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Simplifying 55q = -1q2 + 8750 Reorder the terms: 55q = 8750 + -1q2 Solving 55q = 8750 + -1q2 Solving for variable 'q'. Reorder the terms: -8750 + 55q + q2 = 8750 + -1q2 + -8750 + q2 Reorder the terms: -8750 + 55q + q2 = 8750 + -8750 + -1q2 + q2 Combine like terms: 8750 + -8750 = 0 -8750 + 55q + q2 = 0 + -1q2 + q2 -8750 + 55q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -8750 + 55q + q2 = 0 Factor a trinomial. (-125 + -1q)(70 + -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 '(70 + -1q)' equal to zero and attempt to solve: Simplifying 70 + -1q = 0 Solving 70 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1q = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1q = 0 + -70 -1q = 0 + -70 Combine like terms: 0 + -70 = -70 -1q = -70 Divide each side by '-1'. q = 70 Simplifying q = 70Solution
q = {-125, 70}
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