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Simplifying 2x2 + 2x = 1012 Reorder the terms: 2x + 2x2 = 1012 Solving 2x + 2x2 = 1012 Solving for variable 'x'. Reorder the terms: -1012 + 2x + 2x2 = 1012 + -1012 Combine like terms: 1012 + -1012 = 0 -1012 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-506 + x + x2) = 0 Factor a trinomial. 2((-23 + -1x)(22 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve: Simplifying -23 + -1x = 0 Solving -23 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1x = 0 + 23 -1x = 0 + 23 Combine like terms: 0 + 23 = 23 -1x = 23 Divide each side by '-1'. x = -23 Simplifying x = -23Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve: Simplifying 22 + -1x = 0 Solving 22 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -1x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -1x = 0 + -22 -1x = 0 + -22 Combine like terms: 0 + -22 = -22 -1x = -22 Divide each side by '-1'. x = 22 Simplifying x = 22Solution
x = {-23, 22}
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