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Simplifying 6q2 + -2q = 5q2 + -4q + 63 Reorder the terms: -2q + 6q2 = 5q2 + -4q + 63 Reorder the terms: -2q + 6q2 = 63 + -4q + 5q2 Solving -2q + 6q2 = 63 + -4q + 5q2 Solving for variable 'q'. Reorder the terms: -63 + -2q + 4q + 6q2 + -5q2 = 63 + -4q + 5q2 + -63 + 4q + -5q2 Combine like terms: -2q + 4q = 2q -63 + 2q + 6q2 + -5q2 = 63 + -4q + 5q2 + -63 + 4q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -63 + 2q + 1q2 = 63 + -4q + 5q2 + -63 + 4q + -5q2 Reorder the terms: -63 + 2q + 1q2 = 63 + -63 + -4q + 4q + 5q2 + -5q2 Combine like terms: 63 + -63 = 0 -63 + 2q + 1q2 = 0 + -4q + 4q + 5q2 + -5q2 -63 + 2q + 1q2 = -4q + 4q + 5q2 + -5q2 Combine like terms: -4q + 4q = 0 -63 + 2q + 1q2 = 0 + 5q2 + -5q2 -63 + 2q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -63 + 2q + 1q2 = 0 Factor a trinomial. (-9 + -1q)(7 + -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 '(7 + -1q)' equal to zero and attempt to solve: Simplifying 7 + -1q = 0 Solving 7 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1q = 0 + -7 -1q = 0 + -7 Combine like terms: 0 + -7 = -7 -1q = -7 Divide each side by '-1'. q = 7 Simplifying q = 7Solution
q = {-9, 7}
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