input
stringlengths
13
66
output
stringlengths
30
276
Find x and y such that 4x + 10y = 788/45 1x + 1y = 122/45
4x + 10y = 788/45 1x + 1y = 122/45 Using elimination 1*(4x + 10y = 788/45) 4*(1x + 1y = 122/45) 4x + 10y = 788/45 4x + 4y = 488/45 Subtract equations 6y = 20/3 y = 20/3/6 y = 10/9 Substitute y 4x + 10(10/9) = 788/45 4x = 32/5 x = 32/5/4 x = 8/5
Solve quickly: 10x - 160 = 0
10x - 160 = 0 10x = 160 x = 160 / 10 x = 16
Determine x in x^3 + 91/5x^2 + 14/5x - 72/5 = 0
x^3 + 91/5x^2 + 14/5x - 72/5 = 0 (x - -1)(x - -18)(x - 4/5) = 0 x - -1 = 0 x - -18 = 0 x - 4/5 = 0 x = -1 x = -18 x = 4/5
Solve the equations: 9x + 3y = 1/2 7x + 3y = 5/2
9x + 3y = 1/2 7x + 3y = 5/2 Using elimination 7*(9x + 3y = 1/2) 9*(7x + 3y = 5/2) 63x + 21y = 7/2 63x + 27y = 45/2 Subtract equations -6y = -19 y = -19/-6 y = 19/6 Substitute y 9x + 3(19/6) = 1/2 9x = -9 x = -9/9 x = -1
Determine x in 2x - 15/4 = 0
2x - 15/4 = 0 2x = 15/4 x = 15/4 / 2 x = 15/8
Solve the equation x^2 + 1/2x - 1/2 = 0
x^2 + 1/2x - 1/2 = 0 (x - 1/2)(x - -1) = 0 x - 1/2 = 0 or x - -1 = 0 x = 1/2 x = -1
Find the solution to 3x + 1/2 = 0
3x + 1/2 = 0 3x = -1/2 x = -1/2 / 3 x = -1/6
Solve quickly: x^2 - 7/18x - 104/27 = 0
x^2 - 7/18x - 104/27 = 0 (x - 13/6)(x - -16/9) = 0 x - 13/6 = 0 or x - -16/9 = 0 x = 13/6 x = -16/9
Solve the equations: 5x + 9y = 42 4x + 4y = 296/9
5x + 9y = 42 4x + 4y = 296/9 Using elimination 4*(5x + 9y = 42) 5*(4x + 4y = 296/9) 20x + 36y = 168 20x + 20y = 1480/9 Subtract equations 16y = 32/9 y = 32/9/16 y = 2/9 Substitute y 5x + 9(2/9) = 42 5x = 40 x = 40/5 x = 8
Solve quickly: x^3 - 20/3x^2 = 0
x^3 - 20/3x^2 = 0 (x - 20/3)(x - 0)(x - 0) = 0 x - 20/3 = 0 x - 0 = 0 x - 0 = 0 x = 20/3 x = 0 x = 0
Compute the solution of x^2 + 5/2x - 25/2 = 0
x^2 + 5/2x - 25/2 = 0 (x - 5/2)(x - -5) = 0 x - 5/2 = 0 or x - -5 = 0 x = 5/2 x = -5
Solve 10x - 100 = 0
10x - 100 = 0 10x = 100 x = 100 / 10 x = 10
Solve simultaneously: 1x + 1y = -31/12 1x + 9y = 41/12
1x + 1y = -31/12 1x + 9y = 41/12 Using elimination 1*(1x + 1y = -31/12) 1*(1x + 9y = 41/12) 1x + 1y = -31/12 1x + 9y = 41/12 Subtract equations -8y = -6 y = -6/-8 y = 3/4 Substitute y 1x + 1(3/4) = -31/12 1x = -10/3 x = -10/3/1 x = -10/3
Find x and y such that 6x + 5y = 43/4 2x + 4y = 3
