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Simplifying 2x2 + 2x + 25 = 289 Reorder the terms: 25 + 2x + 2x2 = 289 Solving 25 + 2x + 2x2 = 289 Solving for variable 'x'. Reorder the terms: 25 + -289 + 2x + 2x2 = 289 + -289 Combine like terms: 25 + -289 = -264 -264 + 2x + 2x2 = 289 + -289 Combine like terms: 289 + -289 = 0 -264 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-132 + x + x2) = 0 Factor a trinomial. 2((-12 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {-12, 11}
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