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Simplifying -2Q2 + 20Q + -32 = 0 Reorder the terms: -32 + 20Q + -2Q2 = 0 Solving -32 + 20Q + -2Q2 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 10Q + -1Q2) = 0 Factor a trinomial. 2((-8 + Q)(2 + -1Q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + Q)' equal to zero and attempt to solve: Simplifying -8 + Q = 0 Solving -8 + Q = 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 + Q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + Q = 0 + 8 Q = 0 + 8 Combine like terms: 0 + 8 = 8 Q = 8 Simplifying Q = 8Subproblem 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 = {8, 2}
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