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Simplifying 8q2 + -5q = 7q2 + -8q + 54 Reorder the terms: -5q + 8q2 = 7q2 + -8q + 54 Reorder the terms: -5q + 8q2 = 54 + -8q + 7q2 Solving -5q + 8q2 = 54 + -8q + 7q2 Solving for variable 'q'. Reorder the terms: -54 + -5q + 8q + 8q2 + -7q2 = 54 + -8q + 7q2 + -54 + 8q + -7q2 Combine like terms: -5q + 8q = 3q -54 + 3q + 8q2 + -7q2 = 54 + -8q + 7q2 + -54 + 8q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -54 + 3q + 1q2 = 54 + -8q + 7q2 + -54 + 8q + -7q2 Reorder the terms: -54 + 3q + 1q2 = 54 + -54 + -8q + 8q + 7q2 + -7q2 Combine like terms: 54 + -54 = 0 -54 + 3q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2 -54 + 3q + 1q2 = -8q + 8q + 7q2 + -7q2 Combine like terms: -8q + 8q = 0 -54 + 3q + 1q2 = 0 + 7q2 + -7q2 -54 + 3q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -54 + 3q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(6 + -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 '(6 + -1q)' equal to zero and attempt to solve: Simplifying 6 + -1q = 0 Solving 6 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1q = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1q = 0 + -6 -1q = 0 + -6 Combine like terms: 0 + -6 = -6 -1q = -6 Divide each side by '-1'. q = 6 Simplifying q = 6Solution
q = {-9, 6}
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