^3 + 175/36x^2 + 17/9x - 56/9 = 0
(x - -7/4)(x - -4)(x - 8/9) = 0
x - -7/4 = 0
x - -4 = 0
x - 8/9 = 0
x = -7/4
x = -4
x = 8/9


Input:
Solve the equations:
10x + 2y = -88/5
6x + 7y = -123/10

Output:
10x + 2y = -88/5
6x + 7y = -123/10

Using elimination
6*(10x + 2y = -88/5)
10*(6x + 7y = -123/10)
60x + 12y = -528/5
60x + 70y = -123
Subtract equations
-58y = 87/5
y = 87/5/-58
y = -3/10

Substitute y
10x + 2(-3/10) = -88/5
10x = -17
x = -17/10
x = -17/10


Input:
Solve simultaneously:
5x + 10y = 85/4
9x + 9y = 63/4

Output:
5x + 10y = 85/4
9x + 9y = 63/4

Using elimination
9*(5x + 10y = 85/4)
5*(9x + 9y = 63/4)
45x + 90y = 765/4
45x + 45y = 315/4
Subtract equations
45y = 225/2
y = 225/2/45
y = 5/2

Substitute y
5x + 10(5/2) = 85/4
5x = -15/4
x = -15/4/5
x = -3/4


Input: Find x in x^2 - 9/10x - 4 = 0

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


Input: What value of x satisfies x^3 + 25/7x^2 - 83/7x - 165/7 = 0

Output:
x^3 + 25/7x^2 - 83/7x - 165/7 = 0
(x - -5)(x - -11/7)(x - 3) = 0
x - -5 = 0
x - -11/7 = 0
x - 3 = 0
x = -5
x = -11/7
x = 3


Input: Solve the equation 1x + 19/10 = 0

Output:
1x + 19/10 = 0
1x = -19/10
x = -19/10 / 1
x = -19/10


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

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


Input: Solve quickly: x^2 + 19/9x - 40/27 = 0

Output:
x^2 + 19/9x - 40/27 = 0
(x - 5/9)(x - -8/3) = 0
x - 5/9 = 0  or  x - -8/3 = 0
x = 5/9
x = -8/3


Input: Find x in x^2 - 101/24x + 209/48 = 0

Output:
x^2 - 101/24x + 209/48 = 0
(x - 19/8)(x - 11/6) = 0
x - 19/8 = 0  or  x - 11/6 = 0
x = 19/8
x = 11/6


Input: Find the solution to x^3 - 41/12x^2 - 223/12x + 119/2 = 0

Output:
x^3 - 41/12x^2 - 223/12x + 119/2 = 0
(x - 3)(x - -17/4)(x - 14/3) = 0
x - 3 = 0
x - -17/4 = 0
x - 14/3 = 0
x = 3
x = -17/4
x = 14/3


Input: Solve the equation x^2 - 14x + 24 = 0

Output:
x^2 - 14x + 24 = 0
(x - 12)(x - 2) = 0
x - 12 = 0  or  x - 2 = 0
x = 12
x = 2


Input: Find x for x^2 + 121/9x + 52/3 = 0

Output:
x^2 + 121/9x + 52/3 = 0
(x - -13/9)(x - -12) = 0
x - -13/9 = 0  or  x - -12 = 0
x = -13/9
x = -12


Input: Compute the solution of x^3 - 213/8x^2 + 1039/8x + 105/2 = 0

Output:
x^3 - 213/8x^2 + 1039/8x + 105/2 = 0
(x - -3/8)(x - 7)(x - 20) = 0
x - -3/8 = 0
x - 7 = 0
x - 20 = 0
x = -3/8
x = 7
x = 20


Input:
Solve simultaneously:
6x + 4y = -538/9
2x + 7y = -253/9

Output:
6x + 4y = -538/9
2x + 7y = -253/9

Using elimination
2*(6x + 4y = -538/9)
6*(2x + 7y = -253/9)
12x + 8y = -1076/9
12x + 42y = -506/3
Subtract equations
-34y = 442/9
y = 442/9/-34
y = -13/9

Substitute y
6x + 4(-13/9) = -538/9
6x = -54
x = -54/6
x = -9


Input: Find x for x^2 - 2x - 8 = 0

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


Input: Find the solution to 5x + 65/6 = 0

Output:
5x + 65/6 = 0
5x = -65/6
x = -65/6 / 5
x = -13/6


Input: What value of x satisfies x^3 + 12/7x^2 - 655/448x + 57/224 = 0

Output:
x^3 + 12/7x^2 - 655/448x + 57/224 = 0
(x - -19/8)(x - 3/8)(x - 2/7) = 0
x - -19/8 = 0
x - 3/8 = 0
x - 2/7 = 0
x = -19/8
x = 3/8
x = 2/7


Input: Find the solution to 3x + 51/8 = 0

Output:
3x + 51/8 = 0
3x = -51/8
x = -51/8 / 3
x = -17/8


Input:
Solve the system:
6x + 8y = -164/3
4x + 6y = -37

Output:
6x + 8y = -164/3
4x + 6y = -37

Using elimination
4*(6x + 8y = -164/3)
6*(4x + 6y = -37)
24x + 32y = -656/3
24x + 36y = -222
Subtract equations
-4y = 10/3
y = 10/3/-4
y = -5/6

Substitute y
6x + 8(-5/6) = -164/3
6x = -48
x = -48/6
x = -8


Input: Solve quickly: x^2 + 15x - 76 = 0

Output:
x^2 + 15x - 76 = 0
(x - -19)(x - 4) = 0
x - -19 = 0  or  x - 4 = 0
x = -19
x = 4


Input: Find the solution to x^2 + 3x + 20/49 = 0

Output:
x^2 + 3x + 20/49 = 0
(x - -20/7)(x - -1/7) = 0
x - -20/7 = 0  or  x - -1/7 = 0
x = -20/7
x = -1/7


Input: What value of x satisfies 7x - 7/3 = 0

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


Input: Solve 9x + 4 = 0

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


Input: Find x for x^3 - 71/4x^2 + 115/4x - 12 = 0

Output:
x^3 - 71/4x^2 + 115/4x - 12 = 0
(x - 16)(x - 3/4)(x - 1) = 0
x - 16 = 0
x - 3/4 = 0
x - 1 = 0
x = 16
x = 3/4
x = 1


Input: Find x for 8x + 160 = 0

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


Input: Find x in x^2 - 53/35x - 114/35 = 0

Output:
x^2 - 53/35x - 114/35 = 0
(x - 19/7)(x - -6/5) = 0
x - 19/7 = 0  or  x - -6/5 = 0
x = 19/7
x = -6/5


