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Simplifying 72q2 + -12q + -40 = 0 Reorder the terms: -40 + -12q + 72q2 = 0 Solving -40 + -12q + 72q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -3q + 18q2) = 0 Factor a trinomial. 4((-2 + -3q)(5 + -6q)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -3q)' equal to zero and attempt to solve: Simplifying -2 + -3q = 0 Solving -2 + -3q = 0 Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3q = 0 + 2 -3q = 0 + 2 Combine like terms: 0 + 2 = 2 -3q = 2 Divide each side by '-3'. q = -0.6666666667 Simplifying q = -0.6666666667Subproblem 2
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 = 0.8333333333Solution
q = {-0.6666666667, 0.8333333333}
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