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Simplifying 4x2 = -2x + 2 Reorder the terms: 4x2 = 2 + -2x Solving 4x2 = 2 + -2x Solving for variable 'x'. Reorder the terms: -2 + 2x + 4x2 = 2 + -2x + -2 + 2x Reorder the terms: -2 + 2x + 4x2 = 2 + -2 + -2x + 2x Combine like terms: 2 + -2 = 0 -2 + 2x + 4x2 = 0 + -2x + 2x -2 + 2x + 4x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -2 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + x + 2x2) = 0 Factor a trinomial. 2((-1 + -1x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-1, 0.5}
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