Input: Find x in x^2 - 3x - 10/9 = 0

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


Input: Solve the equation 6x + 10 = 0

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


Input: Solve the equation 4x + 68/7 = 0

Output:
4x + 68/7 = 0
4x = -68/7
x = -68/7 / 4
x = -17/7


Input:
Solve simultaneously:
5x + 6y = -12
2x + 9y = -13/5

Output:
5x + 6y = -12
2x + 9y = -13/5

Using elimination
2*(5x + 6y = -12)
5*(2x + 9y = -13/5)
10x + 12y = -24
10x + 45y = -13
Subtract equations
-33y = -11
y = -11/-33
y = 1/3

Substitute y
5x + 6(1/3) = -12
5x = -14
x = -14/5
x = -14/5


Input:
Solve simultaneously:
1x + 7y = -129/8
6x + 10y = -131/4

Output:
1x + 7y = -129/8
6x + 10y = -131/4

Using elimination
6*(1x + 7y = -129/8)
1*(6x + 10y = -131/4)
6x + 42y = -387/4
6x + 10y = -131/4
Subtract equations
32y = -64
y = -64/32
y = -2

Substitute y
1x + 7(-2) = -129/8
1x = -17/8
x = -17/8/1
x = -17/8


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: What value of x satisfies x^3 + 27/10x^2 + 2x + 3/10 = 0

Output:
x^3 + 27/10x^2 + 2x + 3/10 = 0
(x - -3/2)(x - -1/5)(x - -1) = 0
x - -3/2 = 0
x - -1/5 = 0
x - -1 = 0
x = -3/2
x = -1/5
x = -1


Input:
Solve simultaneously:
3x + 8y = -20/3
3x + 9y = -15/2

Output:
3x + 8y = -20/3
3x + 9y = -15/2

Using elimination
3*(3x + 8y = -20/3)
3*(3x + 9y = -15/2)
9x + 24y = -20
9x + 27y = -45/2
Subtract equations
-3y = 5/2
y = 5/2/-3
y = -5/6

Substitute y
3x + 8(-5/6) = -20/3
3x = 0
x = 0/3
x = 0


Input: Find the solution to x^3 + 36/5x^2 + 37/5x + 6/5 = 0

Output:
x^3 + 36/5x^2 + 37/5x + 6/5 = 0
(x - -6)(x - -1/5)(x - -1) = 0
x - -6 = 0
x - -1/5 = 0
x - -1 = 0
x = -6
x = -1/5
x = -1


Input: Find x for x^2 + 33/2x + 54 = 0

Output:
x^2 + 33/2x + 54 = 0
(x - -9/2)(x - -12) = 0
x - -9/2 = 0  or  x - -12 = 0
x = -9/2
x = -12


Input: Solve the equation x^3 - 39/20x^2 - 173/20x + 9/5 = 0

Output:
x^3 - 39/20x^2 - 173/20x + 9/5 = 0
(x - 4)(x - -9/4)(x - 1/5) = 0
x - 4 = 0
x - -9/4 = 0
x - 1/5 = 0
x = 4
x = -9/4
x = 1/5


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

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


Input: Find x for x^3 - 113/63x^2 - 865/189x + 209/27 = 0

Output:
x^3 - 113/63x^2 - 865/189x + 209/27 = 0
(x - 11/7)(x - 7/3)(x - -19/9) = 0
x - 11/7 = 0
x - 7/3 = 0
x - -19/9 = 0
x = 11/7
x = 7/3
x = -19/9


Input:
Find x and y such that
10x + 2y = 166/3
2x + 8y = -20/3

Output:
10x + 2y = 166/3
2x + 8y = -20/3

Using elimination
2*(10x + 2y = 166/3)
10*(2x + 8y = -20/3)
20x + 4y = 332/3
20x + 80y = -200/3
Subtract equations
-76y = 532/3
y = 532/3/-76
y = -7/3

Substitute y
10x + 2(-7/3) = 166/3
10x = 60
x = 60/10
x = 6


Input: Compute the solution of x^2 - 33/2x - 95/2 = 0

Output:
x^2 - 33/2x - 95/2 = 0
(x - 19)(x - -5/2) = 0
x - 19 = 0  or  x - -5/2 = 0
x = 19
x = -5/2


Input: Solve quickly: 3x + 14/3 = 0

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


Input: Solve 10x - 40/3 = 0

Output:
10x - 40/3 = 0
10x = 40/3
x = 40/3 / 10
x = 4/3


Input: Find the solution to x^2 - 62/3x + 48 = 0

Output:
x^2 - 62/3x + 48 = 0
(x - 18)(x - 8/3) = 0
x - 18 = 0  or  x - 8/3 = 0
x = 18
x = 8/3


Input: Solve the equation 5x + 55 = 0

Output:
5x + 55 = 0
5x = -55
x = -55 / 5
x = -11


Input: Find the solution to x^2 + 7/6x - 13/6 = 0

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


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

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


Input: Find x in x^3 - 49/12x^2 + 5/6x + 25/16 = 0

Output:
x^3 - 49/12x^2 + 5/6x + 25/16 = 0
(x - 15/4)(x - -1/2)(x - 5/6) = 0
x - 15/4 = 0
x - -1/2 = 0
x - 5/6 = 0
x = 15/4
x = -1/2
x = 5/6


Input:
Solve the system:
4x + 6y = 191/15
3x + 5y = 21/2

Output:
4x + 6y = 191/15
3x + 5y = 21/2

Using elimination
3*(4x + 6y = 191/15)
4*(3x + 5y = 21/2)
12x + 18y = 191/5
12x + 20y = 42
Subtract equations
-2y = -19/5
y = -19/5/-2
y = 19/10

Substitute y
4x + 6(19/10) = 191/15
4x = 4/3
x = 4/3/4
x = 1/3


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

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


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

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


Input: What value of x satisfies x^2 + 52/45x - 32/45 = 0

Output:
x^2 + 52/45x - 32/45 = 0
(x - 4/9)(x - -8/5) = 0
x - 4/9 = 0  or  x - -8/5 = 0
x = 4/9
x = -8/5


Input: Solve quickly: x^3 + 1075/56x^2 - 1109/56x - 1045/14 = 0

Output:
x^3 + 1075/56x^2 - 1109/56x - 1045/14 = 0
(x - 19/8)(x - -11/7)(x - -20) = 0
x - 19/8 = 0
x - -11/7 = 0
x - -20 = 0
x = 19/8
x = -11/7
x = -20


