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Simplifying 50q = -1q2 + 8400 Reorder the terms: 50q = 8400 + -1q2 Solving 50q = 8400 + -1q2 Solving for variable 'q'. Reorder the terms: -8400 + 50q + q2 = 8400 + -1q2 + -8400 + q2 Reorder the terms: -8400 + 50q + q2 = 8400 + -8400 + -1q2 + q2 Combine like terms: 8400 + -8400 = 0 -8400 + 50q + q2 = 0 + -1q2 + q2 -8400 + 50q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -8400 + 50q + q2 = 0 Factor a trinomial. (-120 + -1q)(70 + -1q) = 0Subproblem 1
Set the factor '(-120 + -1q)' equal to zero and attempt to solve: Simplifying -120 + -1q = 0 Solving -120 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + -1q = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -1q = 0 + 120 -1q = 0 + 120 Combine like terms: 0 + 120 = 120 -1q = 120 Divide each side by '-1'. q = -120 Simplifying q = -120Subproblem 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 = {-120, 70}
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