6x + 5y = 43/4 2x + 4y = 3 Using elimination 2*(6x + 5y = 43/4) 6*(2x + 4y = 3) 12x + 10y = 43/2 12x + 24y = 18 Subtract equations -14y = 7/2 y = 7/2/-14 y = -1/4 Substitute y 6x + 5(-1/4) = 43/4 6x = 12 x = 12/6 x = 2
Solve quickly: x^3 - 17/7x^2 - 460/63x + 100/7 = 0
x^3 - 17/7x^2 - 460/63x + 100/7 = 0 (x - 10/3)(x - -18/7)(x - 5/3) = 0 x - 10/3 = 0 x - -18/7 = 0 x - 5/3 = 0 x = 10/3 x = -18/7 x = 5/3
What value of x satisfies x^2 - 2/3x - 16/3 = 0
x^2 - 2/3x - 16/3 = 0 (x - 8/3)(x - -2) = 0 x - 8/3 = 0 or x - -2 = 0 x = 8/3 x = -2
Find x and y such that 7x + 5y = 40/3 5x + 7y = 80/3
7x + 5y = 40/3 5x + 7y = 80/3 Using elimination 5*(7x + 5y = 40/3) 7*(5x + 7y = 80/3) 35x + 25y = 200/3 35x + 49y = 560/3 Subtract equations -24y = -120 y = -120/-24 y = 5 Substitute y 7x + 5(5) = 40/3 7x = -35/3 x = -35/3/7 x = -5/3
What value of x satisfies x^2 + 61/5x - 52/5 = 0
x^2 + 61/5x - 52/5 = 0 (x - -13)(x - 4/5) = 0 x - -13 = 0 or x - 4/5 = 0 x = -13 x = 4/5
Solve the equations: 4x + 9y = 26 10x + 10y = 460/9
4x + 9y = 26 10x + 10y = 460/9 Using elimination 10*(4x + 9y = 26) 4*(10x + 10y = 460/9) 40x + 90y = 260 40x + 40y = 1840/9 Subtract equations 50y = 500/9 y = 500/9/50 y = 10/9 Substitute y 4x + 9(10/9) = 26 4x = 16 x = 16/4 x = 4
Find x and y such that 9x + 4y = 13/10 7x + 1y = 241/40
9x + 4y = 13/10 7x + 1y = 241/40 Using elimination 7*(9x + 4y = 13/10) 9*(7x + 1y = 241/40) 63x + 28y = 91/10 63x + 9y = 2169/40 Subtract equations 19y = -361/8 y = -361/8/19 y = -19/8 Substitute y 9x + 4(-19/8) = 13/10 9x = 54/5 x = 54/5/9 x = 6/5
Find x for x^2 + 82/5x - 51/5 = 0
x^2 + 82/5x - 51/5 = 0 (x - -17)(x - 3/5) = 0 x - -17 = 0 or x - 3/5 = 0 x = -17 x = 3/5
Solve x^2 + 1/2x - 1/2 = 0
x^2 + 1/2x - 1/2 = 0 (x - 1/2)(x - -1) = 0 x - 1/2 = 0 or x - -1 = 0 x = 1/2 x = -1
Find x for x^3 - 62/63x^2 - 655/189x + 100/63 = 0
x^3 - 62/63x^2 - 655/189x + 100/63 = 0 (x - 20/9)(x - 3/7)(x - -5/3) = 0 x - 20/9 = 0 x - 3/7 = 0 x - -5/3 = 0 x = 20/9 x = 3/7 x = -5/3
Solve quickly: x^2 - 103/8x + 21/2 = 0
x^2 - 103/8x + 21/2 = 0 (x - 12)(x - 7/8) = 0 x - 12 = 0 or x - 7/8 = 0 x = 12 x = 7/8
Solve quickly: x^2 - 58/3x + 19/3 = 0
x^2 - 58/3x + 19/3 = 0 (x - 1/3)(x - 19) = 0 x - 1/3 = 0 or x - 19 = 0 x = 1/3 x = 19
Find x for x^3 - 281/120x^2 - 1283/240x + 143/80 = 0