Input:
Find x and y such that
6x + 5y = -38/5
5x + 3y = -19/10

Output:
6x + 5y = -38/5
5x + 3y = -19/10

Using elimination
5*(6x + 5y = -38/5)
6*(5x + 3y = -19/10)
30x + 25y = -38
30x + 18y = -57/5
Subtract equations
7y = -133/5
y = -133/5/7
y = -19/5

Substitute y
6x + 5(-19/5) = -38/5
6x = 57/5
x = 57/5/6
x = 19/10


Input:
Find x and y such that
3x + 5y = 253/24
4x + 9y = 1411/72

Output:
3x + 5y = 253/24
4x + 9y = 1411/72

Using elimination
4*(3x + 5y = 253/24)
3*(4x + 9y = 1411/72)
12x + 20y = 253/6
12x + 27y = 1411/24
Subtract equations
-7y = -133/8
y = -133/8/-7
y = 19/8

Substitute y
3x + 5(19/8) = 253/24
3x = -4/3
x = -4/3/3
x = -4/9


Input:
Solve the system:
4x + 4y = 16/15
4x + 7y = 91/15

Output:
4x + 4y = 16/15
4x + 7y = 91/15

Using elimination
4*(4x + 4y = 16/15)
4*(4x + 7y = 91/15)
16x + 16y = 64/15
16x + 28y = 364/15
Subtract equations
-12y = -20
y = -20/-12
y = 5/3

Substitute y
4x + 4(5/3) = 16/15
4x = -28/5
x = -28/5/4
x = -7/5


Input:
Solve the system:
7x + 10y = -1304/45
6x + 1y = -512/45

Output:
7x + 10y = -1304/45
6x + 1y = -512/45

Using elimination
6*(7x + 10y = -1304/45)
7*(6x + 1y = -512/45)
42x + 60y = -2608/15
42x + 7y = -3584/45
Subtract equations
53y = -848/9
y = -848/9/53
y = -16/9

Substitute y
7x + 10(-16/9) = -1304/45
7x = -56/5
x = -56/5/7
x = -8/5


Input: Find the solution to x^3 - 386/63x^2 + 311/63x + 220/63 = 0

Output:
x^3 - 386/63x^2 + 311/63x + 220/63 = 0
(x - 5)(x - 11/7)(x - -4/9) = 0
x - 5 = 0
x - 11/7 = 0
x - -4/9 = 0
x = 5
x = 11/7
x = -4/9


Input: Compute the solution of x^2 + 94/15x - 8/3 = 0

Output:
x^2 + 94/15x - 8/3 = 0
(x - 2/5)(x - -20/3) = 0
x - 2/5 = 0  or  x - -20/3 = 0
x = 2/5
x = -20/3


Input:
Find x and y such that
4x + 6y = -18
5x + 10y = -45/2

Output:
4x + 6y = -18
5x + 10y = -45/2

Using elimination
5*(4x + 6y = -18)
4*(5x + 10y = -45/2)
20x + 30y = -90
20x + 40y = -90
Subtract equations
-10y = 0
y = 0/-10
y = 0

Substitute y
4x + 6(0) = -18
4x = -18
x = -18/4
x = -9/2


Input:
Solve the equations:
1x + 8y = -179/10
9x + 8y = -331/10

Output:
1x + 8y = -179/10
9x + 8y = -331/10

Using elimination
9*(1x + 8y = -179/10)
1*(9x + 8y = -331/10)
9x + 72y = -1611/10
9x + 8y = -331/10
Subtract equations
64y = -128
y = -128/64
y = -2

Substitute y
1x + 8(-2) = -179/10
1x = -19/10
x = -19/10/1
x = -19/10


Input: Determine x in x^3 + 46/5x^2 - 197/25x + 6/5 = 0

Output:
x^3 + 46/5x^2 - 197/25x + 6/5 = 0
(x - 3/5)(x - -10)(x - 1/5) = 0
x - 3/5 = 0
x - -10 = 0
x - 1/5 = 0
x = 3/5
x = -10
x = 1/5


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: Find x in x^3 + 587/105x^2 + 338/35x + 24/5 = 0

Output:
x^3 + 587/105x^2 + 338/35x + 24/5 = 0
(x - -7/3)(x - -6/7)(x - -12/5) = 0
x - -7/3 = 0
x - -6/7 = 0
x - -12/5 = 0
x = -7/3
x = -6/7
x = -12/5


Input: Find x for x^3 - 16/15x^2 - 37/60x - 1/20 = 0

Output:
x^3 - 16/15x^2 - 37/60x - 1/20 = 0
(x - 3/2)(x - -1/3)(x - -1/10) = 0
x - 3/2 = 0
x - -1/3 = 0
x - -1/10 = 0
x = 3/2
x = -1/3
x = -1/10


Input: What value of x satisfies x^3 + 61/18x^2 - 64/9x - 19/2 = 0

Output:
x^3 + 61/18x^2 - 64/9x - 19/2 = 0
(x - -9/2)(x - 19/9)(x - -1) = 0
x - -9/2 = 0
x - 19/9 = 0
x - -1 = 0
x = -9/2
x = 19/9
x = -1


Input: Solve quickly: x^2 - 51/4x + 38 = 0

Output:
x^2 - 51/4x + 38 = 0
(x - 8)(x - 19/4) = 0
x - 8 = 0  or  x - 19/4 = 0
x = 8
x = 19/4


Input:
Solve the equations:
10x + 5y = 37/4
6x + 7y = 291/20

Output:
10x + 5y = 37/4
6x + 7y = 291/20

Using elimination
6*(10x + 5y = 37/4)
10*(6x + 7y = 291/20)
60x + 30y = 111/2
60x + 70y = 291/2
Subtract equations
-40y = -90
y = -90/-40
y = 9/4

Substitute y
10x + 5(9/4) = 37/4
10x = -2
x = -2/10
x = -1/5


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

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


Input:
Solve the system:
3x + 5y = -311/35
10x + 9y = -215/7

Output:
3x + 5y = -311/35
10x + 9y = -215/7

Using elimination
10*(3x + 5y = -311/35)
3*(10x + 9y = -215/7)
30x + 50y = -622/7
30x + 27y = -645/7
Subtract equations
23y = 23/7
y = 23/7/23
y = 1/7

Substitute y
3x + 5(1/7) = -311/35
3x = -48/5
x = -48/5/3
x = -16/5


Input:
Solve simultaneously:
4x + 5y = -101/6
9x + 9y = -42

Output:
4x + 5y = -101/6
9x + 9y = -42

Using elimination
9*(4x + 5y = -101/6)
4*(9x + 9y = -42)
36x + 45y = -303/2
36x + 36y = -168
Subtract equations
9y = 33/2
y = 33/2/9
y = 11/6

