input stringlengths 13 66 | output stringlengths 30 276 |
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Find x for x^3 - 233/20x^2 - 2163/40x + 459/8 = 0 | x^3 - 233/20x^2 - 2163/40x + 459/8 = 0
(x - 15)(x - 9/10)(x - -17/4) = 0
x - 15 = 0
x - 9/10 = 0
x - -17/4 = 0
x = 15
x = 9/10
x = -17/4 |
Compute the solution of 8x + 19 = 0 | 8x + 19 = 0
8x = -19
x = -19 / 8
x = -19/8 |
Find the solution to x^3 - 37/14x^2 - 27/7x + 117/14 = 0 | x^3 - 37/14x^2 - 27/7x + 117/14 = 0
(x - 3/2)(x - 3)(x - -13/7) = 0
x - 3/2 = 0
x - 3 = 0
x - -13/7 = 0
x = 3/2
x = 3
x = -13/7 |
Solve the equation 8x - 112/3 = 0 | 8x - 112/3 = 0
8x = 112/3
x = 112/3 / 8
x = 14/3 |
Solve the system:
6x + 10y = -19/4
1x + 5y = -3/8 | 6x + 10y = -19/4
1x + 5y = -3/8
Using elimination
1*(6x + 10y = -19/4)
6*(1x + 5y = -3/8)
6x + 10y = -19/4
6x + 30y = -9/4
Subtract equations
-20y = -5/2
y = -5/2/-20
y = 1/8
Substitute y
6x + 10(1/8) = -19/4
6x = -6
x = -6/6
x = -1 |
Find x in x^3 + 10/9x^2 - 101/27x + 88/81 = 0 | x^3 + 10/9x^2 - 101/27x + 88/81 = 0
(x - 1/3)(x - -8/3)(x - 11/9) = 0
x - 1/3 = 0
x - -8/3 = 0
x - 11/9 = 0
x = 1/3
x = -8/3
x = 11/9 |
Solve x^2 - 98/9x + 80/9 = 0 | x^2 - 98/9x + 80/9 = 0
(x - 10)(x - 8/9) = 0
x - 10 = 0 or x - 8/9 = 0
x = 10
x = 8/9 |
Solve simultaneously:
6x + 2y = 97
9x + 4y = 149 | 6x + 2y = 97
9x + 4y = 149
Using elimination
9*(6x + 2y = 97)
6*(9x + 4y = 149)
54x + 18y = 873
54x + 24y = 894
Subtract equations
-6y = -21
y = -21/-6
y = 7/2
Substitute y
6x + 2(7/2) = 97
6x = 90
x = 90/6
x = 15 |
Compute the solution of x^2 - 104/5x + 252/5 = 0 | x^2 - 104/5x + 252/5 = 0
(x - 14/5)(x - 18) = 0
x - 14/5 = 0 or x - 18 = 0
x = 14/5
x = 18 |
Find the solution to x^2 + 45/14x - 81/14 = 0 | x^2 + 45/14x - 81/14 = 0
(x - 9/7)(x - -9/2) = 0
x - 9/7 = 0 or x - -9/2 = 0
x = 9/7
x = -9/2 |
Find x for 4x - 32 = 0 | 4x - 32 = 0
4x = 32
x = 32 / 4
x = 8 |
Solve x^2 - 63/40x - 11/8 = 0 | x^2 - 63/40x - 11/8 = 0
(x - 11/5)(x - -5/8) = 0
x - 11/5 = 0 or x - -5/8 = 0
x = 11/5
x = -5/8 |
What value of x satisfies 5x - 35/9 = 0 | 5x - 35/9 = 0
5x = 35/9
x = 35/9 / 5
x = 7/9 |
Find x and y such that
6x + 3y = -69/2
9x + 1y = -51/2 | 6x + 3y = -69/2
9x + 1y = -51/2
Using elimination
9*(6x + 3y = -69/2)
6*(9x + 1y = -51/2)
54x + 27y = -621/2
54x + 6y = -153
Subtract equations
21y = -315/2
