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Simplifying 2x2 = 3x + -4x2 Solving 2x2 = 3x + -4x2 Solving for variable 'x'. Reorder the terms: -3x + 2x2 + 4x2 = 3x + -4x2 + -3x + 4x2 Combine like terms: 2x2 + 4x2 = 6x2 -3x + 6x2 = 3x + -4x2 + -3x + 4x2 Reorder the terms: -3x + 6x2 = 3x + -3x + -4x2 + 4x2 Combine like terms: 3x + -3x = 0 -3x + 6x2 = 0 + -4x2 + 4x2 -3x + 6x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-1 + 2x) = 0 Ignore the factor 3.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 '(-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 = {0, 0.5}
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