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Simplifying 1500 = (800 + -100x) * x Reorder the terms for easier multiplication: 1500 = x(800 + -100x) 1500 = (800 * x + -100x * x) 1500 = (800x + -100x2) Solving 1500 = 800x + -100x2 Solving for variable 'x'. Reorder the terms: 1500 + -800x + 100x2 = 800x + -800x + -100x2 + 100x2 Combine like terms: 800x + -800x = 0 1500 + -800x + 100x2 = 0 + -100x2 + 100x2 1500 + -800x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 1500 + -800x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(15 + -8x + x2) = 0 Factor a trinomial. 100((3 + -1x)(5 + -1x)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
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 = 5Solution
x = {3, 5}
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