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Simplifying 12q2 = 17q + 5 Reorder the terms: 12q2 = 5 + 17q Solving 12q2 = 5 + 17q Solving for variable 'q'. Reorder the terms: -5 + -17q + 12q2 = 5 + 17q + -5 + -17q Reorder the terms: -5 + -17q + 12q2 = 5 + -5 + 17q + -17q Combine like terms: 5 + -5 = 0 -5 + -17q + 12q2 = 0 + 17q + -17q -5 + -17q + 12q2 = 17q + -17q Combine like terms: 17q + -17q = 0 -5 + -17q + 12q2 = 0 Factor a trinomial. (-1 + -4q)(5 + -3q) = 0Subproblem 1
Set the factor '(-1 + -4q)' equal to zero and attempt to solve: Simplifying -1 + -4q = 0 Solving -1 + -4q = 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 + -4q = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4q = 0 + 1 -4q = 0 + 1 Combine like terms: 0 + 1 = 1 -4q = 1 Divide each side by '-4'. q = -0.25 Simplifying q = -0.25Subproblem 2
Set the factor '(5 + -3q)' equal to zero and attempt to solve: Simplifying 5 + -3q = 0 Solving 5 + -3q = 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 + -3q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3q = 0 + -5 -3q = 0 + -5 Combine like terms: 0 + -5 = -5 -3q = -5 Divide each side by '-3'. q = 1.666666667 Simplifying q = 1.666666667Solution
q = {-0.25, 1.666666667}
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