x^3 - 281/120x^2 - 1283/240x + 143/80 = 0 (x - 11/3)(x - 3/10)(x - -13/8) = 0 x - 11/3 = 0 x - 3/10 = 0 x - -13/8 = 0 x = 11/3 x = 3/10 x = -13/8
Find x for x^2 + 167/45x + 2/5 = 0
x^2 + 167/45x + 2/5 = 0 (x - -18/5)(x - -1/9) = 0 x - -18/5 = 0 or x - -1/9 = 0 x = -18/5 x = -1/9
Solve the equation x^2 - 5x - 39/4 = 0
x^2 - 5x - 39/4 = 0 (x - -3/2)(x - 13/2) = 0 x - -3/2 = 0 or x - 13/2 = 0 x = -3/2 x = 13/2
Solve quickly: 2x + 1/3 = 0
2x + 1/3 = 0 2x = -1/3 x = -1/3 / 2 x = -1/6
What value of x satisfies 6x = 0
6x = 0 6x = 0 x = 0 / 6 x = 0
Determine x in x^2 + 2/5x - 3/25 = 0
x^2 + 2/5x - 3/25 = 0 (x - 1/5)(x - -3/5) = 0 x - 1/5 = 0 or x - -3/5 = 0 x = 1/5 x = -3/5
Solve x^3 + 382/63x^2 + 760/189x + 128/189 = 0
x^3 + 382/63x^2 + 760/189x + 128/189 = 0 (x - -4/9)(x - -2/7)(x - -16/3) = 0 x - -4/9 = 0 x - -2/7 = 0 x - -16/3 = 0 x = -4/9 x = -2/7 x = -16/3
Compute the solution of 3x - 33/4 = 0
3x - 33/4 = 0 3x = 33/4 x = 33/4 / 3 x = 11/4
Solve the equations: 10x + 6y = -39 6x + 8y = -46/3
10x + 6y = -39 6x + 8y = -46/3 Using elimination 6*(10x + 6y = -39) 10*(6x + 8y = -46/3) 60x + 36y = -234 60x + 80y = -460/3 Subtract equations -44y = -242/3 y = -242/3/-44 y = 11/6 Substitute y 10x + 6(11/6) = -39 10x = -50 x = -50/10 x = -5
Solve the equation 9x - 45/4 = 0
9x - 45/4 = 0 9x = 45/4 x = 45/4 / 9 x = 5/4
Find x and y such that 10x + 10y = -210 4x + 10y = -102
10x + 10y = -210 4x + 10y = -102 Using elimination 4*(10x + 10y = -210) 10*(4x + 10y = -102) 40x + 40y = -840 40x + 100y = -1020 Subtract equations -60y = 180 y = 180/-60 y = -3 Substitute y 10x + 10(-3) = -210 10x = -180 x = -180/10 x = -18
What value of x satisfies 9x + 45 = 0
9x + 45 = 0 9x = -45 x = -45 / 9 x = -5
Determine x in 10x - 130/9 = 0
10x - 130/9 = 0 10x = 130/9 x = 130/9 / 10 x = 13/9
Find x for x^2 + 5x - 75/4 = 0
x^2 + 5x - 75/4 = 0 (x - -15/2)(x - 5/2) = 0 x - -15/2 = 0 or x - 5/2 = 0 x = -15/2 x = 5/2
Solve the equations: 9x + 1y = 27/4 4x + 10y = 46
9x + 1y = 27/4 4x + 10y = 46 Using elimination 4*(9x + 1y = 27/4) 9*(4x + 10y = 46) 36x + 4y = 27 36x + 90y = 414 Subtract equations -86y = -387 y = -387/-86 y = 9/2 Substitute y 9x + 1(9/2) = 27/4 9x = 9/4 x = 9/4/9 x = 1/4
Solve x^3 - 18/7x^2 - 40/7x = 0
x^3 - 18/7x^2 - 40/7x = 0 (x - 4)(x - -10/7)(x - 0) = 0 x - 4 = 0 x - -10/7 = 0 x - 0 = 0 x = 4 x = -10/7 x = 0