y = -315/2/21
y = -15/2
Substitute y
6x + 3(-15/2) = -69/2
6x = -12
x = -12/6
x = -2 |
Find the solution to x^3 - 143/24x^2 + 31/3x - 35/8 = 0 | x^3 - 143/24x^2 + 31/3x - 35/8 = 0
(x - 7/3)(x - 3)(x - 5/8) = 0
x - 7/3 = 0
x - 3 = 0
x - 5/8 = 0
x = 7/3
x = 3
x = 5/8 |
What value of x satisfies 6x + 32/3 = 0 | 6x + 32/3 = 0
6x = -32/3
x = -32/3 / 6
x = -16/9 |
Solve the equations:
7x + 4y = -101/10
7x + 8y = -237/10 | 7x + 4y = -101/10
7x + 8y = -237/10
Using elimination
7*(7x + 4y = -101/10)
7*(7x + 8y = -237/10)
49x + 28y = -707/10
49x + 56y = -1659/10
Subtract equations
-28y = 476/5
y = 476/5/-28
y = -17/5
Substitute y
7x + 4(-17/5) = -101/10
7x = 7/2
x = 7/2/7
x = 1/2 |
Find x in x^3 - 13/15x^2 - 674/15x - 1456/15 = 0 | x^3 - 13/15x^2 - 674/15x - 1456/15 = 0
(x - 8)(x - -14/5)(x - -13/3) = 0
x - 8 = 0
x - -14/5 = 0
x - -13/3 = 0
x = 8
x = -14/5
x = -13/3 |
Solve simultaneously:
1x + 6y = 187/15
1x + 10y = 71/3 | 1x + 6y = 187/15
1x + 10y = 71/3
Using elimination
1*(1x + 6y = 187/15)
1*(1x + 10y = 71/3)
1x + 6y = 187/15
1x + 10y = 71/3
Subtract equations
-4y = -56/5
y = -56/5/-4
y = 14/5
Substitute y
1x + 6(14/5) = 187/15
1x = -13/3
x = -13/3/1
x = -13/3 |
Find the solution to x^2 + 18/7x - 85/7 = 0 | x^2 + 18/7x - 85/7 = 0
(x - -5)(x - 17/7) = 0
x - -5 = 0 or x - 17/7 = 0
x = -5
x = 17/7 |
Find x for 5x + 55/2 = 0 | 5x + 55/2 = 0
5x = -55/2
x = -55/2 / 5
x = -11/2 |
Solve the equation 5x + 80/3 = 0 | 5x + 80/3 = 0
5x = -80/3
x = -80/3 / 5
x = -16/3 |
Determine x in x^3 + 669/40x^2 + 2489/40x + 663/10 = 0 | x^3 + 669/40x^2 + 2489/40x + 663/10 = 0
(x - -17/8)(x - -13/5)(x - -12) = 0
x - -17/8 = 0
x - -13/5 = 0
x - -12 = 0
x = -17/8
x = -13/5
x = -12 |
Solve 6x - 114/7 = 0 | 6x - 114/7 = 0
6x = 114/7
x = 114/7 / 6
x = 19/7 |
Solve the equations:
9x + 7y = 58/5
3x + 8y = 127/5 | 9x + 7y = 58/5
3x + 8y = 127/5
Using elimination
3*(9x + 7y = 58/5)
9*(3x + 8y = 127/5)
27x + 21y = 174/5
27x + 72y = 1143/5
Subtract equations
-51y = -969/5
y = -969/5/-51
y = 19/5
Substitute y
9x + 7(19/5) = 58/5
9x = -15
x = -15/9
x = -5/3 |
Compute the solution of x^2 - 19/5x - 4/5 = 0 | x^2 - 19/5x - 4/5 = 0
(x - -1/5)(x - 4) = 0
x - -1/5 = 0 or x - 4 = 0
x = -1/5
x = 4 |
What value of x satisfies x^2 + 3/2x - 10 = 0 | x^2 + 3/2x - 10 = 0
(x - 5/2)(x - -4) = 0
x - 5/2 = 0 or x - -4 = 0
x = 5/2
