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Simplifying 45q = -1q2 + 10000 Reorder the terms: 45q = 10000 + -1q2 Solving 45q = 10000 + -1q2 Solving for variable 'q'. Reorder the terms: -10000 + 45q + q2 = 10000 + -1q2 + -10000 + q2 Reorder the terms: -10000 + 45q + q2 = 10000 + -10000 + -1q2 + q2 Combine like terms: 10000 + -10000 = 0 -10000 + 45q + q2 = 0 + -1q2 + q2 -10000 + 45q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -10000 + 45q + q2 = 0 Factor a trinomial. (-125 + -1q)(80 + -1q) = 0Subproblem 1
Set the factor '(-125 + -1q)' equal to zero and attempt to solve: Simplifying -125 + -1q = 0 Solving -125 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + -1q = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -1q = 0 + 125 -1q = 0 + 125 Combine like terms: 0 + 125 = 125 -1q = 125 Divide each side by '-1'. q = -125 Simplifying q = -125Subproblem 2
Set the factor '(80 + -1q)' equal to zero and attempt to solve: Simplifying 80 + -1q = 0 Solving 80 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + -1q = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -1q = 0 + -80 -1q = 0 + -80 Combine like terms: 0 + -80 = -80 -1q = -80 Divide each side by '-1'. q = 80 Simplifying q = 80Solution
q = {-125, 80}
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