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Simplifying -170q = 90 + -20q2 Solving -170q = 90 + -20q2 Solving for variable 'q'. Reorder the terms: -90 + -170q + 20q2 = 90 + -20q2 + -90 + 20q2 Reorder the terms: -90 + -170q + 20q2 = 90 + -90 + -20q2 + 20q2 Combine like terms: 90 + -90 = 0 -90 + -170q + 20q2 = 0 + -20q2 + 20q2 -90 + -170q + 20q2 = -20q2 + 20q2 Combine like terms: -20q2 + 20q2 = 0 -90 + -170q + 20q2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-9 + -17q + 2q2) = 0 Factor a trinomial. 10((-1 + -2q)(9 + -1q)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1 + -2q)' equal to zero and attempt to solve: Simplifying -1 + -2q = 0 Solving -1 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2q = 0 + 1 -2q = 0 + 1 Combine like terms: 0 + 1 = 1 -2q = 1 Divide each side by '-2'. q = -0.5 Simplifying q = -0.5Subproblem 2
Set the factor '(9 + -1q)' equal to zero and attempt to solve: Simplifying 9 + -1q = 0 Solving 9 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1q = 0 + -9 -1q = 0 + -9 Combine like terms: 0 + -9 = -9 -1q = -9 Divide each side by '-1'. q = 9 Simplifying q = 9Solution
q = {-0.5, 9}
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