x = -4 |
Solve x^3 + 116/15x^2 + 239/15x + 26/5 = 0 | x^3 + 116/15x^2 + 239/15x + 26/5 = 0
(x - -13/3)(x - -2/5)(x - -3) = 0
x - -13/3 = 0
x - -2/5 = 0
x - -3 = 0
x = -13/3
x = -2/5
x = -3 |
Solve quickly: x^2 - 12/5x - 9/5 = 0 | x^2 - 12/5x - 9/5 = 0
(x - 3)(x - -3/5) = 0
x - 3 = 0 or x - -3/5 = 0
x = 3
x = -3/5 |
Find x for x^3 - 101/6x^2 + 43x + 760/3 = 0 | x^3 - 101/6x^2 + 43x + 760/3 = 0
(x - 19/2)(x - -8/3)(x - 10) = 0
x - 19/2 = 0
x - -8/3 = 0
x - 10 = 0
x = 19/2
x = -8/3
x = 10 |
Solve quickly: x^3 + 5/3x^2 - 17x - 39 = 0 | x^3 + 5/3x^2 - 17x - 39 = 0
(x - -3)(x - -3)(x - 13/3) = 0
x - -3 = 0
x - -3 = 0
x - 13/3 = 0
x = -3
x = -3
x = 13/3 |
Compute the solution of 5x + 75/7 = 0 | 5x + 75/7 = 0
5x = -75/7
x = -75/7 / 5
x = -15/7 |
Solve the system:
6x + 1y = -20
5x + 4y = -23 | 6x + 1y = -20
5x + 4y = -23
Using elimination
5*(6x + 1y = -20)
6*(5x + 4y = -23)
30x + 5y = -100
30x + 24y = -138
Subtract equations
-19y = 38
y = 38/-19
y = -2
Substitute y
6x + 1(-2) = -20
6x = -18
x = -18/6
x = -3 |
Solve the system:
8x + 5y = 200/3
8x + 3y = 64 | 8x + 5y = 200/3
8x + 3y = 64
Using elimination
8*(8x + 5y = 200/3)
8*(8x + 3y = 64)
64x + 40y = 1600/3
64x + 24y = 512
Subtract equations
16y = 64/3
y = 64/3/16
y = 4/3
Substitute y
8x + 5(4/3) = 200/3
8x = 60
x = 60/8
x = 15/2 |
Find x for x^3 - 143/70x^2 - 491/50x + 418/35 = 0 | x^3 - 143/70x^2 - 491/50x + 418/35 = 0
(x - -20/7)(x - 19/5)(x - 11/10) = 0
x - -20/7 = 0
x - 19/5 = 0
x - 11/10 = 0
x = -20/7
x = 19/5
x = 11/10 |
Find x in x^3 - 14/3x^2 - 139/4x - 153/4 = 0 | x^3 - 14/3x^2 - 139/4x - 153/4 = 0
(x - 9)(x - -17/6)(x - -3/2) = 0
x - 9 = 0
x - -17/6 = 0
x - -3/2 = 0
x = 9
x = -17/6
x = -3/2 |
Determine x in 5x - 65/3 = 0 | 5x - 65/3 = 0
5x = 65/3
x = 65/3 / 5
x = 13/3 |
Solve simultaneously:
1x + 7y = -122/35
6x + 7y = 3/35 | 1x + 7y = -122/35
6x + 7y = 3/35
Using elimination
6*(1x + 7y = -122/35)
1*(6x + 7y = 3/35)
6x + 42y = -732/35
6x + 7y = 3/35
Subtract equations
35y = -21
y = -21/35
y = -3/5
Substitute y
1x + 7(-3/5) = -122/35
1x = 5/7
x = 5/7/1
x = 5/7 |
Find x in 10x + 10/3 = 0 | 10x + 10/3 = 0
10x = -10/3
x = -10/3 / 10
x = -1/3 |
Find x and y such that
4x + 9y = -33/10
1x + 6y = 81/20 | 4x + 9y = -33/10
1x + 6y = 81/20
Using elimination
1*(4x + 9y = -33/10)
4*(1x + 6y = 81/20)
4x + 9y = -33/10
4x + 24y = 81/5
