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Simplifying -1x + 69 = 2(x + -6)(x + 1) Reorder the terms: 69 + -1x = 2(x + -6)(x + 1) Reorder the terms: 69 + -1x = 2(-6 + x)(x + 1) Reorder the terms: 69 + -1x = 2(-6 + x)(1 + x) Multiply (-6 + x) * (1 + x) 69 + -1x = 2(-6(1 + x) + x(1 + x)) 69 + -1x = 2((1 * -6 + x * -6) + x(1 + x)) 69 + -1x = 2((-6 + -6x) + x(1 + x)) 69 + -1x = 2(-6 + -6x + (1 * x + x * x)) 69 + -1x = 2(-6 + -6x + (1x + x2)) Combine like terms: -6x + 1x = -5x 69 + -1x = 2(-6 + -5x + x2) 69 + -1x = (-6 * 2 + -5x * 2 + x2 * 2) 69 + -1x = (-12 + -10x + 2x2) Solving 69 + -1x = -12 + -10x + 2x2 Solving for variable 'x'. Reorder the terms: 69 + 12 + -1x + 10x + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Combine like terms: 69 + 12 = 81 81 + -1x + 10x + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Combine like terms: -1x + 10x = 9x 81 + 9x + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Reorder the terms: 81 + 9x + -2x2 = -12 + 12 + -10x + 10x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 81 + 9x + -2x2 = 0 + -10x + 10x + 2x2 + -2x2 81 + 9x + -2x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 81 + 9x + -2x2 = 0 + 2x2 + -2x2 81 + 9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 81 + 9x + -2x2 = 0 Factor a trinomial. (9 + -1x)(9 + 2x) = 0Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Solution
x = {9, -4.5}
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