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Simplifying 6q2 + 2q = 5q2 + -5q + 18 Reorder the terms: 2q + 6q2 = 5q2 + -5q + 18 Reorder the terms: 2q + 6q2 = 18 + -5q + 5q2 Solving 2q + 6q2 = 18 + -5q + 5q2 Solving for variable 'q'. Reorder the terms: -18 + 2q + 5q + 6q2 + -5q2 = 18 + -5q + 5q2 + -18 + 5q + -5q2 Combine like terms: 2q + 5q = 7q -18 + 7q + 6q2 + -5q2 = 18 + -5q + 5q2 + -18 + 5q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -18 + 7q + 1q2 = 18 + -5q + 5q2 + -18 + 5q + -5q2 Reorder the terms: -18 + 7q + 1q2 = 18 + -18 + -5q + 5q + 5q2 + -5q2 Combine like terms: 18 + -18 = 0 -18 + 7q + 1q2 = 0 + -5q + 5q + 5q2 + -5q2 -18 + 7q + 1q2 = -5q + 5q + 5q2 + -5q2 Combine like terms: -5q + 5q = 0 -18 + 7q + 1q2 = 0 + 5q2 + -5q2 -18 + 7q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -18 + 7q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(2 + -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 '(2 + -1q)' equal to zero and attempt to solve: Simplifying 2 + -1q = 0 Solving 2 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1q = 0 + -2 -1q = 0 + -2 Combine like terms: 0 + -2 = -2 -1q = -2 Divide each side by '-1'. q = 2 Simplifying q = 2Solution
q = {-9, 2}
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