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Simplifying 6q2 + 5 = -17q Reorder the terms: 5 + 6q2 = -17q Solving 5 + 6q2 = -17q Solving for variable 'q'. Reorder the terms: 5 + 17q + 6q2 = -17q + 17q Combine like terms: -17q + 17q = 0 5 + 17q + 6q2 = 0 Factor a trinomial. (5 + 2q)(1 + 3q) = 0Subproblem 1
Set the factor '(5 + 2q)' equal to zero and attempt to solve: Simplifying 5 + 2q = 0 Solving 5 + 2q = 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 + 2q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2q = 0 + -5 2q = 0 + -5 Combine like terms: 0 + -5 = -5 2q = -5 Divide each side by '2'. q = -2.5 Simplifying q = -2.5Subproblem 2
Set the factor '(1 + 3q)' equal to zero and attempt to solve: Simplifying 1 + 3q = 0 Solving 1 + 3q = 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 + 3q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3q = 0 + -1 3q = 0 + -1 Combine like terms: 0 + -1 = -1 3q = -1 Divide each side by '3'. q = -0.3333333333 Simplifying q = -0.3333333333Solution
q = {-2.5, -0.3333333333}
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