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Simplifying 0 = x2 + 22x + 120 Reorder the terms: 0 = 120 + 22x + x2 Solving 0 = 120 + 22x + x2 Solving for variable 'x'. Combine like terms: 0 + -120 = -120 -120 + -22x + -1x2 = 120 + 22x + x2 + -120 + -22x + -1x2 Reorder the terms: -120 + -22x + -1x2 = 120 + -120 + 22x + -22x + x2 + -1x2 Combine like terms: 120 + -120 = 0 -120 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2 -120 + -22x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 -120 + -22x + -1x2 = 0 + x2 + -1x2 -120 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -120 + -22x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(120 + 22x + x2) = 0 Factor a trinomial. -1((12 + x)(10 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-12, -10}
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