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Simplifying 2x2 + -4x + 4 = 52 Reorder the terms: 4 + -4x + 2x2 = 52 Solving 4 + -4x + 2x2 = 52 Solving for variable 'x'. Reorder the terms: 4 + -52 + -4x + 2x2 = 52 + -52 Combine like terms: 4 + -52 = -48 -48 + -4x + 2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -48 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -2x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(6 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 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 = {-4, 6}
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