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Simplifying -85 = q2 + 22q Reorder the terms: -85 = 22q + q2 Solving -85 = 22q + q2 Solving for variable 'q'. Reorder the terms: -85 + -22q + -1q2 = 22q + -22q + q2 + -1q2 Combine like terms: 22q + -22q = 0 -85 + -22q + -1q2 = 0 + q2 + -1q2 -85 + -22q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -85 + -22q + -1q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(85 + 22q + q2) = 0 Factor a trinomial. -1((17 + q)(5 + q)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + q)' equal to zero and attempt to solve: Simplifying 17 + q = 0 Solving 17 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + q = 0 + -17 Combine like terms: 17 + -17 = 0 0 + q = 0 + -17 q = 0 + -17 Combine like terms: 0 + -17 = -17 q = -17 Simplifying q = -17Subproblem 2
Set the factor '(5 + q)' equal to zero and attempt to solve: Simplifying 5 + q = 0 Solving 5 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + q = 0 + -5 q = 0 + -5 Combine like terms: 0 + -5 = -5 q = -5 Simplifying q = -5Solution
q = {-17, -5}
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