Subtract equations
-15y = -39/2
y = -39/2/-15
y = 13/10
Substitute y
4x + 9(13/10) = -33/10
4x = -15
x = -15/4
x = -15/4 |
Compute the solution of x^2 + 131/56x + 15/14 = 0 | x^2 + 131/56x + 15/14 = 0
(x - -12/7)(x - -5/8) = 0
x - -12/7 = 0 or x - -5/8 = 0
x = -12/7
x = -5/8 |
Solve the equations:
10x + 8y = -208/35
8x + 3y = -71/70 | 10x + 8y = -208/35
8x + 3y = -71/70
Using elimination
8*(10x + 8y = -208/35)
10*(8x + 3y = -71/70)
80x + 64y = -1664/35
80x + 30y = -71/7
Subtract equations
34y = -187/5
y = -187/5/34
y = -11/10
Substitute y
10x + 8(-11/10) = -208/35
10x = 20/7
x = 20/7/10
x = 2/7 |
Solve the equations:
9x + 8y = 37
6x + 9y = 21 | 9x + 8y = 37
6x + 9y = 21
Using elimination
6*(9x + 8y = 37)
9*(6x + 9y = 21)
54x + 48y = 222
54x + 81y = 189
Subtract equations
-33y = 33
y = 33/-33
y = -1
Substitute y
9x + 8(-1) = 37
9x = 45
x = 45/9
x = 5 |
Find x and y such that
1x + 10y = -289/7
4x + 6y = -204/7 | 1x + 10y = -289/7
4x + 6y = -204/7
Using elimination
4*(1x + 10y = -289/7)
1*(4x + 6y = -204/7)
4x + 40y = -1156/7
4x + 6y = -204/7
Subtract equations
34y = -136
y = -136/34
y = -4
Substitute y
1x + 10(-4) = -289/7
1x = -9/7
x = -9/7/1
x = -9/7 |
Solve the system:
2x + 5y = -20/9
2x + 10y = -20/9 | 2x + 5y = -20/9
2x + 10y = -20/9
Using elimination
2*(2x + 5y = -20/9)
2*(2x + 10y = -20/9)
4x + 10y = -40/9
4x + 20y = -40/9
Subtract equations
-10y = 0
y = 0/-10
y = 0
Substitute y
2x + 5(0) = -20/9
2x = -20/9
x = -20/9/2
x = -10/9 |
What value of x satisfies 5x - 5/6 = 0 | 5x - 5/6 = 0
5x = 5/6
x = 5/6 / 5
x = 1/6 |
Solve the equations:
8x + 4y = 176/45
8x + 10y = -154/45 | 8x + 4y = 176/45
8x + 10y = -154/45
Using elimination
8*(8x + 4y = 176/45)
8*(8x + 10y = -154/45)
64x + 32y = 1408/45
64x + 80y = -1232/45
Subtract equations
-48y = 176/3
y = 176/3/-48
y = -11/9
Substitute y
8x + 4(-11/9) = 176/45
8x = 44/5
x = 44/5/8
x = 11/10 |
Find x for 10x - 20/9 = 0 | 10x - 20/9 = 0
10x = 20/9
x = 20/9 / 10
x = 2/9 |
Solve the equation x^3 - 46/3x^2 + 17x + 520/3 = 0 | x^3 - 46/3x^2 + 17x + 520/3 = 0
(x - -8/3)(x - 13)(x - 5) = 0
x - -8/3 = 0
x - 13 = 0
x - 5 = 0
x = -8/3
x = 13
x = 5 |
Solve the equation x^3 + 297/20x^2 - 51/20x - 2023/10 = 0 | x^3 + 297/20x^2 - 51/20x - 2023/10 = 0
(x - 17/5)(x - -14)(x - -17/4) = 0
x - 17/5 = 0
x - -14 = 0
x - -17/4 = 0
x = 17/5
