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Simplifying 2x2 + 12x + -32 = 1008 Reorder the terms: -32 + 12x + 2x2 = 1008 Solving -32 + 12x + 2x2 = 1008 Solving for variable 'x'. Reorder the terms: -32 + -1008 + 12x + 2x2 = 1008 + -1008 Combine like terms: -32 + -1008 = -1040 -1040 + 12x + 2x2 = 1008 + -1008 Combine like terms: 1008 + -1008 = 0 -1040 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-520 + 6x + x2) = 0 Factor a trinomial. 2((-26 + -1x)(20 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve: Simplifying -26 + -1x = 0 Solving -26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + -1x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -1x = 0 + 26 -1x = 0 + 26 Combine like terms: 0 + 26 = 26 -1x = 26 Divide each side by '-1'. x = -26 Simplifying x = -26Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {-26, 20}
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