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Simplifying q2 + 20q = -2q2 + 10q + 3000 Reorder the terms: 20q + q2 = -2q2 + 10q + 3000 Reorder the terms: 20q + q2 = 3000 + 10q + -2q2 Solving 20q + q2 = 3000 + 10q + -2q2 Solving for variable 'q'. Reorder the terms: -3000 + 20q + -10q + q2 + 2q2 = 3000 + 10q + -2q2 + -3000 + -10q + 2q2 Combine like terms: 20q + -10q = 10q -3000 + 10q + q2 + 2q2 = 3000 + 10q + -2q2 + -3000 + -10q + 2q2 Combine like terms: q2 + 2q2 = 3q2 -3000 + 10q + 3q2 = 3000 + 10q + -2q2 + -3000 + -10q + 2q2 Reorder the terms: -3000 + 10q + 3q2 = 3000 + -3000 + 10q + -10q + -2q2 + 2q2 Combine like terms: 3000 + -3000 = 0 -3000 + 10q + 3q2 = 0 + 10q + -10q + -2q2 + 2q2 -3000 + 10q + 3q2 = 10q + -10q + -2q2 + 2q2 Combine like terms: 10q + -10q = 0 -3000 + 10q + 3q2 = 0 + -2q2 + 2q2 -3000 + 10q + 3q2 = -2q2 + 2q2 Combine like terms: -2q2 + 2q2 = 0 -3000 + 10q + 3q2 = 0 Factor a trinomial. (-100 + -3q)(30 + -1q) = 0Subproblem 1
Set the factor '(-100 + -3q)' equal to zero and attempt to solve: Simplifying -100 + -3q = 0 Solving -100 + -3q = 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 + -3q = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -3q = 0 + 100 -3q = 0 + 100 Combine like terms: 0 + 100 = 100 -3q = 100 Divide each side by '-3'. q = -33.33333333 Simplifying q = -33.33333333Subproblem 2
Set the factor '(30 + -1q)' equal to zero and attempt to solve: Simplifying 30 + -1q = 0 Solving 30 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1q = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1q = 0 + -30 -1q = 0 + -30 Combine like terms: 0 + -30 = -30 -1q = -30 Divide each side by '-1'. q = 30 Simplifying q = 30Solution
q = {-33.33333333, 30}
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