x = -14
x = -17/4 |
What value of x satisfies x^3 - 814/45x^2 + 17x + 1156/45 = 0 | x^3 - 814/45x^2 + 17x + 1156/45 = 0
(x - 17/9)(x - -4/5)(x - 17) = 0
x - 17/9 = 0
x - -4/5 = 0
x - 17 = 0
x = 17/9
x = -4/5
x = 17 |
Solve quickly: x^2 + 57/14x + 55/14 = 0 | x^2 + 57/14x + 55/14 = 0
(x - -11/7)(x - -5/2) = 0
x - -11/7 = 0 or x - -5/2 = 0
x = -11/7
x = -5/2 |
Solve simultaneously:
6x + 5y = 74/3
10x + 8y = 122/3 | 6x + 5y = 74/3
10x + 8y = 122/3
Using elimination
10*(6x + 5y = 74/3)
6*(10x + 8y = 122/3)
60x + 50y = 740/3
60x + 48y = 244
Subtract equations
2y = 8/3
y = 8/3/2
y = 4/3
Substitute y
6x + 5(4/3) = 74/3
6x = 18
x = 18/6
x = 3 |
Solve simultaneously:
8x + 10y = 54
2x + 3y = 16 | 8x + 10y = 54
2x + 3y = 16
Using elimination
2*(8x + 10y = 54)
8*(2x + 3y = 16)
16x + 20y = 108
16x + 24y = 128
Subtract equations
-4y = -20
y = -20/-4
y = 5
Substitute y
8x + 10(5) = 54
8x = 4
x = 4/8
x = 1/2 |
Find x for x^3 - 181/12x^2 - 311/6x - 12 = 0 | x^3 - 181/12x^2 - 311/6x - 12 = 0
(x - -8/3)(x - -1/4)(x - 18) = 0
x - -8/3 = 0
x - -1/4 = 0
x - 18 = 0
x = -8/3
x = -1/4
x = 18 |
Find x and y such that
7x + 5y = -319/10
10x + 8y = -49 | 7x + 5y = -319/10
10x + 8y = -49
Using elimination
10*(7x + 5y = -319/10)
7*(10x + 8y = -49)
70x + 50y = -319
70x + 56y = -343
Subtract equations
-6y = 24
y = 24/-6
y = -4
Substitute y
7x + 5(-4) = -319/10
7x = -119/10
x = -119/10/7
x = -17/10 |
Determine x in 5x + 75/8 = 0 | 5x + 75/8 = 0
5x = -75/8
x = -75/8 / 5
x = -15/8 |
Solve simultaneously:
4x + 1y = -57/4
7x + 8y = -39 | 4x + 1y = -57/4
7x + 8y = -39
Using elimination
7*(4x + 1y = -57/4)
4*(7x + 8y = -39)
28x + 7y = -399/4
28x + 32y = -156
Subtract equations
-25y = 225/4
y = 225/4/-25
y = -9/4
Substitute y
4x + 1(-9/4) = -57/4
4x = -12
x = -12/4
x = -3 |
Solve quickly: x^3 + 65/8x^2 - 171/4x + 45 = 0 | x^3 + 65/8x^2 - 171/4x + 45 = 0
(x - -12)(x - 2)(x - 15/8) = 0
x - -12 = 0
x - 2 = 0
x - 15/8 = 0
x = -12
x = 2
x = 15/8 |
Find x in x^3 + 61/10x^2 - 1/5x - 57/2 = 0 | x^3 + 61/10x^2 - 1/5x - 57/2 = 0
(x - -5)(x - 19/10)(x - -3) = 0
x - -5 = 0
x - 19/10 = 0
x - -3 = 0
x = -5
x = 19/10
x = -3 |
Find x in x^2 - 39/28x + 5/28 = 0 | x^2 - 39/28x + 5/28 = 0
(x - 1/7)(x - 5/4) = 0
x - 1/7 = 0 or x - 5/4 = 0
x = 1/7
x = 5/4 |
Solve x^3 - 133/24x^2 + 6583/648x - 665/108 = 0 | x^3 - 133/24x^2 + 6583/648x - 665/108 = 0
