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Simplifying 9q2 + -5q = 8q2 + -9q + 45 Reorder the terms: -5q + 9q2 = 8q2 + -9q + 45 Reorder the terms: -5q + 9q2 = 45 + -9q + 8q2 Solving -5q + 9q2 = 45 + -9q + 8q2 Solving for variable 'q'. Reorder the terms: -45 + -5q + 9q + 9q2 + -8q2 = 45 + -9q + 8q2 + -45 + 9q + -8q2 Combine like terms: -5q + 9q = 4q -45 + 4q + 9q2 + -8q2 = 45 + -9q + 8q2 + -45 + 9q + -8q2 Combine like terms: 9q2 + -8q2 = 1q2 -45 + 4q + 1q2 = 45 + -9q + 8q2 + -45 + 9q + -8q2 Reorder the terms: -45 + 4q + 1q2 = 45 + -45 + -9q + 9q + 8q2 + -8q2 Combine like terms: 45 + -45 = 0 -45 + 4q + 1q2 = 0 + -9q + 9q + 8q2 + -8q2 -45 + 4q + 1q2 = -9q + 9q + 8q2 + -8q2 Combine like terms: -9q + 9q = 0 -45 + 4q + 1q2 = 0 + 8q2 + -8q2 -45 + 4q + 1q2 = 8q2 + -8q2 Combine like terms: 8q2 + -8q2 = 0 -45 + 4q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(5 + -1q) = 0Subproblem 1
Set the factor '(-9 + -1q)' equal to zero and attempt to solve: Simplifying -9 + -1q = 0 Solving -9 + -1q = 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 + -1q = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1q = 0 + 9 -1q = 0 + 9 Combine like terms: 0 + 9 = 9 -1q = 9 Divide each side by '-1'. q = -9 Simplifying q = -9Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve: Simplifying 5 + -1q = 0 Solving 5 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1q = 0 + -5 -1q = 0 + -5 Combine like terms: 0 + -5 = -5 -1q = -5 Divide each side by '-1'. q = 5 Simplifying q = 5Solution
q = {-9, 5}
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