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Simplifying 2(q2 + -20) + 17q = -10q2 Reorder the terms: 2(-20 + q2) + 17q = -10q2 (-20 * 2 + q2 * 2) + 17q = -10q2 (-40 + 2q2) + 17q = -10q2 Reorder the terms: -40 + 17q + 2q2 = -10q2 Solving -40 + 17q + 2q2 = -10q2 Solving for variable 'q'. Combine like terms: 2q2 + 10q2 = 12q2 -40 + 17q + 12q2 = -10q2 + 10q2 Combine like terms: -10q2 + 10q2 = 0 -40 + 17q + 12q2 = 0 Factor a trinomial. (-8 + -3q)(5 + -4q) = 0Subproblem 1
Set the factor '(-8 + -3q)' equal to zero and attempt to solve: Simplifying -8 + -3q = 0 Solving -8 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3q = 0 + 8 -3q = 0 + 8 Combine like terms: 0 + 8 = 8 -3q = 8 Divide each side by '-3'. q = -2.666666667 Simplifying q = -2.666666667Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve: Simplifying 5 + -4q = 0 Solving 5 + -4q = 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 + -4q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4q = 0 + -5 -4q = 0 + -5 Combine like terms: 0 + -5 = -5 -4q = -5 Divide each side by '-4'. q = 1.25 Simplifying q = 1.25Solution
q = {-2.666666667, 1.25}
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