(x - 15/8)(x - 19/9)(x - 14/9) = 0
x - 15/8 = 0
x - 19/9 = 0
x - 14/9 = 0
x = 15/8
x = 19/9
x = 14/9 |
Find the solution to 7x + 1 = 0 | 7x + 1 = 0
7x = -1
x = -1 / 7
x = -1/7 |
Compute the solution of 4x + 38 = 0 | 4x + 38 = 0
4x = -38
x = -38 / 4
x = -19/2 |
Find the solution to x^2 - 7/2x - 2 = 0 | x^2 - 7/2x - 2 = 0
(x - 4)(x - -1/2) = 0
x - 4 = 0 or x - -1/2 = 0
x = 4
x = -1/2 |
What value of x satisfies x^3 + 682/105x^2 + 397/35x + 374/105 = 0 | x^3 + 682/105x^2 + 397/35x + 374/105 = 0
(x - -11/3)(x - -17/7)(x - -2/5) = 0
x - -11/3 = 0
x - -17/7 = 0
x - -2/5 = 0
x = -11/3
x = -17/7
x = -2/5 |
What value of x satisfies x^2 + 41/14x + 15/14 = 0 | x^2 + 41/14x + 15/14 = 0
(x - -3/7)(x - -5/2) = 0
x - -3/7 = 0 or x - -5/2 = 0
x = -3/7
x = -5/2 |
Solve the system:
4x + 5y = -15/2
5x + 1y = -69/4 | 4x + 5y = -15/2
5x + 1y = -69/4
Using elimination
5*(4x + 5y = -15/2)
4*(5x + 1y = -69/4)
20x + 25y = -75/2
20x + 4y = -69
Subtract equations
21y = 63/2
y = 63/2/21
y = 3/2
Substitute y
4x + 5(3/2) = -15/2
4x = -15
x = -15/4
x = -15/4 |
Find the solution to x^3 + 109/18x^2 - 457/18x + 10 = 0 | x^3 + 109/18x^2 - 457/18x + 10 = 0
(x - 5/2)(x - 4/9)(x - -9) = 0
x - 5/2 = 0
x - 4/9 = 0
x - -9 = 0
x = 5/2
x = 4/9
x = -9 |
Find x for 5x + 10 = 0 | 5x + 10 = 0
5x = -10
x = -10 / 5
x = -2 |
What value of x satisfies 10x + 2 = 0 | 10x + 2 = 0
10x = -2
x = -2 / 10
x = -1/5 |
Solve quickly: x^2 - 1/3x - 80/3 = 0 | x^2 - 1/3x - 80/3 = 0
(x - 16/3)(x - -5) = 0
x - 16/3 = 0 or x - -5 = 0
x = 16/3
x = -5 |
Find x in 3x + 27/4 = 0 | 3x + 27/4 = 0
3x = -27/4
x = -27/4 / 3
x = -9/4 |
Find x for x^3 + 29/12x^2 - 55/4x - 91/6 = 0 | x^3 + 29/12x^2 - 55/4x - 91/6 = 0
(x - 13/4)(x - -14/3)(x - -1) = 0
x - 13/4 = 0
x - -14/3 = 0
x - -1 = 0
x = 13/4
x = -14/3
x = -1 |
Find x in x^3 + 55/3x^2 + 637/12x - 845/4 = 0 | x^3 + 55/3x^2 + 637/12x - 845/4 = 0
(x - -13)(x - -15/2)(x - 13/6) = 0
x - -13 = 0
x - -15/2 = 0
x - 13/6 = 0
x = -13
x = -15/2
x = 13/6 |
Find x in x^3 + 69/8x^2 + 727/32x + 1197/64 = 0 | x^3 + 69/8x^2 + 727/32x + 1197/64 = 0
(x - -19/8)(x - -7/4)(x - -9/2) = 0
x - -19/8 = 0
x - -7/4 = 0
x - -9/2 = 0
x = -19/8
x = -7/4
x = -9/2 |
Solve quickly: x^3 + 91/72x^2 - 161/288x + 13/288 = 0 | x^3 + 91/72x^2 - 161/288x + 13/288 = 0
(x - -13/8)(x - 1/4)(x - 1/9) = 0
x - -13/8 = 0