Substitute y
4x + 5(11/6) = -101/6
4x = -26
x = -26/4
x = -13/2


Input:
Solve simultaneously:
8x + 9y = -128/3
8x + 1y = -32/3

Output:
8x + 9y = -128/3
8x + 1y = -32/3

Using elimination
8*(8x + 9y = -128/3)
8*(8x + 1y = -32/3)
64x + 72y = -1024/3
64x + 8y = -256/3
Subtract equations
64y = -256
y = -256/64
y = -4

Substitute y
8x + 9(-4) = -128/3
8x = -20/3
x = -20/3/8
x = -5/6


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

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


Input: Determine x in x^3 - 59/4x^2 + 35x + 275/4 = 0

Output:
x^3 - 59/4x^2 + 35x + 275/4 = 0
(x - 11)(x - -5/4)(x - 5) = 0
x - 11 = 0
x - -5/4 = 0
x - 5 = 0
x = 11
x = -5/4
x = 5


Input: What value of x satisfies x^2 + 30/7x + 27/7 = 0

Output:
x^2 + 30/7x + 27/7 = 0
(x - -9/7)(x - -3) = 0
x - -9/7 = 0  or  x - -3 = 0
x = -9/7
x = -3


Input: Compute the solution of 6x - 3/4 = 0

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


Input: Solve quickly: 4x + 28 = 0

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


Input: What value of x satisfies 7x + 28 = 0

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


Input: Determine x in 1x - 19/10 = 0

Output:
1x - 19/10 = 0
1x = 19/10
x = 19/10 / 1
x = 19/10


Input: Compute the solution of x^2 + 19/6x + 5/2 = 0

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


Input:
Solve the equations:
9x + 1y = 181/12
3x + 5y = 23/12

Output:
9x + 1y = 181/12
3x + 5y = 23/12

Using elimination
3*(9x + 1y = 181/12)
9*(3x + 5y = 23/12)
27x + 3y = 181/4
27x + 45y = 69/4
Subtract equations
-42y = 28
y = 28/-42
y = -2/3

Substitute y
9x + 1(-2/3) = 181/12
9x = 63/4
x = 63/4/9
x = 7/4


Input:
Find x and y such that
4x + 2y = 268/9
9x + 7y = 102

Output:
4x + 2y = 268/9
9x + 7y = 102

Using elimination
9*(4x + 2y = 268/9)
4*(9x + 7y = 102)
36x + 18y = 268
36x + 28y = 408
Subtract equations
-10y = -140
y = -140/-10
y = 14

Substitute y
4x + 2(14) = 268/9
4x = 16/9
x = 16/9/4
x = 4/9


Input: What value of x satisfies 8x - 128/3 = 0

Output:
8x - 128/3 = 0
8x = 128/3
x = 128/3 / 8
x = 16/3


Input: Find x for x^3 + 27/5x^2 - 29/5x - 39 = 0

Output:
x^3 + 27/5x^2 - 29/5x - 39 = 0
(x - 13/5)(x - -3)(x - -5) = 0
x - 13/5 = 0
x - -3 = 0
x - -5 = 0
x = 13/5
x = -3
x = -5


Input: Compute the solution of x^2 + 4/5x - 33/100 = 0

Output:
x^2 + 4/5x - 33/100 = 0
(x - 3/10)(x - -11/10) = 0
x - 3/10 = 0  or  x - -11/10 = 0
x = 3/10
x = -11/10


Input: Solve x^2 - 67/8x - 17/16 = 0

Output:
x^2 - 67/8x - 17/16 = 0
(x - -1/8)(x - 17/2) = 0
x - -1/8 = 0  or  x - 17/2 = 0
x = -1/8
x = 17/2


Input: Solve the equation x^2 + 223/63x + 190/63 = 0

Output:
x^2 + 223/63x + 190/63 = 0
(x - -19/9)(x - -10/7) = 0
x - -19/9 = 0  or  x - -10/7 = 0
x = -19/9
x = -10/7


Input:
Solve the system:
1x + 10y = 22/3
3x + 1y = 15/2

Output:
1x + 10y = 22/3
3x + 1y = 15/2

Using elimination
3*(1x + 10y = 22/3)
1*(3x + 1y = 15/2)
3x + 30y = 22
3x + 1y = 15/2
Subtract equations
29y = 29/2
y = 29/2/29
y = 1/2

Substitute y
1x + 10(1/2) = 22/3
1x = 7/3
x = 7/3/1
x = 7/3


Input: Determine x in x^3 - 121/60x^2 - 323/24x + 2023/120 = 0

Output:
x^3 - 121/60x^2 - 323/24x + 2023/120 = 0
(x - 7/6)(x - 17/4)(x - -17/5) = 0
x - 7/6 = 0
x - 17/4 = 0
x - -17/5 = 0
x = 7/6
x = 17/4
x = -17/5


Input: Find x in x^2 + 3/7x - 34/7 = 0

Output:
x^2 + 3/7x - 34/7 = 0
(x - -17/7)(x - 2) = 0
x - -17/7 = 0  or  x - 2 = 0
x = -17/7
x = 2


Input: Find x in 9x  = 0

Output:
9x  = 0
9x = 0
x = 0 / 9
x = 0


Input: Solve quickly: x^3 - 479/120x^2 + 27/10x - 133/480 = 0

Output:
x^3 - 479/120x^2 + 27/10x - 133/480 = 0
(x - 7/10)(x - 1/8)(x - 19/6) = 0
x - 7/10 = 0
x - 1/8 = 0
x - 19/6 = 0
x = 7/10
x = 1/8
x = 19/6


Input: Find x in x^3 + 19/6x^2 + 7/3x  = 0

Output:
x^3 + 19/6x^2 + 7/3x  = 0
(x - -7/6)(x - -2)(x - 0) = 0
x - -7/6 = 0
x - -2 = 0
x - 0 = 0
x = -7/6
x = -2
x = 0


Input:
Solve the equations:
6x + 2y = -267/20
5x + 10y = -7/4

Output:
6x + 2y = -267/20
5x + 10y = -7/4

Using elimination
5*(6x + 2y = -267/20)
6*(5x + 10y = -7/4)
30x + 10y = -267/4
30x + 60y = -21/2
Subtract equations
-50y = -225/4
y = -225/4/-50
y = 9/8

Substitute y
6x + 2(9/8) = -267/20
6x = -78/5
x = -78/5/6
x = -13/5


Input: Find the solution to x^3 - 131/15x^2 - 69/20x + 189/20 = 0

Output:
x^3 - 131/15x^2 - 69/20x + 189/20 = 0
(x - -7/6)(x - 9)(x - 9/10) = 0
x - -7/6 = 0
x - 9 = 0
x - 9/10 = 0
x = -7/6
x = 9
x = 9/10


