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Simplifying 5(x2 + -2x + 1) = 500 Reorder the terms: 5(1 + -2x + x2) = 500 (1 * 5 + -2x * 5 + x2 * 5) = 500 (5 + -10x + 5x2) = 500 Solving 5 + -10x + 5x2 = 500 Solving for variable 'x'. Reorder the terms: 5 + -500 + -10x + 5x2 = 500 + -500 Combine like terms: 5 + -500 = -495 -495 + -10x + 5x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -495 + -10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-99 + -2x + x2) = 0 Factor a trinomial. 5((-9 + -1x)(11 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Solution
x = {-9, 11}
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