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Simplifying 0 = x2 + 12x + 32 Reorder the terms: 0 = 32 + 12x + x2 Solving 0 = 32 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -12x + -1x2 = 32 + 12x + x2 + -32 + -12x + -1x2 Reorder the terms: -32 + -12x + -1x2 = 32 + -32 + 12x + -12x + x2 + -1x2 Combine like terms: 32 + -32 = 0 -32 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 -32 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -32 + -12x + -1x2 = 0 + x2 + -1x2 -32 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 12x + x2) = 0 Factor a trinomial. -1((8 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-8, -4}
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