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Simplifying 8q2 + -4q = 7q2 + -7q + 10 Reorder the terms: -4q + 8q2 = 7q2 + -7q + 10 Reorder the terms: -4q + 8q2 = 10 + -7q + 7q2 Solving -4q + 8q2 = 10 + -7q + 7q2 Solving for variable 'q'. Reorder the terms: -10 + -4q + 7q + 8q2 + -7q2 = 10 + -7q + 7q2 + -10 + 7q + -7q2 Combine like terms: -4q + 7q = 3q -10 + 3q + 8q2 + -7q2 = 10 + -7q + 7q2 + -10 + 7q + -7q2 Combine like terms: 8q2 + -7q2 = 1q2 -10 + 3q + 1q2 = 10 + -7q + 7q2 + -10 + 7q + -7q2 Reorder the terms: -10 + 3q + 1q2 = 10 + -10 + -7q + 7q + 7q2 + -7q2 Combine like terms: 10 + -10 = 0 -10 + 3q + 1q2 = 0 + -7q + 7q + 7q2 + -7q2 -10 + 3q + 1q2 = -7q + 7q + 7q2 + -7q2 Combine like terms: -7q + 7q = 0 -10 + 3q + 1q2 = 0 + 7q2 + -7q2 -10 + 3q + 1q2 = 7q2 + -7q2 Combine like terms: 7q2 + -7q2 = 0 -10 + 3q + 1q2 = 0 Factor a trinomial. (-5 + -1q)(2 + -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 '(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 = {-5, 2}
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