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Simplifying 0 = 4x2 + -6x + 2 Reorder the terms: 0 = 2 + -6x + 4x2 Solving 0 = 2 + -6x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 6x + -4x2 = 2 + -6x + 4x2 + -2 + 6x + -4x2 Reorder the terms: -2 + 6x + -4x2 = 2 + -2 + -6x + 6x + 4x2 + -4x2 Combine like terms: 2 + -2 = 0 -2 + 6x + -4x2 = 0 + -6x + 6x + 4x2 + -4x2 -2 + 6x + -4x2 = -6x + 6x + 4x2 + -4x2 Combine like terms: -6x + 6x = 0 -2 + 6x + -4x2 = 0 + 4x2 + -4x2 -2 + 6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2 + 6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 3x + -2x2) = 0 Factor a trinomial. 2((-1 + x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 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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