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Simplifying x2 + -6x + 9 + x2 = 225 Reorder the terms: 9 + -6x + x2 + x2 = 225 Combine like terms: x2 + x2 = 2x2 9 + -6x + 2x2 = 225 Solving 9 + -6x + 2x2 = 225 Solving for variable 'x'. Reorder the terms: 9 + -225 + -6x + 2x2 = 225 + -225 Combine like terms: 9 + -225 = -216 -216 + -6x + 2x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -216 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + -3x + x2) = 0 Factor a trinomial. 2((-9 + -1x)(12 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
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 = 12Solution
x = {-9, 12}
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