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Simplifying 0 = x2 + -1650x + 650000 Reorder the terms: 0 = 650000 + -1650x + x2 Solving 0 = 650000 + -1650x + x2 Solving for variable 'x'. Combine like terms: 0 + -650000 = -650000 -650000 + 1650x + -1x2 = 650000 + -1650x + x2 + -650000 + 1650x + -1x2 Reorder the terms: -650000 + 1650x + -1x2 = 650000 + -650000 + -1650x + 1650x + x2 + -1x2 Combine like terms: 650000 + -650000 = 0 -650000 + 1650x + -1x2 = 0 + -1650x + 1650x + x2 + -1x2 -650000 + 1650x + -1x2 = -1650x + 1650x + x2 + -1x2 Combine like terms: -1650x + 1650x = 0 -650000 + 1650x + -1x2 = 0 + x2 + -1x2 -650000 + 1650x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -650000 + 1650x + -1x2 = 0 Factor a trinomial. (-1000 + x)(650 + -1x) = 0Subproblem 1
Set the factor '(-1000 + x)' equal to zero and attempt to solve: Simplifying -1000 + x = 0 Solving -1000 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1000' to each side of the equation. -1000 + 1000 + x = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + x = 0 + 1000 x = 0 + 1000 Combine like terms: 0 + 1000 = 1000 x = 1000 Simplifying x = 1000Subproblem 2
Set the factor '(650 + -1x)' equal to zero and attempt to solve: Simplifying 650 + -1x = 0 Solving 650 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-650' to each side of the equation. 650 + -650 + -1x = 0 + -650 Combine like terms: 650 + -650 = 0 0 + -1x = 0 + -650 -1x = 0 + -650 Combine like terms: 0 + -650 = -650 -1x = -650 Divide each side by '-1'. x = 650 Simplifying x = 650Solution
x = {1000, 650}
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