Solve the equations: 2x + 9y = 242/35 9x + 2y = -66/35
2x + 9y = 242/35 9x + 2y = -66/35 Using elimination 9*(2x + 9y = 242/35) 2*(9x + 2y = -66/35) 18x + 81y = 2178/35 18x + 4y = -132/35 Subtract equations 77y = 66 y = 66/77 y = 6/7 Substitute y 2x + 9(6/7) = 242/35 2x = -4/5 x = -4/5/2 x = -2/5
Find x in x^3 - 41/6x^2 - 374/9x - 847/18 = 0
x^3 - 41/6x^2 - 374/9x - 847/18 = 0 (x - -7/3)(x - 11)(x - -11/6) = 0 x - -7/3 = 0 x - 11 = 0 x - -11/6 = 0 x = -7/3 x = 11 x = -11/6
Find the solution to 4x - 36 = 0
4x - 36 = 0 4x = 36 x = 36 / 4 x = 9
Solve the equations: 3x + 7y = -14/5 5x + 3y = 112/15
3x + 7y = -14/5 5x + 3y = 112/15 Using elimination 5*(3x + 7y = -14/5) 3*(5x + 3y = 112/15) 15x + 35y = -14 15x + 9y = 112/5 Subtract equations 26y = -182/5 y = -182/5/26 y = -7/5 Substitute y 3x + 7(-7/5) = -14/5 3x = 7 x = 7/3 x = 7/3
Find the solution to 1x + 11/3 = 0
1x + 11/3 = 0 1x = -11/3 x = -11/3 / 1 x = -11/3
Solve the system: 3x + 9y = -28/3 10x + 3y = -91/9
3x + 9y = -28/3 10x + 3y = -91/9 Using elimination 10*(3x + 9y = -28/3) 3*(10x + 3y = -91/9) 30x + 90y = -280/3 30x + 9y = -91/3 Subtract equations 81y = -63 y = -63/81 y = -7/9 Substitute y 3x + 9(-7/9) = -28/3 3x = -7/3 x = -7/3/3 x = -7/9
Solve the system: 1x + 8y = 70/3 5x + 2y = -11/3
1x + 8y = 70/3 5x + 2y = -11/3 Using elimination 5*(1x + 8y = 70/3) 1*(5x + 2y = -11/3) 5x + 40y = 350/3 5x + 2y = -11/3 Subtract equations 38y = 361/3 y = 361/3/38 y = 19/6 Substitute y 1x + 8(19/6) = 70/3 1x = -2 x = -2/1 x = -2
What value of x satisfies x^2 + 77/6x + 85/3 = 0
x^2 + 77/6x + 85/3 = 0 (x - -10)(x - -17/6) = 0 x - -10 = 0 or x - -17/6 = 0 x = -10 x = -17/6
Find x and y such that 6x + 9y = -12 9x + 1y = 13/9
6x + 9y = -12 9x + 1y = 13/9 Using elimination 9*(6x + 9y = -12) 6*(9x + 1y = 13/9) 54x + 81y = -108 54x + 6y = 26/3 Subtract equations 75y = -350/3 y = -350/3/75 y = -14/9 Substitute y 6x + 9(-14/9) = -12 6x = 2 x = 2/6 x = 1/3
Solve the equations: 10x + 5y = 245/18 9x + 4y = 455/36
10x + 5y = 245/18 9x + 4y = 455/36 Using elimination 9*(10x + 5y = 245/18) 10*(9x + 4y = 455/36) 90x + 45y = 245/2 90x + 40y = 2275/18 Subtract equations 5y = -35/9 y = -35/9/5 y = -7/9 Substitute y 10x + 5(-7/9) = 245/18 10x = 35/2 x = 35/2/10 x = 7/4
