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Simplifying 30q2 + 9q + -12 = 0 Reorder the terms: -12 + 9q + 30q2 = 0 Solving -12 + 9q + 30q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3q + 10q2) = 0 Factor a trinomial. 3((-4 + -5q)(1 + -2q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -5q)' equal to zero and attempt to solve: Simplifying -4 + -5q = 0 Solving -4 + -5q = 0 Move all terms containing q to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5q = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5q = 0 + 4 -5q = 0 + 4 Combine like terms: 0 + 4 = 4 -5q = 4 Divide each side by '-5'. q = -0.8 Simplifying q = -0.8Subproblem 2
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 = 0.5Solution
q = {-0.8, 0.5}
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