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Simplifying -126q + 81 + -72q2 = 0 Reorder the terms: 81 + -126q + -72q2 = 0 Solving 81 + -126q + -72q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '9'. 9(9 + -14q + -8q2) = 0 Factor a trinomial. 9((1 + -2q)(9 + 4q)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -2q)' equal to zero and attempt to solve: Simplifying 1 + -2q = 0 Solving 1 + -2q = 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 + -2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2q = 0 + -1 -2q = 0 + -1 Combine like terms: 0 + -1 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5Subproblem 2
Set the factor '(9 + 4q)' equal to zero and attempt to solve: Simplifying 9 + 4q = 0 Solving 9 + 4q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4q = 0 + -9 4q = 0 + -9 Combine like terms: 0 + -9 = -9 4q = -9 Divide each side by '4'. q = -2.25 Simplifying q = -2.25Solution
q = {0.5, -2.25}
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