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Simplifying 8q2 + -3q = 7q2 + -8q + 36 Reorder the terms: -3q + 8q2 = 7q2 + -8q + 36 Reorder the terms: -3q + 8q2 = 36 + -8q + 7q2 Solving -3q + 8q2 = 36 + -8q + 7q2 Solving for variable 'q'. Reorder the terms: -36 + -3q + 8q + 8q2 + -7q2 = 36 + -8q + 7q2 + -36 + 8q + -7q2 Combine like terms: -3q + 8q = 5q -36 + 5q + 8q2 + -7q2 = 36 + -8q + 7q2 + -36 + 8q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -36 + 5q + 1q2 = 36 + -8q + 7q2 + -36 + 8q + -7q2 Reorder the terms: -36 + 5q + 1q2 = 36 + -36 + -8q + 8q + 7q2 + -7q2 Combine like terms: 36 + -36 = 0 -36 + 5q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2 -36 + 5q + 1q2 = -8q + 8q + 7q2 + -7q2 Combine like terms: -8q + 8q = 0 -36 + 5q + 1q2 = 0 + 7q2 + -7q2 -36 + 5q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -36 + 5q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(4 + -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 '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 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 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4Solution
q = {-9, 4}
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