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Simplifying q2 + 10q + 25 = -11q2 + 96q + 365 Reorder the terms: 25 + 10q + q2 = -11q2 + 96q + 365 Reorder the terms: 25 + 10q + q2 = 365 + 96q + -11q2 Solving 25 + 10q + q2 = 365 + 96q + -11q2 Solving for variable 'q'. Reorder the terms: 25 + -365 + 10q + -96q + q2 + 11q2 = 365 + 96q + -11q2 + -365 + -96q + 11q2 Combine like terms: 25 + -365 = -340 -340 + 10q + -96q + q2 + 11q2 = 365 + 96q + -11q2 + -365 + -96q + 11q2 Combine like terms: 10q + -96q = -86q -340 + -86q + q2 + 11q2 = 365 + 96q + -11q2 + -365 + -96q + 11q2 Combine like terms: q2 + 11q2 = 12q2 -340 + -86q + 12q2 = 365 + 96q + -11q2 + -365 + -96q + 11q2 Reorder the terms: -340 + -86q + 12q2 = 365 + -365 + 96q + -96q + -11q2 + 11q2 Combine like terms: 365 + -365 = 0 -340 + -86q + 12q2 = 0 + 96q + -96q + -11q2 + 11q2 -340 + -86q + 12q2 = 96q + -96q + -11q2 + 11q2 Combine like terms: 96q + -96q = 0 -340 + -86q + 12q2 = 0 + -11q2 + 11q2 -340 + -86q + 12q2 = -11q2 + 11q2 Combine like terms: -11q2 + 11q2 = 0 -340 + -86q + 12q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-170 + -43q + 6q2) = 0 Factor a trinomial. 2((-17 + -6q)(10 + -1q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + -6q)' equal to zero and attempt to solve: Simplifying -17 + -6q = 0 Solving -17 + -6q = 0 Move all terms containing q to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -6q = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -6q = 0 + 17 -6q = 0 + 17 Combine like terms: 0 + 17 = 17 -6q = 17 Divide each side by '-6'. q = -2.833333333 Simplifying q = -2.833333333Subproblem 2
Set the factor '(10 + -1q)' equal to zero and attempt to solve: Simplifying 10 + -1q = 0 Solving 10 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1q = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1q = 0 + -10 -1q = 0 + -10 Combine like terms: 0 + -10 = -10 -1q = -10 Divide each side by '-1'. q = 10 Simplifying q = 10Solution
q = {-2.833333333, 10}
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