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Simplifying 84q = -32q2 + -54 Reorder the terms: 84q = -54 + -32q2 Solving 84q = -54 + -32q2 Solving for variable 'q'. Reorder the terms: 54 + 84q + 32q2 = -54 + -32q2 + 54 + 32q2 Reorder the terms: 54 + 84q + 32q2 = -54 + 54 + -32q2 + 32q2 Combine like terms: -54 + 54 = 0 54 + 84q + 32q2 = 0 + -32q2 + 32q2 54 + 84q + 32q2 = -32q2 + 32q2 Combine like terms: -32q2 + 32q2 = 0 54 + 84q + 32q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 42q + 16q2) = 0 Factor a trinomial. 2((3 + 2q)(9 + 8q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2q)' equal to zero and attempt to solve: Simplifying 3 + 2q = 0 Solving 3 + 2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2q = 0 + -3 2q = 0 + -3 Combine like terms: 0 + -3 = -3 2q = -3 Divide each side by '2'. q = -1.5 Simplifying q = -1.5Subproblem 2
Set the factor '(9 + 8q)' equal to zero and attempt to solve: Simplifying 9 + 8q = 0 Solving 9 + 8q = 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 + 8q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8q = 0 + -9 8q = 0 + -9 Combine like terms: 0 + -9 = -9 8q = -9 Divide each side by '8'. q = -1.125 Simplifying q = -1.125Solution
q = {-1.5, -1.125}
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