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Simplifying 0 = -10x2 + 3500x + -216000 Reorder the terms: 0 = -216000 + 3500x + -10x2 Solving 0 = -216000 + 3500x + -10x2 Solving for variable 'x'. Combine like terms: 0 + 216000 = 216000 216000 + -3500x + 10x2 = -216000 + 3500x + -10x2 + 216000 + -3500x + 10x2 Reorder the terms: 216000 + -3500x + 10x2 = -216000 + 216000 + 3500x + -3500x + -10x2 + 10x2 Combine like terms: -216000 + 216000 = 0 216000 + -3500x + 10x2 = 0 + 3500x + -3500x + -10x2 + 10x2 216000 + -3500x + 10x2 = 3500x + -3500x + -10x2 + 10x2 Combine like terms: 3500x + -3500x = 0 216000 + -3500x + 10x2 = 0 + -10x2 + 10x2 216000 + -3500x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 216000 + -3500x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(21600 + -350x + x2) = 0 Factor a trinomial. 10((80 + -1x)(270 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(80 + -1x)' equal to zero and attempt to solve: Simplifying 80 + -1x = 0 Solving 80 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + -1x = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -1x = 0 + -80 -1x = 0 + -80 Combine like terms: 0 + -80 = -80 -1x = -80 Divide each side by '-1'. x = 80 Simplifying x = 80Subproblem 2
Set the factor '(270 + -1x)' equal to zero and attempt to solve: Simplifying 270 + -1x = 0 Solving 270 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-270' to each side of the equation. 270 + -270 + -1x = 0 + -270 Combine like terms: 270 + -270 = 0 0 + -1x = 0 + -270 -1x = 0 + -270 Combine like terms: 0 + -270 = -270 -1x = -270 Divide each side by '-1'. x = 270 Simplifying x = 270Solution
x = {80, 270}
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