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Simplifying 180 = x2 + 16x + 243 Reorder the terms: 180 = 243 + 16x + x2 Solving 180 = 243 + 16x + x2 Solving for variable 'x'. Combine like terms: 180 + -243 = -63 -63 + -16x + -1x2 = 243 + 16x + x2 + -243 + -16x + -1x2 Reorder the terms: -63 + -16x + -1x2 = 243 + -243 + 16x + -16x + x2 + -1x2 Combine like terms: 243 + -243 = 0 -63 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 -63 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 -63 + -16x + -1x2 = 0 + x2 + -1x2 -63 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -63 + -16x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(63 + 16x + x2) = 0 Factor a trinomial. -1((9 + x)(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {-9, -7}
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