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Simplifying 17500 = x(600 + -5x) 17500 = (600 * x + -5x * x) 17500 = (600x + -5x2) Solving 17500 = 600x + -5x2 Solving for variable 'x'. Reorder the terms: 17500 + -600x + 5x2 = 600x + -600x + -5x2 + 5x2 Combine like terms: 600x + -600x = 0 17500 + -600x + 5x2 = 0 + -5x2 + 5x2 17500 + -600x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 17500 + -600x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3500 + -120x + x2) = 0 Factor a trinomial. 5((50 + -1x)(70 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Subproblem 2
Set the factor '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70Solution
x = {50, 70}
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