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Simplifying 5(5x + -4)(2x + -1) = 0 Reorder the terms: 5(-4 + 5x)(2x + -1) = 0 Reorder the terms: 5(-4 + 5x)(-1 + 2x) = 0 Multiply (-4 + 5x) * (-1 + 2x) 5(-4(-1 + 2x) + 5x * (-1 + 2x)) = 0 5((-1 * -4 + 2x * -4) + 5x * (-1 + 2x)) = 0 5((4 + -8x) + 5x * (-1 + 2x)) = 0 5(4 + -8x + (-1 * 5x + 2x * 5x)) = 0 5(4 + -8x + (-5x + 10x2)) = 0 Combine like terms: -8x + -5x = -13x 5(4 + -13x + 10x2) = 0 (4 * 5 + -13x * 5 + 10x2 * 5) = 0 (20 + -65x + 50x2) = 0 Solving 20 + -65x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -13x + 10x2) = 0 Factor a trinomial. 5((1 + -2x)(4 + -5x)) = 0 Ignore the factor 5.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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Solution
x = {0.5, 0.8}
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