Solve the system: 5x + 5y = -37/9 8x + 4y = -436/45
5x + 5y = -37/9 8x + 4y = -436/45 Using elimination 8*(5x + 5y = -37/9) 5*(8x + 4y = -436/45) 40x + 40y = -296/9 40x + 20y = -436/9 Subtract equations 20y = 140/9 y = 140/9/20 y = 7/9 Substitute y 5x + 5(7/9) = -37/9 5x = -8 x = -8/5 x = -8/5
Determine x in x^2 - 8/9x - 17/9 = 0
x^2 - 8/9x - 17/9 = 0 (x - 17/9)(x - -1) = 0 x - 17/9 = 0 or x - -1 = 0 x = 17/9 x = -1
Find x for x^3 + 3/4x^2 - 64/9x - 16/3 = 0
x^3 + 3/4x^2 - 64/9x - 16/3 = 0 (x - 8/3)(x - -8/3)(x - -3/4) = 0 x - 8/3 = 0 x - -8/3 = 0 x - -3/4 = 0 x = 8/3 x = -8/3 x = -3/4
Solve quickly: x^2 - 13/15x + 2/15 = 0
x^2 - 13/15x + 2/15 = 0 (x - 1/5)(x - 2/3) = 0 x - 1/5 = 0 or x - 2/3 = 0 x = 1/5 x = 2/3
What value of x satisfies 8x - 80 = 0
8x - 80 = 0 8x = 80 x = 80 / 8 x = 10
Solve simultaneously: 5x + 7y = 227/3 7x + 4y = 196/3
5x + 7y = 227/3 7x + 4y = 196/3 Using elimination 7*(5x + 7y = 227/3) 5*(7x + 4y = 196/3) 35x + 49y = 1589/3 35x + 20y = 980/3 Subtract equations 29y = 203 y = 203/29 y = 7 Substitute y 5x + 7(7) = 227/3 5x = 80/3 x = 80/3/5 x = 16/3
Solve quickly: x^3 - 127/21x^2 + 220/21x - 100/21 = 0
x^3 - 127/21x^2 + 220/21x - 100/21 = 0 (x - 5/7)(x - 2)(x - 10/3) = 0 x - 5/7 = 0 x - 2 = 0 x - 10/3 = 0 x = 5/7 x = 2 x = 10/3
Solve the equations: 1x + 3y = 3 10x + 7y = 44/3
1x + 3y = 3 10x + 7y = 44/3 Using elimination 10*(1x + 3y = 3) 1*(10x + 7y = 44/3) 10x + 30y = 30 10x + 7y = 44/3 Subtract equations 23y = 46/3 y = 46/3/23 y = 2/3 Substitute y 1x + 3(2/3) = 3 1x = 1 x = 1/1 x = 1
Solve the system: 7x + 7y = -490/9 5x + 7y = -458/9
7x + 7y = -490/9 5x + 7y = -458/9 Using elimination 5*(7x + 7y = -490/9) 7*(5x + 7y = -458/9) 35x + 35y = -2450/9 35x + 49y = -3206/9 Subtract equations -14y = 84 y = 84/-14 y = -6 Substitute y 7x + 7(-6) = -490/9 7x = -112/9 x = -112/9/7 x = -16/9
Find the solution to 8x - 36 = 0
8x - 36 = 0 8x = 36 x = 36 / 8 x = 9/2
What value of x satisfies x^3 - 7/2x^2 - 5/2x + 2 = 0
x^3 - 7/2x^2 - 5/2x + 2 = 0 (x - 1/2)(x - -1)(x - 4) = 0 x - 1/2 = 0 x - -1 = 0 x - 4 = 0 x = 1/2 x = -1 x = 4
Find the solution to x^3 - 111/10x^2 + 81/2x - 243/5 = 0
x^3 - 111/10x^2 + 81/2x - 243/5 = 0 (x - 9/2)(x - 18/5)(x - 3) = 0 x - 9/2 = 0 x - 18/5 = 0 x - 3 = 0 x = 9/2 x = 18/5 x = 3
Find x and y such that 2x + 8y = -34 3x + 10y = -45
