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Simplifying 0 = 4x2 + -10x + 4 Reorder the terms: 0 = 4 + -10x + 4x2 Solving 0 = 4 + -10x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 10x + -4x2 = 4 + -10x + 4x2 + -4 + 10x + -4x2 Reorder the terms: -4 + 10x + -4x2 = 4 + -4 + -10x + 10x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 -4 + 10x + -4x2 = 0 + -10x + 10x + 4x2 + -4x2 -4 + 10x + -4x2 = -10x + 10x + 4x2 + -4x2 Combine like terms: -10x + 10x = 0 -4 + 10x + -4x2 = 0 + 4x2 + -4x2 -4 + 10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4 + 10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 5x + -2x2) = 0 Factor a trinomial. 2((-2 + x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 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 = {2, 0.5}
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