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Simplifying x(2x + 2) = 312 Reorder the terms: x(2 + 2x) = 312 (2 * x + 2x * x) = 312 (2x + 2x2) = 312 Solving 2x + 2x2 = 312 Solving for variable 'x'. Reorder the terms: -312 + 2x + 2x2 = 312 + -312 Combine like terms: 312 + -312 = 0 -312 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-156 + x + x2) = 0 Factor a trinomial. 2((-13 + -1x)(12 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve: Simplifying -13 + -1x = 0 Solving -13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x = 0 + 13 -1x = 0 + 13 Combine like terms: 0 + 13 = 13 -1x = 13 Divide each side by '-1'. x = -13 Simplifying x = -13Subproblem 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 = {-13, 12}
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