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Simplifying q2 + -24 = 5q Reorder the terms: -24 + q2 = 5q Solving -24 + q2 = 5q Solving for variable 'q'. Reorder the terms: -24 + -5q + q2 = 5q + -5q Combine like terms: 5q + -5q = 0 -24 + -5q + q2 = 0 Factor a trinomial. (-3 + -1q)(8 + -1q) = 0Subproblem 1
Set the factor '(-3 + -1q)' equal to zero and attempt to solve: Simplifying -3 + -1q = 0 Solving -3 + -1q = 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 + -1q = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1q = 0 + 3 -1q = 0 + 3 Combine like terms: 0 + 3 = 3 -1q = 3 Divide each side by '-1'. q = -3 Simplifying q = -3Subproblem 2
Set the factor '(8 + -1q)' equal to zero and attempt to solve: Simplifying 8 + -1q = 0 Solving 8 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1q = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1q = 0 + -8 -1q = 0 + -8 Combine like terms: 0 + -8 = -8 -1q = -8 Divide each side by '-1'. q = 8 Simplifying q = 8Solution
q = {-3, 8}
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