Input: What value of x satisfies x^2 - 21x + 38 = 0

Output:
x^2 - 21x + 38 = 0
(x - 2)(x - 19) = 0
x - 2 = 0  or  x - 19 = 0
x = 2
x = 19


Input: Find x in x^2 - 41/15x - 114/5 = 0

Output:
x^2 - 41/15x - 114/5 = 0
(x - 19/3)(x - -18/5) = 0
x - 19/3 = 0  or  x - -18/5 = 0
x = 19/3
x = -18/5


Input: Find x in x^3 + 147/8x^2 - 117/8x - 209/4 = 0

Output:
x^3 + 147/8x^2 - 117/8x - 209/4 = 0
(x - 2)(x - -11/8)(x - -19) = 0
x - 2 = 0
x - -11/8 = 0
x - -19 = 0
x = 2
x = -11/8
x = -19


Input: What value of x satisfies x^3 - 1007/315x^2 - 83/35x + 19/63 = 0

Output:
x^3 - 1007/315x^2 - 83/35x + 19/63 = 0
(x - 1/9)(x - -5/7)(x - 19/5) = 0
x - 1/9 = 0
x - -5/7 = 0
x - 19/5 = 0
x = 1/9
x = -5/7
x = 19/5


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

Output:
7x + 7/10 = 0
7x = -7/10
x = -7/10 / 7
x = -1/10


Input: Compute the solution of 6x - 102/5 = 0

Output:
6x - 102/5 = 0
6x = 102/5
x = 102/5 / 6
x = 17/5


Input: Determine x in x^3 + 71/12x^2 + 55/9x - 25/3 = 0

Output:
x^3 + 71/12x^2 + 55/9x - 25/3 = 0
(x - 3/4)(x - -10/3)(x - -10/3) = 0
x - 3/4 = 0
x - -10/3 = 0
x - -10/3 = 0
x = 3/4
x = -10/3
x = -10/3


Input: Find x in 10x - 20/3 = 0

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


Input: Find the solution to x^2 - 14/5x  = 0

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


Input:
Solve the equations:
2x + 1y = 21/5
2x + 4y = 69/5

Output:
2x + 1y = 21/5
2x + 4y = 69/5

Using elimination
2*(2x + 1y = 21/5)
2*(2x + 4y = 69/5)
4x + 2y = 42/5
4x + 8y = 138/5
Subtract equations
-6y = -96/5
y = -96/5/-6
y = 16/5

Substitute y
2x + 1(16/5) = 21/5
2x = 1
x = 1/2
x = 1/2


Input:
Solve the equations:
8x + 6y = -45
5x + 8y = -61/3

Output:
8x + 6y = -45
5x + 8y = -61/3

Using elimination
5*(8x + 6y = -45)
8*(5x + 8y = -61/3)
40x + 30y = -225
40x + 64y = -488/3
Subtract equations
-34y = -187/3
y = -187/3/-34
y = 11/6

Substitute y
8x + 6(11/6) = -45
8x = -56
x = -56/8
x = -7


Input:
Solve the equations:
7x + 9y = 27/4
7x + 5y = 15/4

Output:
7x + 9y = 27/4
7x + 5y = 15/4

Using elimination
7*(7x + 9y = 27/4)
7*(7x + 5y = 15/4)
49x + 63y = 189/4
49x + 35y = 105/4
Subtract equations
28y = 21
y = 21/28
y = 3/4

Substitute y
7x + 9(3/4) = 27/4
7x = 0
x = 0/7
x = 0


Input:
Find x and y such that
3x + 10y = -67/4
5x + 1y = -57/20

Output:
3x + 10y = -67/4
5x + 1y = -57/20

Using elimination
5*(3x + 10y = -67/4)
3*(5x + 1y = -57/20)
15x + 50y = -335/4
15x + 3y = -171/20
Subtract equations
47y = -376/5
y = -376/5/47
y = -8/5

Substitute y
3x + 10(-8/5) = -67/4
3x = -3/4
x = -3/4/3
x = -1/4


Input: Solve quickly: 7x - 112/5 = 0

Output:
7x - 112/5 = 0
7x = 112/5
x = 112/5 / 7
x = 16/5


Input: Solve quickly: x^2 - 3/70x - 247/70 = 0

Output:
x^2 - 3/70x - 247/70 = 0
(x - 19/10)(x - -13/7) = 0
x - 19/10 = 0  or  x - -13/7 = 0
x = 19/10
x = -13/7


Input: Compute the solution of 6x - 102/7 = 0

Output:
6x - 102/7 = 0
6x = 102/7
x = 102/7 / 6
x = 17/7


Input: Find x in x^3 - 11/3x^2 - 28/3x + 32 = 0

Output:
x^3 - 11/3x^2 - 28/3x + 32 = 0
(x - 8/3)(x - 4)(x - -3) = 0
x - 8/3 = 0
x - 4 = 0
x - -3 = 0
x = 8/3
x = 4
x = -3


Input: Solve x^3 - 9/4x^2 - 95/8x  = 0

Output:
x^3 - 9/4x^2 - 95/8x  = 0
(x - 0)(x - 19/4)(x - -5/2) = 0
x - 0 = 0
x - 19/4 = 0
x - -5/2 = 0
x = 0
x = 19/4
x = -5/2


Input: Find the solution to x^2 - 23x + 76 = 0

Output:
x^2 - 23x + 76 = 0
(x - 4)(x - 19) = 0
x - 4 = 0  or  x - 19 = 0
x = 4
x = 19


Input:
Find x and y such that
5x + 4y = 761/56
6x + 2y = 423/28

Output:
5x + 4y = 761/56
6x + 2y = 423/28

Using elimination
6*(5x + 4y = 761/56)
5*(6x + 2y = 423/28)
30x + 24y = 2283/28
30x + 10y = 2115/28
Subtract equations
14y = 6
y = 6/14
y = 3/7

Substitute y
5x + 4(3/7) = 761/56
5x = 95/8
x = 95/8/5
x = 19/8


Input:
Solve the equations:
10x + 5y = -295/9
4x + 4y = -92/9

Output:
10x + 5y = -295/9
4x + 4y = -92/9

Using elimination
4*(10x + 5y = -295/9)
10*(4x + 4y = -92/9)
40x + 20y = -1180/9
40x + 40y = -920/9
Subtract equations
-20y = -260/9
y = -260/9/-20
y = 13/9

