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Simplifying 48q2 + 52q + -16 = 0 Reorder the terms: -16 + 52q + 48q2 = 0 Solving -16 + 52q + 48q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 13q + 12q2) = 0 Factor a trinomial. 4((-4 + -3q)(1 + -4q)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -3q)' equal to zero and attempt to solve: Simplifying -4 + -3q = 0 Solving -4 + -3q = 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 + -3q = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3q = 0 + 4 -3q = 0 + 4 Combine like terms: 0 + 4 = 4 -3q = 4 Divide each side by '-3'. q = -1.333333333 Simplifying q = -1.333333333Subproblem 2
Set the factor '(1 + -4q)' equal to zero and attempt to solve: Simplifying 1 + -4q = 0 Solving 1 + -4q = 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 + -4q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4q = 0 + -1 -4q = 0 + -1 Combine like terms: 0 + -1 = -1 -4q = -1 Divide each side by '-4'. q = 0.25 Simplifying q = 0.25Solution
q = {-1.333333333, 0.25}
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