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Simplifying 10000 = 520x + -1x2 Solving 10000 = 520x + -1x2 Solving for variable 'x'. Reorder the terms: 10000 + -520x + x2 = 520x + -520x + -1x2 + x2 Combine like terms: 520x + -520x = 0 10000 + -520x + x2 = 0 + -1x2 + x2 10000 + -520x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 10000 + -520x + x2 = 0 Factor a trinomial. (20 + -1x)(500 + -1x) = 0Subproblem 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 '(500 + -1x)' equal to zero and attempt to solve: Simplifying 500 + -1x = 0 Solving 500 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + -1x = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -1x = 0 + -500 -1x = 0 + -500 Combine like terms: 0 + -500 = -500 -1x = -500 Divide each side by '-1'. x = 500 Simplifying x = 500Solution
x = {20, 500}
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