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Simplifying 8q2 + 4q = 7q2 + -2q + 27 Reorder the terms: 4q + 8q2 = 7q2 + -2q + 27 Reorder the terms: 4q + 8q2 = 27 + -2q + 7q2 Solving 4q + 8q2 = 27 + -2q + 7q2 Solving for variable 'q'. Reorder the terms: -27 + 4q + 2q + 8q2 + -7q2 = 27 + -2q + 7q2 + -27 + 2q + -7q2 Combine like terms: 4q + 2q = 6q -27 + 6q + 8q2 + -7q2 = 27 + -2q + 7q2 + -27 + 2q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -27 + 6q + 1q2 = 27 + -2q + 7q2 + -27 + 2q + -7q2 Reorder the terms: -27 + 6q + 1q2 = 27 + -27 + -2q + 2q + 7q2 + -7q2 Combine like terms: 27 + -27 = 0 -27 + 6q + 1q2 = 0 + -2q + 2q + 7q2 + -7q2 -27 + 6q + 1q2 = -2q + 2q + 7q2 + -7q2 Combine like terms: -2q + 2q = 0 -27 + 6q + 1q2 = 0 + 7q2 + -7q2 -27 + 6q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -27 + 6q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(3 + -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 '(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 = {-9, 3}
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