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Simplifying 8q2 + -5q + -7q2 + 9q + -32 = 0 Reorder the terms: -32 + -5q + 9q + 8q2 + -7q2 = 0 Combine like terms: -5q + 9q = 4q -32 + 4q + 8q2 + -7q2 = 0 Combine like terms: 8q2 + -7q2 = 1q2 -32 + 4q + 1q2 = 0 Solving -32 + 4q + 1q2 = 0 Solving for variable 'q'. Factor a trinomial. (-8 + -1q)(4 + -1q) = 0Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve: Simplifying -8 + -1q = 0 Solving -8 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1q = 0 + 8 -1q = 0 + 8 Combine like terms: 0 + 8 = 8 -1q = 8 Divide each side by '-1'. q = -8 Simplifying q = -8Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4Solution
q = {-8, 4}
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