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Simplifying 0 = 625x + -15000 + -1x2 Reorder the terms: 0 = -15000 + 625x + -1x2 Solving 0 = -15000 + 625x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 15000 = 15000 15000 + -625x + x2 = -15000 + 625x + -1x2 + 15000 + -625x + x2 Reorder the terms: 15000 + -625x + x2 = -15000 + 15000 + 625x + -625x + -1x2 + x2 Combine like terms: -15000 + 15000 = 0 15000 + -625x + x2 = 0 + 625x + -625x + -1x2 + x2 15000 + -625x + x2 = 625x + -625x + -1x2 + x2 Combine like terms: 625x + -625x = 0 15000 + -625x + x2 = 0 + -1x2 + x2 15000 + -625x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 15000 + -625x + x2 = 0 Factor a trinomial. (25 + -1x)(600 + -1x) = 0Subproblem 1
Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25Subproblem 2
Set the factor '(600 + -1x)' equal to zero and attempt to solve: Simplifying 600 + -1x = 0 Solving 600 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-600' to each side of the equation. 600 + -600 + -1x = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -1x = 0 + -600 -1x = 0 + -600 Combine like terms: 0 + -600 = -600 -1x = -600 Divide each side by '-1'. x = 600 Simplifying x = 600Solution
x = {25, 600}
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