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Simplifying 30q = -1q2 + 7000 Reorder the terms: 30q = 7000 + -1q2 Solving 30q = 7000 + -1q2 Solving for variable 'q'. Reorder the terms: -7000 + 30q + q2 = 7000 + -1q2 + -7000 + q2 Reorder the terms: -7000 + 30q + q2 = 7000 + -7000 + -1q2 + q2 Combine like terms: 7000 + -7000 = 0 -7000 + 30q + q2 = 0 + -1q2 + q2 -7000 + 30q + q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -7000 + 30q + q2 = 0 Factor a trinomial. (-100 + -1q)(70 + -1q) = 0Subproblem 1
Set the factor '(-100 + -1q)' equal to zero and attempt to solve: Simplifying -100 + -1q = 0 Solving -100 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + -1q = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1q = 0 + 100 -1q = 0 + 100 Combine like terms: 0 + 100 = 100 -1q = 100 Divide each side by '-1'. q = -100 Simplifying q = -100Subproblem 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 = {-100, 70}
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