2x + 8y = -34 3x + 10y = -45 Using elimination 3*(2x + 8y = -34) 2*(3x + 10y = -45) 6x + 24y = -102 6x + 20y = -90 Subtract equations 4y = -12 y = -12/4 y = -3 Substitute y 2x + 8(-3) = -34 2x = -10 x = -10/2 x = -5
Find x for x^3 + 19/10x^2 - 76/5x + 3/2 = 0
x^3 + 19/10x^2 - 76/5x + 3/2 = 0 (x - 1/10)(x - -5)(x - 3) = 0 x - 1/10 = 0 x - -5 = 0 x - 3 = 0 x = 1/10 x = -5 x = 3
Find the solution to x^2 + 91/9x + 10 = 0
x^2 + 91/9x + 10 = 0 (x - -10/9)(x - -9) = 0 x - -10/9 = 0 or x - -9 = 0 x = -10/9 x = -9
Compute the solution of x^2 + 46/9x - 280/27 = 0
x^2 + 46/9x - 280/27 = 0 (x - -20/3)(x - 14/9) = 0 x - -20/3 = 0 or x - 14/9 = 0 x = -20/3 x = 14/9
Solve the system: 2x + 9y = -194/9 7x + 4y = -184/9
2x + 9y = -194/9 7x + 4y = -184/9 Using elimination 7*(2x + 9y = -194/9) 2*(7x + 4y = -184/9) 14x + 63y = -1358/9 14x + 8y = -368/9 Subtract equations 55y = -110 y = -110/55 y = -2 Substitute y 2x + 9(-2) = -194/9 2x = -32/9 x = -32/9/2 x = -16/9
Solve the equation 4x + 12 = 0
4x + 12 = 0 4x = -12 x = -12 / 4 x = -3
Solve the system: 9x + 10y = -248/7 1x + 1y = -29/7
9x + 10y = -248/7 1x + 1y = -29/7 Using elimination 1*(9x + 10y = -248/7) 9*(1x + 1y = -29/7) 9x + 10y = -248/7 9x + 9y = -261/7 Subtract equations 1y = 13/7 y = 13/7/1 y = 13/7 Substitute y 9x + 10(13/7) = -248/7 9x = -54 x = -54/9 x = -6
Solve the equations: 5x + 10y = 137/7 1x + 6y = 397/35
5x + 10y = 137/7 1x + 6y = 397/35 Using elimination 1*(5x + 10y = 137/7) 5*(1x + 6y = 397/35) 5x + 10y = 137/7 5x + 30y = 397/7 Subtract equations -20y = -260/7 y = -260/7/-20 y = 13/7 Substitute y 5x + 10(13/7) = 137/7 5x = 1 x = 1/5 x = 1/5
Find x for x^3 - 185/14x^2 - 163/14x + 9 = 0
x^3 - 185/14x^2 - 163/14x + 9 = 0 (x - 1/2)(x - 14)(x - -9/7) = 0 x - 1/2 = 0 x - 14 = 0 x - -9/7 = 0 x = 1/2 x = 14 x = -9/7
Find x for 1x - 3/2 = 0
1x - 3/2 = 0 1x = 3/2 x = 3/2 / 1 x = 3/2
Find x in x^2 - 5x - 24 = 0
x^2 - 5x - 24 = 0 (x - -3)(x - 8) = 0 x - -3 = 0 or x - 8 = 0 x = -3 x = 8
Solve the equations: 2x + 1y = 58/21 9x + 5y = 78/7
2x + 1y = 58/21 9x + 5y = 78/7 Using elimination 9*(2x + 1y = 58/21) 2*(9x + 5y = 78/7) 18x + 9y = 174/7 18x + 10y = 156/7 Subtract equations -1y = 18/7 y = 18/7/-1 y = -18/7 Substitute y 2x + 1(-18/7) = 58/21 2x = 16/3 x = 16/3/2 x = 8/3
