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Simplifying 24q + 3456 = 2q2 Reorder the terms: 3456 + 24q = 2q2 Solving 3456 + 24q = 2q2 Solving for variable 'q'. Combine like terms: 2q2 + -2q2 = 0 3456 + 24q + -2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1728 + 12q + -1q2) = 0 Factor a trinomial. 2((48 + -1q)(36 + q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -1q)' equal to zero and attempt to solve: Simplifying 48 + -1q = 0 Solving 48 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + -1q = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -1q = 0 + -48 -1q = 0 + -48 Combine like terms: 0 + -48 = -48 -1q = -48 Divide each side by '-1'. q = 48 Simplifying q = 48Subproblem 2
Set the factor '(36 + q)' equal to zero and attempt to solve: Simplifying 36 + q = 0 Solving 36 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + q = 0 + -36 Combine like terms: 36 + -36 = 0 0 + q = 0 + -36 q = 0 + -36 Combine like terms: 0 + -36 = -36 q = -36 Simplifying q = -36Solution
q = {48, -36}
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