x - 1/4 = 0
x - 1/9 = 0
x = -13/8
x = 1/4
x = 1/9 |
Find x and y such that
7x + 5y = 32
10x + 4y = 254/7 | 7x + 5y = 32
10x + 4y = 254/7
Using elimination
10*(7x + 5y = 32)
7*(10x + 4y = 254/7)
70x + 50y = 320
70x + 28y = 254
Subtract equations
22y = 66
y = 66/22
y = 3
Substitute y
7x + 5(3) = 32
7x = 17
x = 17/7
x = 17/7 |
Find x in x^2 - 183/70x + 19/14 = 0 | x^2 - 183/70x + 19/14 = 0
(x - 5/7)(x - 19/10) = 0
x - 5/7 = 0 or x - 19/10 = 0
x = 5/7
x = 19/10 |
Find x in x^3 - 38/3x^2 - 409/12x - 55/4 = 0 | x^3 - 38/3x^2 - 409/12x - 55/4 = 0
(x - 15)(x - -11/6)(x - -1/2) = 0
x - 15 = 0
x - -11/6 = 0
x - -1/2 = 0
x = 15
x = -11/6
x = -1/2 |
Determine x in 9x + 45 = 0 | 9x + 45 = 0
9x = -45
x = -45 / 9
x = -5 |
Solve the system:
3x + 8y = -749/40
4x + 4y = -103/10 | 3x + 8y = -749/40
4x + 4y = -103/10
Using elimination
4*(3x + 8y = -749/40)
3*(4x + 4y = -103/10)
12x + 32y = -749/10
12x + 12y = -309/10
Subtract equations
20y = -44
y = -44/20
y = -11/5
Substitute y
3x + 8(-11/5) = -749/40
3x = -9/8
x = -9/8/3
x = -3/8 |
Find x for x^2 - 25/18x - 133/18 = 0 | x^2 - 25/18x - 133/18 = 0
(x - -19/9)(x - 7/2) = 0
x - -19/9 = 0 or x - 7/2 = 0
x = -19/9
x = 7/2 |
Solve simultaneously:
8x + 4y = 10/3
8x + 8y = 32/3 | 8x + 4y = 10/3
8x + 8y = 32/3
Using elimination
8*(8x + 4y = 10/3)
8*(8x + 8y = 32/3)
64x + 32y = 80/3
64x + 64y = 256/3
Subtract equations
-32y = -176/3
y = -176/3/-32
y = 11/6
Substitute y
8x + 4(11/6) = 10/3
8x = -4
x = -4/8
x = -1/2 |
What value of x satisfies x^3 + 10/63x^2 - 17/189x - 2/189 = 0 | x^3 + 10/63x^2 - 17/189x - 2/189 = 0
(x - -1/3)(x - -1/9)(x - 2/7) = 0
x - -1/3 = 0
x - -1/9 = 0
x - 2/7 = 0
x = -1/3
x = -1/9
x = 2/7 |
Find x for x^3 - 152/21x^2 + 31/3x + 30/7 = 0 | x^3 - 152/21x^2 + 31/3x + 30/7 = 0
(x - 5)(x - -1/3)(x - 18/7) = 0
x - 5 = 0
x - -1/3 = 0
x - 18/7 = 0
x = 5
x = -1/3
x = 18/7 |
Find x and y such that
7x + 4y = -74/5
6x + 3y = -867/70 | 7x + 4y = -74/5
6x + 3y = -867/70
Using elimination
6*(7x + 4y = -74/5)
7*(6x + 3y = -867/70)
42x + 24y = -444/5
42x + 21y = -867/10
Subtract equations
3y = -21/10
y = -21/10/3
y = -7/10
Substitute y
7x + 4(-7/10) = -74/5
7x = -12
x = -12/7
x = -12/7 |
Solve simultaneously:
7x + 4y = -129/5
8x + 3y = -138/5 | 7x + 4y = -129/5
8x + 3y = -138/5
Using elimination
8*(7x + 4y = -129/5)
7*(8x + 3y = -138/5)
