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Simplifying -114q + -120 + 36q2 = 0 Reorder the terms: -120 + -114q + 36q2 = 0 Solving -120 + -114q + 36q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + -19q + 6q2) = 0 Factor a trinomial. 6((-5 + -6q)(4 + -1q)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + -6q)' equal to zero and attempt to solve: Simplifying -5 + -6q = 0 Solving -5 + -6q = 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 + -6q = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6q = 0 + 5 -6q = 0 + 5 Combine like terms: 0 + 5 = 5 -6q = 5 Divide each side by '-6'. q = -0.8333333333 Simplifying q = -0.8333333333Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4Solution
q = {-0.8333333333, 4}
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