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Simplifying (5 + -10x)(-1 + x) = 0 Multiply (5 + -10x) * (-1 + x) (5(-1 + x) + -10x * (-1 + x)) = 0 ((-1 * 5 + x * 5) + -10x * (-1 + x)) = 0 ((-5 + 5x) + -10x * (-1 + x)) = 0 (-5 + 5x + (-1 * -10x + x * -10x)) = 0 (-5 + 5x + (10x + -10x2)) = 0 Combine like terms: 5x + 10x = 15x (-5 + 15x + -10x2) = 0 Solving -5 + 15x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 3x + -2x2) = 0 Factor a trinomial. 5((-1 + x)(1 + -2x)) = 0 Ignore the factor 5.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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