Find x in x^2 + 3/4x = 0
x^2 + 3/4x = 0 (x - -3/4)(x - 0) = 0 x - -3/4 = 0 or x - 0 = 0 x = -3/4 x = 0
Solve simultaneously: 5x + 7y = 179/5 2x + 9y = 53/5
5x + 7y = 179/5 2x + 9y = 53/5 Using elimination 2*(5x + 7y = 179/5) 5*(2x + 9y = 53/5) 10x + 14y = 358/5 10x + 45y = 53 Subtract equations -31y = 93/5 y = 93/5/-31 y = -3/5 Substitute y 5x + 7(-3/5) = 179/5 5x = 40 x = 40/5 x = 8
Solve the equations: 10x + 5y = -165/2 10x + 9y = -233/2
10x + 5y = -165/2 10x + 9y = -233/2 Using elimination 10*(10x + 5y = -165/2) 10*(10x + 9y = -233/2) 100x + 50y = -825 100x + 90y = -1165 Subtract equations -40y = 340 y = 340/-40 y = -17/2 Substitute y 10x + 5(-17/2) = -165/2 10x = -40 x = -40/10 x = -4
Find x for x^2 - 17/6x + 5/3 = 0
x^2 - 17/6x + 5/3 = 0 (x - 2)(x - 5/6) = 0 x - 2 = 0 or x - 5/6 = 0 x = 2 x = 5/6
Solve quickly: x^3 - 139/30x^2 + 139/30x - 1 = 0
x^3 - 139/30x^2 + 139/30x - 1 = 0 (x - 10/3)(x - 1)(x - 3/10) = 0 x - 10/3 = 0 x - 1 = 0 x - 3/10 = 0 x = 10/3 x = 1 x = 3/10
Find the solution to 8x + 8/3 = 0
8x + 8/3 = 0 8x = -8/3 x = -8/3 / 8 x = -1/3
Solve x^2 - 8x + 95/9 = 0
x^2 - 8x + 95/9 = 0 (x - 19/3)(x - 5/3) = 0 x - 19/3 = 0 or x - 5/3 = 0 x = 19/3 x = 5/3
Find the solution to x^3 + 7x^2 - 105x + 225 = 0
x^3 + 7x^2 - 105x + 225 = 0 (x - 5)(x - 3)(x - -15) = 0 x - 5 = 0 x - 3 = 0 x - -15 = 0 x = 5 x = 3 x = -15
Solve x^2 + 13/6x - 5/2 = 0
x^2 + 13/6x - 5/2 = 0 (x - 5/6)(x - -3) = 0 x - 5/6 = 0 or x - -3 = 0 x = 5/6 x = -3
Solve the system: 5x + 4y = 71/28 5x + 7y = 29/4
5x + 4y = 71/28 5x + 7y = 29/4 Using elimination 5*(5x + 4y = 71/28) 5*(5x + 7y = 29/4) 25x + 20y = 355/28 25x + 35y = 145/4 Subtract equations -15y = -165/7 y = -165/7/-15 y = 11/7 Substitute y 5x + 4(11/7) = 71/28 5x = -15/4 x = -15/4/5 x = -3/4
Find x and y such that 3x + 6y = 53/21 2x + 7y = 64/63
3x + 6y = 53/21 2x + 7y = 64/63 Using elimination 2*(3x + 6y = 53/21) 3*(2x + 7y = 64/63) 6x + 12y = 106/21 6x + 21y = 64/21 Subtract equations -9y = 2 y = 2/-9 y = -2/9 Substitute y 3x + 6(-2/9) = 53/21 3x = 27/7 x = 27/7/3 x = 9/7
What value of x satisfies x^3 - 409/70x^2 + 153/14x - 45/7 = 0
x^3 - 409/70x^2 + 153/14x - 45/7 = 0 (x - 5/2)(x - 15/7)(x - 6/5) = 0 x - 5/2 = 0 x - 15/7 = 0 x - 6/5 = 0 x = 5/2 x = 15/7 x = 6/5
Solve the system: 9x + 4y = -59/14 3x + 4y = 39/14
