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Simplifying 5x2 + -50x + 125 = 500 Reorder the terms: 125 + -50x + 5x2 = 500 Solving 125 + -50x + 5x2 = 500 Solving for variable 'x'. Reorder the terms: 125 + -500 + -50x + 5x2 = 500 + -500 Combine like terms: 125 + -500 = -375 -375 + -50x + 5x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -375 + -50x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-75 + -10x + x2) = 0 Factor a trinomial. 5((-5 + -1x)(15 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-5, 15}
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