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Simplifying 6q2 + -2q = 5q2 + -7q + 14 Reorder the terms: -2q + 6q2 = 5q2 + -7q + 14 Reorder the terms: -2q + 6q2 = 14 + -7q + 5q2 Solving -2q + 6q2 = 14 + -7q + 5q2 Solving for variable 'q'. Reorder the terms: -14 + -2q + 7q + 6q2 + -5q2 = 14 + -7q + 5q2 + -14 + 7q + -5q2 Combine like terms: -2q + 7q = 5q -14 + 5q + 6q2 + -5q2 = 14 + -7q + 5q2 + -14 + 7q + -5q2 Combine like terms: 6q2 + -5q2 = 1q2 -14 + 5q + 1q2 = 14 + -7q + 5q2 + -14 + 7q + -5q2 Reorder the terms: -14 + 5q + 1q2 = 14 + -14 + -7q + 7q + 5q2 + -5q2 Combine like terms: 14 + -14 = 0 -14 + 5q + 1q2 = 0 + -7q + 7q + 5q2 + -5q2 -14 + 5q + 1q2 = -7q + 7q + 5q2 + -5q2 Combine like terms: -7q + 7q = 0 -14 + 5q + 1q2 = 0 + 5q2 + -5q2 -14 + 5q + 1q2 = 5q2 + -5q2 Combine like terms: 5q2 + -5q2 = 0 -14 + 5q + 1q2 = 0 Factor a trinomial. (-7 + -1q)(2 + -1q) = 0Subproblem 1
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 = -7Subproblem 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 = {-7, 2}
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