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Simplifying x2 + x2 + 12x + 36 = 180 Reorder the terms: 36 + 12x + x2 + x2 = 180 Combine like terms: x2 + x2 = 2x2 36 + 12x + 2x2 = 180 Solving 36 + 12x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 36 + -180 + 12x + 2x2 = 180 + -180 Combine like terms: 36 + -180 = -144 -144 + 12x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -144 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + 6x + x2) = 0 Factor a trinomial. 2((-12 + -1x)(6 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 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 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 2
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 = 6Solution
x = {-12, 6}
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