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Simplifying 8(x + -1)(x + -1) = 18(3x + -5)(3x + -5) Reorder the terms: 8(-1 + x)(x + -1) = 18(3x + -5)(3x + -5) Reorder the terms: 8(-1 + x)(-1 + x) = 18(3x + -5)(3x + -5) Multiply (-1 + x) * (-1 + x) 8(-1(-1 + x) + x(-1 + x)) = 18(3x + -5)(3x + -5) 8((-1 * -1 + x * -1) + x(-1 + x)) = 18(3x + -5)(3x + -5) 8((1 + -1x) + x(-1 + x)) = 18(3x + -5)(3x + -5) 8(1 + -1x + (-1 * x + x * x)) = 18(3x + -5)(3x + -5) 8(1 + -1x + (-1x + x2)) = 18(3x + -5)(3x + -5) Combine like terms: -1x + -1x = -2x 8(1 + -2x + x2) = 18(3x + -5)(3x + -5) (1 * 8 + -2x * 8 + x2 * 8) = 18(3x + -5)(3x + -5) (8 + -16x + 8x2) = 18(3x + -5)(3x + -5) Reorder the terms: 8 + -16x + 8x2 = 18(-5 + 3x)(3x + -5) Reorder the terms: 8 + -16x + 8x2 = 18(-5 + 3x)(-5 + 3x) Multiply (-5 + 3x) * (-5 + 3x) 8 + -16x + 8x2 = 18(-5(-5 + 3x) + 3x * (-5 + 3x)) 8 + -16x + 8x2 = 18((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) 8 + -16x + 8x2 = 18((25 + -15x) + 3x * (-5 + 3x)) 8 + -16x + 8x2 = 18(25 + -15x + (-5 * 3x + 3x * 3x)) 8 + -16x + 8x2 = 18(25 + -15x + (-15x + 9x2)) Combine like terms: -15x + -15x = -30x 8 + -16x + 8x2 = 18(25 + -30x + 9x2) 8 + -16x + 8x2 = (25 * 18 + -30x * 18 + 9x2 * 18) 8 + -16x + 8x2 = (450 + -540x + 162x2) Solving 8 + -16x + 8x2 = 450 + -540x + 162x2 Solving for variable 'x'. Reorder the terms: 8 + -450 + -16x + 540x + 8x2 + -162x2 = 450 + -540x + 162x2 + -450 + 540x + -162x2 Combine like terms: 8 + -450 = -442 -442 + -16x + 540x + 8x2 + -162x2 = 450 + -540x + 162x2 + -450 + 540x + -162x2 Combine like terms: -16x + 540x = 524x -442 + 524x + 8x2 + -162x2 = 450 + -540x + 162x2 + -450 + 540x + -162x2 Combine like terms: 8x2 + -162x2 = -154x2 -442 + 524x + -154x2 = 450 + -540x + 162x2 + -450 + 540x + -162x2 Reorder the terms: -442 + 524x + -154x2 = 450 + -450 + -540x + 540x + 162x2 + -162x2 Combine like terms: 450 + -450 = 0 -442 + 524x + -154x2 = 0 + -540x + 540x + 162x2 + -162x2 -442 + 524x + -154x2 = -540x + 540x + 162x2 + -162x2 Combine like terms: -540x + 540x = 0 -442 + 524x + -154x2 = 0 + 162x2 + -162x2 -442 + 524x + -154x2 = 162x2 + -162x2 Combine like terms: 162x2 + -162x2 = 0 -442 + 524x + -154x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-221 + 262x + -77x2) = 0 Factor a trinomial. 2((-13 + 7x)(17 + -11x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 7x)' equal to zero and attempt to solve: Simplifying -13 + 7x = 0 Solving -13 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 7x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 7x = 0 + 13 7x = 0 + 13 Combine like terms: 0 + 13 = 13 7x = 13 Divide each side by '7'. x = 1.857142857 Simplifying x = 1.857142857Subproblem 2
Set the factor '(17 + -11x)' equal to zero and attempt to solve: Simplifying 17 + -11x = 0 Solving 17 + -11x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -11x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -11x = 0 + -17 -11x = 0 + -17 Combine like terms: 0 + -17 = -17 -11x = -17 Divide each side by '-11'. x = 1.545454545 Simplifying x = 1.545454545Solution
x = {1.857142857, 1.545454545}
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