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Simplifying 0 = -20x2 + 40x + 5100 Reorder the terms: 0 = 5100 + 40x + -20x2 Solving 0 = 5100 + 40x + -20x2 Solving for variable 'x'. Combine like terms: 0 + -5100 = -5100 -5100 + -40x + 20x2 = 5100 + 40x + -20x2 + -5100 + -40x + 20x2 Reorder the terms: -5100 + -40x + 20x2 = 5100 + -5100 + 40x + -40x + -20x2 + 20x2 Combine like terms: 5100 + -5100 = 0 -5100 + -40x + 20x2 = 0 + 40x + -40x + -20x2 + 20x2 -5100 + -40x + 20x2 = 40x + -40x + -20x2 + 20x2 Combine like terms: 40x + -40x = 0 -5100 + -40x + 20x2 = 0 + -20x2 + 20x2 -5100 + -40x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -5100 + -40x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-255 + -2x + x2) = 0 Factor a trinomial. 20((-15 + -1x)(17 + -1x)) = 0 Ignore the factor 20.Subproblem 1
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 = -15Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve: Simplifying 17 + -1x = 0 Solving 17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1x = 0 + -17 -1x = 0 + -17 Combine like terms: 0 + -17 = -17 -1x = -17 Divide each side by '-1'. x = 17 Simplifying x = 17Solution
x = {-15, 17}
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