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Simplifying x2 + (x + 6)(x + 6) = (x + 12)(x + 12) Reorder the terms: x2 + (6 + x)(x + 6) = (x + 12)(x + 12) Reorder the terms: x2 + (6 + x)(6 + x) = (x + 12)(x + 12) Multiply (6 + x) * (6 + x) x2 + (6(6 + x) + x(6 + x)) = (x + 12)(x + 12) x2 + ((6 * 6 + x * 6) + x(6 + x)) = (x + 12)(x + 12) x2 + ((36 + 6x) + x(6 + x)) = (x + 12)(x + 12) x2 + (36 + 6x + (6 * x + x * x)) = (x + 12)(x + 12) x2 + (36 + 6x + (6x + x2)) = (x + 12)(x + 12) Combine like terms: 6x + 6x = 12x x2 + (36 + 12x + x2) = (x + 12)(x + 12) Reorder the terms: 36 + 12x + x2 + x2 = (x + 12)(x + 12) Combine like terms: x2 + x2 = 2x2 36 + 12x + 2x2 = (x + 12)(x + 12) Reorder the terms: 36 + 12x + 2x2 = (12 + x)(x + 12) Reorder the terms: 36 + 12x + 2x2 = (12 + x)(12 + x) Multiply (12 + x) * (12 + x) 36 + 12x + 2x2 = (12(12 + x) + x(12 + x)) 36 + 12x + 2x2 = ((12 * 12 + x * 12) + x(12 + x)) 36 + 12x + 2x2 = ((144 + 12x) + x(12 + x)) 36 + 12x + 2x2 = (144 + 12x + (12 * x + x * x)) 36 + 12x + 2x2 = (144 + 12x + (12x + x2)) Combine like terms: 12x + 12x = 24x 36 + 12x + 2x2 = (144 + 24x + x2) Solving 36 + 12x + 2x2 = 144 + 24x + x2 Solving for variable 'x'. Reorder the terms: 36 + -144 + 12x + -24x + 2x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Combine like terms: 36 + -144 = -108 -108 + 12x + -24x + 2x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Combine like terms: 12x + -24x = -12x -108 + -12x + 2x2 + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -108 + -12x + 1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Reorder the terms: -108 + -12x + 1x2 = 144 + -144 + 24x + -24x + x2 + -1x2 Combine like terms: 144 + -144 = 0 -108 + -12x + 1x2 = 0 + 24x + -24x + x2 + -1x2 -108 + -12x + 1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 -108 + -12x + 1x2 = 0 + x2 + -1x2 -108 + -12x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -108 + -12x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(18 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {-6, 18}
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