Substitute y
10x + 5(13/9) = -295/9
10x = -40
x = -40/10
x = -4


Input: Find x in x^2 + 6x + 5 = 0

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


Input: Compute the solution of x^2 - 37/12x - 12 = 0

Output:
x^2 - 37/12x - 12 = 0
(x - -9/4)(x - 16/3) = 0
x - -9/4 = 0  or  x - 16/3 = 0
x = -9/4
x = 16/3


Input:
Solve the equations:
3x + 5y = -91/5
9x + 1y = -98/5

Output:
3x + 5y = -91/5
9x + 1y = -98/5

Using elimination
9*(3x + 5y = -91/5)
3*(9x + 1y = -98/5)
27x + 45y = -819/5
27x + 3y = -294/5
Subtract equations
42y = -105
y = -105/42
y = -5/2

Substitute y
3x + 5(-5/2) = -91/5
3x = -57/10
x = -57/10/3
x = -19/10


Input:
Find x and y such that
8x + 9y = -723/14
7x + 5y = -53/2

Output:
8x + 9y = -723/14
7x + 5y = -53/2

Using elimination
7*(8x + 9y = -723/14)
8*(7x + 5y = -53/2)
56x + 63y = -723/2
56x + 40y = -212
Subtract equations
23y = -299/2
y = -299/2/23
y = -13/2

Substitute y
8x + 9(-13/2) = -723/14
8x = 48/7
x = 48/7/8
x = 6/7


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

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


Input:
Solve the system:
3x + 2y = -41/6
3x + 7y = -247/12

Output:
3x + 2y = -41/6
3x + 7y = -247/12

Using elimination
3*(3x + 2y = -41/6)
3*(3x + 7y = -247/12)
9x + 6y = -41/2
9x + 21y = -247/4
Subtract equations
-15y = 165/4
y = 165/4/-15
y = -11/4

Substitute y
3x + 2(-11/4) = -41/6
3x = -4/3
x = -4/3/3
x = -4/9


Input: Solve x^3 - 2/9x^2 - 565/27x - 304/9 = 0

Output:
x^3 - 2/9x^2 - 565/27x - 304/9 = 0
(x - -3)(x - 16/3)(x - -19/9) = 0
x - -3 = 0
x - 16/3 = 0
x - -19/9 = 0
x = -3
x = 16/3
x = -19/9


Input: Solve quickly: x^2 - 2/15x - 187/60 = 0

Output:
x^2 - 2/15x - 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: Find x in 4x + 28 = 0

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


Input: Determine x in x^2 + 54/5x - 72/5 = 0

Output:
x^2 + 54/5x - 72/5 = 0
(x - 6/5)(x - -12) = 0
x - 6/5 = 0  or  x - -12 = 0
x = 6/5
x = -12


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

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


Input: What value of x satisfies x^3 - 103/18x^2 + 694/81x - 224/81 = 0

Output:
x^3 - 103/18x^2 + 694/81x - 224/81 = 0
(x - 7/2)(x - 16/9)(x - 4/9) = 0
x - 7/2 = 0
x - 16/9 = 0
x - 4/9 = 0
x = 7/2
x = 16/9
x = 4/9


Input: Find x in 7x - 63/10 = 0

Output:
7x - 63/10 = 0
7x = 63/10
x = 63/10 / 7
x = 9/10


Input: What value of x satisfies x^2 - 13/8x + 11/32 = 0

Output:
x^2 - 13/8x + 11/32 = 0
(x - 11/8)(x - 1/4) = 0
x - 11/8 = 0  or  x - 1/4 = 0
x = 11/8
x = 1/4


Input: Solve the equation x^3 - 41/5x^2 + 22x - 96/5 = 0

Output:
x^3 - 41/5x^2 + 22x - 96/5 = 0
(x - 2)(x - 3)(x - 16/5) = 0
x - 2 = 0
x - 3 = 0
x - 16/5 = 0
x = 2
x = 3
x = 16/5


Input: Solve the equation x^3 - 54/5x^2 + 67/5x + 462/5 = 0

Output:
x^3 - 54/5x^2 + 67/5x + 462/5 = 0
(x - 6)(x - 7)(x - -11/5) = 0
x - 6 = 0
x - 7 = 0
x - -11/5 = 0
x = 6
x = 7
x = -11/5


Input: Find x for x^3 - 152/21x^2 + 47/3x - 66/7 = 0

Output:
x^3 - 152/21x^2 + 47/3x - 66/7 = 0
(x - 1)(x - 18/7)(x - 11/3) = 0
x - 1 = 0
x - 18/7 = 0
x - 11/3 = 0
x = 1
x = 18/7
x = 11/3


Input: Find x in 7x - 112 = 0

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


Input:
Find x and y such that
8x + 10y = -11
9x + 10y = -31/2

Output:
8x + 10y = -11
9x + 10y = -31/2

Using elimination
9*(8x + 10y = -11)
8*(9x + 10y = -31/2)
72x + 90y = -99
72x + 80y = -124
Subtract equations
10y = 25
y = 25/10
y = 5/2

Substitute y
8x + 10(5/2) = -11
8x = -36
x = -36/8
x = -9/2


Input:
Solve simultaneously:
2x + 5y = 82/9
7x + 2y = 256/9

Output:
2x + 5y = 82/9
7x + 2y = 256/9

Using elimination
7*(2x + 5y = 82/9)
2*(7x + 2y = 256/9)
14x + 35y = 574/9
14x + 4y = 512/9
Subtract equations
31y = 62/9
y = 62/9/31
y = 2/9

Substitute y
2x + 5(2/9) = 82/9
2x = 8
x = 8/2
x = 4


Input: Compute the solution of x^2 - 17/10x + 7/10 = 0

Output:
x^2 - 17/10x + 7/10 = 0
(x - 1)(x - 7/10) = 0
x - 1 = 0  or  x - 7/10 = 0
x = 1
x = 7/10


Input:
Solve simultaneously:
7x + 7y = 301/2
10x + 1y = 385/2

Output:
7x + 7y = 301/2
10x + 1y = 385/2

Using elimination
10*(7x + 7y = 301/2)
7*(10x + 1y = 385/2)
70x + 70y = 1505
70x + 7y = 2695/2
Subtract equations
63y = 315/2
y = 315/2/63
y = 5/2

Substitute y
7x + 7(5/2) = 301/2
7x = 133
x = 133/7
x = 19


Input: Solve the equation x^2 + 29/2x + 39/2 = 0

Output:
x^2 + 29/2x + 39/2 = 0
(x - -3/2)(x - -13) = 0
x - -3/2 = 0  or  x - -13 = 0
x = -3/2
x = -13


