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Simplifying 8q2 + -5q = 7q2 + -8q + 18 Reorder the terms: -5q + 8q2 = 7q2 + -8q + 18 Reorder the terms: -5q + 8q2 = 18 + -8q + 7q2 Solving -5q + 8q2 = 18 + -8q + 7q2 Solving for variable 'q'. Reorder the terms: -18 + -5q + 8q + 8q2 + -7q2 = 18 + -8q + 7q2 + -18 + 8q + -7q2 Combine like terms: -5q + 8q = 3q -18 + 3q + 8q2 + -7q2 = 18 + -8q + 7q2 + -18 + 8q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -18 + 3q + 1q2 = 18 + -8q + 7q2 + -18 + 8q + -7q2 Reorder the terms: -18 + 3q + 1q2 = 18 + -18 + -8q + 8q + 7q2 + -7q2 Combine like terms: 18 + -18 = 0 -18 + 3q + 1q2 = 0 + -8q + 8q + 7q2 + -7q2 -18 + 3q + 1q2 = -8q + 8q + 7q2 + -7q2 Combine like terms: -8q + 8q = 0 -18 + 3q + 1q2 = 0 + 7q2 + -7q2 -18 + 3q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -18 + 3q + 1q2 = 0 Factor a trinomial. (-6 + -1q)(3 + -1q) = 0Subproblem 1
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 = -6Subproblem 2
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 = 3Solution
q = {-6, 3}
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