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Simplifying 18000 = x(600 + -5x) 18000 = (600 * x + -5x * x) 18000 = (600x + -5x2) Solving 18000 = 600x + -5x2 Solving for variable 'x'. Reorder the terms: 18000 + -600x + 5x2 = 600x + -600x + -5x2 + 5x2 Combine like terms: 600x + -600x = 0 18000 + -600x + 5x2 = 0 + -5x2 + 5x2 18000 + -600x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 18000 + -600x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3600 + -120x + x2) = 0 Factor a trinomial. 5((60 + -1x)(60 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Subproblem 2
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Solution
x = {60, 60}
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