Input: Find x for 6x + 8 = 0

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


Input: Solve 7x + 70/3 = 0

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


Input:
Find x and y such that
8x + 10y = -29
5x + 1y = -31/2

Output:
8x + 10y = -29
5x + 1y = -31/2

Using elimination
5*(8x + 10y = -29)
8*(5x + 1y = -31/2)
40x + 50y = -145
40x + 8y = -124
Subtract equations
42y = -21
y = -21/42
y = -1/2

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


Input: What value of x satisfies x^3 - 97/6x^2 - 55/3x + 425/6 = 0

Output:
x^3 - 97/6x^2 - 55/3x + 425/6 = 0
(x - 17)(x - 5/3)(x - -5/2) = 0
x - 17 = 0
x - 5/3 = 0
x - -5/2 = 0
x = 17
x = 5/3
x = -5/2


Input:
Find x and y such that
9x + 8y = -20
9x + 3y = -115/8

Output:
9x + 8y = -20
9x + 3y = -115/8

Using elimination
9*(9x + 8y = -20)
9*(9x + 3y = -115/8)
81x + 72y = -180
81x + 27y = -1035/8
Subtract equations
45y = -405/8
y = -405/8/45
y = -9/8

Substitute y
9x + 8(-9/8) = -20
9x = -11
x = -11/9
x = -11/9


Input:
Solve the equations:
7x + 8y = 1699/56
5x + 4y = 1049/56

Output:
7x + 8y = 1699/56
5x + 4y = 1049/56

Using elimination
5*(7x + 8y = 1699/56)
7*(5x + 4y = 1049/56)
35x + 40y = 8495/56
35x + 28y = 1049/8
Subtract equations
12y = 144/7
y = 144/7/12
y = 12/7

Substitute y
7x + 8(12/7) = 1699/56
7x = 133/8
x = 133/8/7
x = 19/8


Input:
Solve the system:
4x + 2y = 0
1x + 1y = 3/8

Output:
4x + 2y = 0
1x + 1y = 3/8

Using elimination
1*(4x + 2y = 0)
4*(1x + 1y = 3/8)
4x + 2y = 0
4x + 4y = 3/2
Subtract equations
-2y = -3/2
y = -3/2/-2
y = 3/4

Substitute y
4x + 2(3/4) = 0
4x = -3/2
x = -3/2/4
x = -3/8


Input: Find the solution to 5x + 50 = 0

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


Input:
Solve simultaneously:
10x + 9y = -105/2
3x + 5y = -43/2

Output:
10x + 9y = -105/2
3x + 5y = -43/2

Using elimination
3*(10x + 9y = -105/2)
10*(3x + 5y = -43/2)
30x + 27y = -315/2
30x + 50y = -215
Subtract equations
-23y = 115/2
y = 115/2/-23
y = -5/2

Substitute y
10x + 9(-5/2) = -105/2
10x = -30
x = -30/10
x = -3


Input: What value of x satisfies x^3 - 22/3x^2 - 47/3x + 6 = 0

Output:
x^3 - 22/3x^2 - 47/3x + 6 = 0
(x - -2)(x - 1/3)(x - 9) = 0
x - -2 = 0
x - 1/3 = 0
x - 9 = 0
x = -2
x = 1/3
x = 9


Input: Find the solution to x^3 - 83/14x^2 + 69/7x - 45/14 = 0

Output:
x^3 - 83/14x^2 + 69/7x - 45/14 = 0
(x - 3/7)(x - 5/2)(x - 3) = 0
x - 3/7 = 0
x - 5/2 = 0
x - 3 = 0
x = 3/7
x = 5/2
x = 3


Input:
Find x and y such that
9x + 1y = 1287/70
5x + 4y = 205/14

Output:
9x + 1y = 1287/70
5x + 4y = 205/14

Using elimination
5*(9x + 1y = 1287/70)
9*(5x + 4y = 205/14)
45x + 5y = 1287/14
45x + 36y = 1845/14
Subtract equations
-31y = -279/7
y = -279/7/-31
y = 9/7

Substitute y
9x + 1(9/7) = 1287/70
9x = 171/10
x = 171/10/9
x = 19/10


Input: Find x in x^3 - 17/30x^2 - 1/10x + 1/15 = 0

Output:
x^3 - 17/30x^2 - 1/10x + 1/15 = 0
(x - 2/5)(x - -1/3)(x - 1/2) = 0
x - 2/5 = 0
x - -1/3 = 0
x - 1/2 = 0
x = 2/5
x = -1/3
x = 1/2


Input: Solve the equation x^3 + 25/6x^2 - 1/6x - 10/3 = 0

Output:
x^3 + 25/6x^2 - 1/6x - 10/3 = 0
(x - 5/6)(x - -1)(x - -4) = 0
x - 5/6 = 0
x - -1 = 0
x - -4 = 0
x = 5/6
x = -1
x = -4


Input:
Solve the equations:
5x + 7y = 761/20
7x + 2y = 691/20

Output:
5x + 7y = 761/20
7x + 2y = 691/20

Using elimination
7*(5x + 7y = 761/20)
5*(7x + 2y = 691/20)
35x + 49y = 5327/20
35x + 10y = 691/4
Subtract equations
39y = 468/5
y = 468/5/39
y = 12/5

Substitute y
5x + 7(12/5) = 761/20
5x = 85/4
x = 85/4/5
x = 17/4


Input:
Solve the system:
6x + 9y = 129/5
1x + 3y = -7/5

Output:
6x + 9y = 129/5
1x + 3y = -7/5

Using elimination
1*(6x + 9y = 129/5)
6*(1x + 3y = -7/5)
6x + 9y = 129/5
6x + 18y = -42/5
Subtract equations
-9y = 171/5
y = 171/5/-9
y = -19/5

Substitute y
6x + 9(-19/5) = 129/5
6x = 60
x = 60/6
x = 10


Input: Find x in x^2 + 16x - 57 = 0

Output:
x^2 + 16x - 57 = 0
(x - 3)(x - -19) = 0
x - 3 = 0  or  x - -19 = 0
x = 3
x = -19


Input: Compute the solution of x^2 + 17/18x - 13/18 = 0

Output:
x^2 + 17/18x - 13/18 = 0
(x - 1/2)(x - -13/9) = 0
x - 1/2 = 0  or  x - -13/9 = 0
x = 1/2
x = -13/9


Input: Solve quickly: 7x - 91/8 = 0

Output:
7x - 91/8 = 0
7x = 91/8
x = 91/8 / 7
x = 13/8


Input: Solve the equation x^3 - 23/9x^2 + 100/81x + 100/243 = 0

Output:
x^3 - 23/9x^2 + 100/81x + 100/243 = 0
(x - -2/9)(x - 10/9)(x - 5/3) = 0
x - -2/9 = 0
x - 10/9 = 0
x - 5/3 = 0
x = -2/9
x = 10/9
x = 5/3


