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Simplifying 25x(x + 3) = 8500 Reorder the terms: 25x(3 + x) = 8500 (3 * 25x + x * 25x) = 8500 (75x + 25x2) = 8500 Solving 75x + 25x2 = 8500 Solving for variable 'x'. Reorder the terms: -8500 + 75x + 25x2 = 8500 + -8500 Combine like terms: 8500 + -8500 = 0 -8500 + 75x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-340 + 3x + x2) = 0 Factor a trinomial. 25((-20 + -1x)(17 + -1x)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 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 = {-20, 17}
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