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Simplifying 8q2 + -5q = 7q2 + -7q + 15 Reorder the terms: -5q + 8q2 = 7q2 + -7q + 15 Reorder the terms: -5q + 8q2 = 15 + -7q + 7q2 Solving -5q + 8q2 = 15 + -7q + 7q2 Solving for variable 'q'. Reorder the terms: -15 + -5q + 7q + 8q2 + -7q2 = 15 + -7q + 7q2 + -15 + 7q + -7q2 Combine like terms: -5q + 7q = 2q -15 + 2q + 8q2 + -7q2 = 15 + -7q + 7q2 + -15 + 7q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -15 + 2q + 1q2 = 15 + -7q + 7q2 + -15 + 7q + -7q2 Reorder the terms: -15 + 2q + 1q2 = 15 + -15 + -7q + 7q + 7q2 + -7q2 Combine like terms: 15 + -15 = 0 -15 + 2q + 1q2 = 0 + -7q + 7q + 7q2 + -7q2 -15 + 2q + 1q2 = -7q + 7q + 7q2 + -7q2 Combine like terms: -7q + 7q = 0 -15 + 2q + 1q2 = 0 + 7q2 + -7q2 -15 + 2q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -15 + 2q + 1q2 = 0 Factor a trinomial. (-5 + -1q)(3 + -1q) = 0Subproblem 1
Set the factor '(-5 + -1q)' equal to zero and attempt to solve: Simplifying -5 + -1q = 0 Solving -5 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1q = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1q = 0 + 5 -1q = 0 + 5 Combine like terms: 0 + 5 = 5 -1q = 5 Divide each side by '-1'. q = -5 Simplifying q = -5Subproblem 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 = {-5, 3}
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