Input: Find x in x^3 + 122/45x^2 + 79/60x + 19/180 = 0

Output:
x^3 + 122/45x^2 + 79/60x + 19/180 = 0
(x - -1/2)(x - -19/9)(x - -1/10) = 0
x - -1/2 = 0
x - -19/9 = 0
x - -1/10 = 0
x = -1/2
x = -19/9
x = -1/10


Input:
Solve the equations:
7x + 9y = -531/10
8x + 3y = -687/10

Output:
7x + 9y = -531/10
8x + 3y = -687/10

Using elimination
8*(7x + 9y = -531/10)
7*(8x + 3y = -687/10)
56x + 72y = -2124/5
56x + 21y = -4809/10
Subtract equations
51y = 561/10
y = 561/10/51
y = 11/10

Substitute y
7x + 9(11/10) = -531/10
7x = -63
x = -63/7
x = -9


Input: Compute the solution of x^2 + 15x + 50 = 0

Output:
x^2 + 15x + 50 = 0
(x - -10)(x - -5) = 0
x - -10 = 0  or  x - -5 = 0
x = -10
x = -5


Input: Solve x^3 + 283/60x^2 + 31/5x + 117/80 = 0

Output:
x^3 + 283/60x^2 + 31/5x + 117/80 = 0
(x - -9/4)(x - -13/6)(x - -3/10) = 0
x - -9/4 = 0
x - -13/6 = 0
x - -3/10 = 0
x = -9/4
x = -13/6
x = -3/10


Input: Solve quickly: x^2 + 73/42x + 2/3 = 0

Output:
x^2 + 73/42x + 2/3 = 0
(x - -7/6)(x - -4/7) = 0
x - -7/6 = 0  or  x - -4/7 = 0
x = -7/6
x = -4/7


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

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


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

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


Input: Find x in 6x - 32 = 0

Output:
6x - 32 = 0
6x = 32
x = 32 / 6
x = 16/3


Input: Find x for x^3 + 8/5x^2 - 143/20x + 2299/500 = 0

Output:
x^3 + 8/5x^2 - 143/20x + 2299/500 = 0
(x - -19/5)(x - 11/10)(x - 11/10) = 0
x - -19/5 = 0
x - 11/10 = 0
x - 11/10 = 0
x = -19/5
x = 11/10
x = 11/10


Input: Compute the solution of x^3 + 176/9x^2 + 257/9x + 10 = 0

Output:
x^3 + 176/9x^2 + 257/9x + 10 = 0
(x - -1)(x - -5/9)(x - -18) = 0
x - -1 = 0
x - -5/9 = 0
x - -18 = 0
x = -1
x = -5/9
x = -18


Input:
Solve the equations:
4x + 2y = -4/9
5x + 8y = 193/9

Output:
4x + 2y = -4/9
5x + 8y = 193/9

Using elimination
5*(4x + 2y = -4/9)
4*(5x + 8y = 193/9)
20x + 10y = -20/9
20x + 32y = 772/9
Subtract equations
-22y = -88
y = -88/-22
y = 4

Substitute y
4x + 2(4) = -4/9
4x = -76/9
x = -76/9/4
x = -19/9


Input: Determine x in x^3 - 19/20x^2 - 43/2x + 165/4 = 0

Output:
x^3 - 19/20x^2 - 43/2x + 165/4 = 0
(x - 11/5)(x - 15/4)(x - -5) = 0
x - 11/5 = 0
x - 15/4 = 0
x - -5 = 0
x = 11/5
x = 15/4
x = -5


Input: Find x in 1x - 10 = 0

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


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

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


Input: Find the solution to x^3 - 57/28x^2 - 5/56x + 75/56 = 0

Output:
x^3 - 57/28x^2 - 5/56x + 75/56 = 0
(x - 5/4)(x - 3/2)(x - -5/7) = 0
x - 5/4 = 0
x - 3/2 = 0
x - -5/7 = 0
x = 5/4
x = 3/2
x = -5/7


Input: Determine x in x^3 - 3/4x^2 - 31/4x + 21/2 = 0

Output:
x^3 - 3/4x^2 - 31/4x + 21/2 = 0
(x - 2)(x - 7/4)(x - -3) = 0
x - 2 = 0
x - 7/4 = 0
x - -3 = 0
x = 2
x = 7/4
x = -3


Input: Find x in 4x + 40/3 = 0

Output:
4x + 40/3 = 0
4x = -40/3
x = -40/3 / 4
x = -10/3


Input: Find the solution to x^3 + 25/18x^2 - 181/18x - 28/3 = 0

Output:
x^3 + 25/18x^2 - 181/18x - 28/3 = 0
(x - -8/9)(x - -7/2)(x - 3) = 0
x - -8/9 = 0
x - -7/2 = 0
x - 3 = 0
x = -8/9
x = -7/2
x = 3


Input: Solve the equation x^2 + 187/10x - 26 = 0

Output:
x^2 + 187/10x - 26 = 0
(x - 13/10)(x - -20) = 0
x - 13/10 = 0  or  x - -20 = 0
x = 13/10
x = -20


Input: Find the solution to x^2 - 11/3x - 14 = 0

Output:
x^2 - 11/3x - 14 = 0
(x - -7/3)(x - 6) = 0
x - -7/3 = 0  or  x - 6 = 0
x = -7/3
x = 6


Input: Compute the solution of 8x + 104 = 0

Output:
8x + 104 = 0
8x = -104
x = -104 / 8
x = -13


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

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


Input: Determine x in x^3 + 77/20x^2 + 57/25x - 297/100 = 0

Output:
x^3 + 77/20x^2 + 57/25x - 297/100 = 0
(x - -11/5)(x - -9/4)(x - 3/5) = 0
x - -11/5 = 0
x - -9/4 = 0
x - 3/5 = 0
x = -11/5
x = -9/4
x = 3/5


Input: Find x in x^2 - 10/3x + 221/81 = 0

Output:
x^2 - 10/3x + 221/81 = 0
(x - 17/9)(x - 13/9) = 0
x - 17/9 = 0  or  x - 13/9 = 0
x = 17/9
x = 13/9


Input: Solve the equation x^3 + 49/20x^2 - 3/100x - 27/25 = 0

Output:
x^3 + 49/20x^2 - 3/100x - 27/25 = 0
(x - -9/4)(x - 3/5)(x - -4/5) = 0
x - -9/4 = 0
x - 3/5 = 0
x - -4/5 = 0
x = -9/4
x = 3/5
x = -4/5