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Simplifying 160q = -1q2 + 8000 Reorder the terms: 160q = 8000 + -1q2 Solving 160q = 8000 + -1q2 Solving for variable 'q'. Reorder the terms: -8000 + 160q + q2 = 8000 + -1q2 + -8000 + q2 Reorder the terms: -8000 + 160q + q2 = 8000 + -8000 + -1q2 + q2 Combine like terms: 8000 + -8000 = 0 -8000 + 160q + q2 = 0 + -1q2 + q2 -8000 + 160q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -8000 + 160q + q2 = 0 Factor a trinomial. (-200 + -1q)(40 + -1q) = 0Subproblem 1
Set the factor '(-200 + -1q)' equal to zero and attempt to solve: Simplifying -200 + -1q = 0 Solving -200 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + -1q = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -1q = 0 + 200 -1q = 0 + 200 Combine like terms: 0 + 200 = 200 -1q = 200 Divide each side by '-1'. q = -200 Simplifying q = -200Subproblem 2
Set the factor '(40 + -1q)' equal to zero and attempt to solve: Simplifying 40 + -1q = 0 Solving 40 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1q = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1q = 0 + -40 -1q = 0 + -40 Combine like terms: 0 + -40 = -40 -1q = -40 Divide each side by '-1'. q = 40 Simplifying q = 40Solution
q = {-200, 40}
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