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Simplifying 0 = x2 + 500x + -60000 Reorder the terms: 0 = -60000 + 500x + x2 Solving 0 = -60000 + 500x + x2 Solving for variable 'x'. Combine like terms: 0 + 60000 = 60000 60000 + -500x + -1x2 = -60000 + 500x + x2 + 60000 + -500x + -1x2 Reorder the terms: 60000 + -500x + -1x2 = -60000 + 60000 + 500x + -500x + x2 + -1x2 Combine like terms: -60000 + 60000 = 0 60000 + -500x + -1x2 = 0 + 500x + -500x + x2 + -1x2 60000 + -500x + -1x2 = 500x + -500x + x2 + -1x2 Combine like terms: 500x + -500x = 0 60000 + -500x + -1x2 = 0 + x2 + -1x2 60000 + -500x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60000 + -500x + -1x2 = 0 Factor a trinomial. (100 + -1x)(600 + x) = 0Subproblem 1
Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100Subproblem 2
Set the factor '(600 + x)' equal to zero and attempt to solve: Simplifying 600 + x = 0 Solving 600 + x = 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 + x = 0 + -600 Combine like terms: 600 + -600 = 0 0 + x = 0 + -600 x = 0 + -600 Combine like terms: 0 + -600 = -600 x = -600 Simplifying x = -600Solution
x = {100, -600}
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