9x + 4y = -59/14 3x + 4y = 39/14 Using elimination 3*(9x + 4y = -59/14) 9*(3x + 4y = 39/14) 27x + 12y = -177/14 27x + 36y = 351/14 Subtract equations -24y = -264/7 y = -264/7/-24 y = 11/7 Substitute y 9x + 4(11/7) = -59/14 9x = -21/2 x = -21/2/9 x = -7/6
Solve the equation x^3 - 5/2x^2 - 9/2x + 9 = 0
x^3 - 5/2x^2 - 9/2x + 9 = 0 (x - -2)(x - 3)(x - 3/2) = 0 x - -2 = 0 x - 3 = 0 x - 3/2 = 0 x = -2 x = 3 x = 3/2
Determine x in 3x + 6 = 0
3x + 6 = 0 3x = -6 x = -6 / 3 x = -2
Find x in x^2 + 3x + 2 = 0
x^2 + 3x + 2 = 0 (x - -2)(x - -1) = 0 x - -2 = 0 or x - -1 = 0 x = -2 x = -1
Solve simultaneously: 8x + 5y = -76 4x + 2y = -34
8x + 5y = -76 4x + 2y = -34 Using elimination 4*(8x + 5y = -76) 8*(4x + 2y = -34) 32x + 20y = -304 32x + 16y = -272 Subtract equations 4y = -32 y = -32/4 y = -8 Substitute y 8x + 5(-8) = -76 8x = -36 x = -36/8 x = -9/2
Determine x in x^3 + 8/3x^2 - 157/12x - 85/12 = 0
x^3 + 8/3x^2 - 157/12x - 85/12 = 0 (x - -5)(x - -1/2)(x - 17/6) = 0 x - -5 = 0 x - -1/2 = 0 x - 17/6 = 0 x = -5 x = -1/2 x = 17/6
Compute the solution of x^3 - 11/3x^2 - 32/9x + 140/9 = 0
x^3 - 11/3x^2 - 32/9x + 140/9 = 0 (x - 7/3)(x - -2)(x - 10/3) = 0 x - 7/3 = 0 x - -2 = 0 x - 10/3 = 0 x = 7/3 x = -2 x = 10/3
Solve the equation x^3 + 92/21x^2 - 65/7x + 18/7 = 0
x^3 + 92/21x^2 - 65/7x + 18/7 = 0 (x - -6)(x - 9/7)(x - 1/3) = 0 x - -6 = 0 x - 9/7 = 0 x - 1/3 = 0 x = -6 x = 9/7 x = 1/3
Find x in 1x + 2/7 = 0
1x + 2/7 = 0 1x = -2/7 x = -2/7 / 1 x = -2/7
What value of x satisfies x^3 - 209/28x^2 - 367/28x + 494/7 = 0
x^3 - 209/28x^2 - 367/28x + 494/7 = 0 (x - -13/4)(x - 8)(x - 19/7) = 0 x - -13/4 = 0 x - 8 = 0 x - 19/7 = 0 x = -13/4 x = 8 x = 19/7
Find x for x^3 - 191/45x^2 + 17/15x + 19/9 = 0
x^3 - 191/45x^2 + 17/15x + 19/9 = 0 (x - 1)(x - -5/9)(x - 19/5) = 0 x - 1 = 0 x - -5/9 = 0 x - 19/5 = 0 x = 1 x = -5/9 x = 19/5
Solve the equations: 1x + 2y = 3/14 9x + 6y = 387/14
1x + 2y = 3/14 9x + 6y = 387/14 Using elimination 9*(1x + 2y = 3/14) 1*(9x + 6y = 387/14) 9x + 18y = 27/14 9x + 6y = 387/14 Subtract equations 12y = -180/7 y = -180/7/12 y = -15/7 Substitute y 1x + 2(-15/7) = 3/14 1x = 9/2 x = 9/2/1 x = 9/2
Determine x in x^2 - 35/8x + 19/4 = 0
x^2 - 35/8x + 19/4 = 0 (x - 19/8)(x - 2) = 0 x - 19/8 = 0 or x - 2 = 0 x = 19/8 x = 2