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Simplifying 2x + 27 = x2 + 12x + 36 Reorder the terms: 27 + 2x = x2 + 12x + 36 Reorder the terms: 27 + 2x = 36 + 12x + x2 Solving 27 + 2x = 36 + 12x + x2 Solving for variable 'x'. Reorder the terms: 27 + -36 + 2x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 27 + -36 = -9 -9 + 2x + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Combine like terms: 2x + -12x = -10x -9 + -10x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: -9 + -10x + -1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 -9 + -10x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -9 + -10x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -9 + -10x + -1x2 = 0 + x2 + -1x2 -9 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + -10x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 10x + x2) = 0 Factor a trinomial. -1((9 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-9, -1}
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