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Simplifying 20000 = -1x2 + 900x + -160000 Reorder the terms: 20000 = -160000 + 900x + -1x2 Solving 20000 = -160000 + 900x + -1x2 Solving for variable 'x'. Combine like terms: 20000 + 160000 = 180000 180000 + -900x + x2 = -160000 + 900x + -1x2 + 160000 + -900x + x2 Reorder the terms: 180000 + -900x + x2 = -160000 + 160000 + 900x + -900x + -1x2 + x2 Combine like terms: -160000 + 160000 = 0 180000 + -900x + x2 = 0 + 900x + -900x + -1x2 + x2 180000 + -900x + x2 = 900x + -900x + -1x2 + x2 Combine like terms: 900x + -900x = 0 180000 + -900x + x2 = 0 + -1x2 + x2 180000 + -900x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 180000 + -900x + x2 = 0 Factor a trinomial. (300 + -1x)(600 + -1x) = 0Subproblem 1
Set the factor '(300 + -1x)' equal to zero and attempt to solve: Simplifying 300 + -1x = 0 Solving 300 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + -1x = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -1x = 0 + -300 -1x = 0 + -300 Combine like terms: 0 + -300 = -300 -1x = -300 Divide each side by '-1'. x = 300 Simplifying x = 300Subproblem 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 = {300, 600}
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