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Simplifying 900 + -1q2 = 10q + 300 Reorder the terms: 900 + -1q2 = 300 + 10q Solving 900 + -1q2 = 300 + 10q Solving for variable 'q'. Reorder the terms: 900 + -300 + -10q + -1q2 = 300 + 10q + -300 + -10q Combine like terms: 900 + -300 = 600 600 + -10q + -1q2 = 300 + 10q + -300 + -10q Reorder the terms: 600 + -10q + -1q2 = 300 + -300 + 10q + -10q Combine like terms: 300 + -300 = 0 600 + -10q + -1q2 = 0 + 10q + -10q 600 + -10q + -1q2 = 10q + -10q Combine like terms: 10q + -10q = 0 600 + -10q + -1q2 = 0 Factor a trinomial. (20 + -1q)(30 + q) = 0Subproblem 1
Set the factor '(20 + -1q)' equal to zero and attempt to solve: Simplifying 20 + -1q = 0 Solving 20 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1q = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1q = 0 + -20 -1q = 0 + -20 Combine like terms: 0 + -20 = -20 -1q = -20 Divide each side by '-1'. q = 20 Simplifying q = 20Subproblem 2
Set the factor '(30 + q)' equal to zero and attempt to solve: Simplifying 30 + q = 0 Solving 30 + q = 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 + q = 0 + -30 Combine like terms: 30 + -30 = 0 0 + q = 0 + -30 q = 0 + -30 Combine like terms: 0 + -30 = -30 q = -30 Simplifying q = -30Solution
q = {20, -30}
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