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Simplifying 0 = 2 + 2x + -4x2 Solving 0 = 2 + 2x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -2x + 4x2 = 2 + 2x + -4x2 + -2 + -2x + 4x2 Reorder the terms: -2 + -2x + 4x2 = 2 + -2 + 2x + -2x + -4x2 + 4x2 Combine like terms: 2 + -2 = 0 -2 + -2x + 4x2 = 0 + 2x + -2x + -4x2 + 4x2 -2 + -2x + 4x2 = 2x + -2x + -4x2 + 4x2 Combine like terms: 2x + -2x = 0 -2 + -2x + 4x2 = 0 + -4x2 + 4x2 -2 + -2x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1x + 2x2) = 0 Factor a trinomial. 2((-1 + -2x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.5Subproblem 2
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 = 1Solution
x = {-0.5, 1}
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