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