56x + 32y = -1032/5
56x + 21y = -966/5
Subtract equations
11y = -66/5
y = -66/5/11
y = -6/5
Substitute y
7x + 4(-6/5) = -129/5
7x = -21
x = -21/7
x = -3 |
Determine x in x^3 - 227/72x^2 + 515/288x + 7/6 = 0 | x^3 - 227/72x^2 + 515/288x + 7/6 = 0
(x - 7/4)(x - -3/8)(x - 16/9) = 0
x - 7/4 = 0
x - -3/8 = 0
x - 16/9 = 0
x = 7/4
x = -3/8
x = 16/9 |
Find the solution to 1x - 14/9 = 0 | 1x - 14/9 = 0
1x = 14/9
x = 14/9 / 1
x = 14/9 |
Determine x in x^3 - 129/8x^2 - 599/8x - 105/2 = 0 | x^3 - 129/8x^2 - 599/8x - 105/2 = 0
(x - -7/8)(x - -3)(x - 20) = 0
x - -7/8 = 0
x - -3 = 0
x - 20 = 0
x = -7/8
x = -3
x = 20 |
Find x and y such that
1x + 8y = -50
3x + 5y = -53/2 | 1x + 8y = -50
3x + 5y = -53/2
Using elimination
3*(1x + 8y = -50)
1*(3x + 5y = -53/2)
3x + 24y = -150
3x + 5y = -53/2
Subtract equations
19y = -247/2
y = -247/2/19
y = -13/2
Substitute y
1x + 8(-13/2) = -50
1x = 2
x = 2/1
x = 2 |
Solve x^3 + 61/14x^2 + 25/14x - 50/7 = 0 | x^3 + 61/14x^2 + 25/14x - 50/7 = 0
(x - 1)(x - -20/7)(x - -5/2) = 0
x - 1 = 0
x - -20/7 = 0
x - -5/2 = 0
x = 1
x = -20/7
x = -5/2 |
Find x in 9x + 21 = 0 | 9x + 21 = 0
9x = -21
x = -21 / 9
x = -7/3 |
Solve the system:
9x + 6y = -5
5x + 6y = -61/9 | 9x + 6y = -5
5x + 6y = -61/9
Using elimination
5*(9x + 6y = -5)
9*(5x + 6y = -61/9)
45x + 30y = -25
45x + 54y = -61
Subtract equations
-24y = 36
y = 36/-24
y = -3/2
Substitute y
9x + 6(-3/2) = -5
9x = 4
x = 4/9
x = 4/9 |
Solve x^2 - 21/10x + 11/10 = 0 | x^2 - 21/10x + 11/10 = 0
(x - 11/10)(x - 1) = 0
x - 11/10 = 0 or x - 1 = 0
x = 11/10
x = 1 |
Find x in 10x + 160 = 0 | 10x + 160 = 0
10x = -160
x = -160 / 10
x = -16 |
Solve the equation x^3 + 115/42x^2 - 401/42x - 51/7 = 0 | x^3 + 115/42x^2 - 401/42x - 51/7 = 0
(x - 17/7)(x - -9/2)(x - -2/3) = 0
x - 17/7 = 0
x - -9/2 = 0
x - -2/3 = 0
x = 17/7
x = -9/2
x = -2/3 |
Determine x in x^3 - 176/21x^2 + 1459/63x - 190/9 = 0 | x^3 - 176/21x^2 + 1459/63x - 190/9 = 0
(x - 7/3)(x - 10/3)(x - 19/7) = 0
x - 7/3 = 0
x - 10/3 = 0
x - 19/7 = 0
x = 7/3
x = 10/3
x = 19/7 |
Find x and y such that
4x + 4y = 20
1x + 3y = 7 | 4x + 4y = 20
1x + 3y = 7
Using elimination
1*(4x + 4y = 20)
4*(1x + 3y = 7)
4x + 4y = 20
4x + 12y = 28
Subtract equations
-8y = -8
y = -8/-8
y = 1
Substitute y
4x + 4(1) = 20
4x = 16
x = 16/4
x = 4 |
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