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Simplifying 3 = x2 + 13x + 39 Reorder the terms: 3 = 39 + 13x + x2 Solving 3 = 39 + 13x + x2 Solving for variable 'x'. Combine like terms: 3 + -39 = -36 -36 + -13x + -1x2 = 39 + 13x + x2 + -39 + -13x + -1x2 Reorder the terms: -36 + -13x + -1x2 = 39 + -39 + 13x + -13x + x2 + -1x2 Combine like terms: 39 + -39 = 0 -36 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2 -36 + -13x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -36 + -13x + -1x2 = 0 + x2 + -1x2 -36 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -36 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 13x + x2) = 0 Factor a trinomial. -1((9 + x)(4 + 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 '(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 = {-9, -4}
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