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Simplifying 0 = q2 + 25q + 100 Reorder the terms: 0 = 100 + 25q + q2 Solving 0 = 100 + 25q + q2 Solving for variable 'q'. Combine like terms: 0 + -100 = -100 -100 + -25q + -1q2 = 100 + 25q + q2 + -100 + -25q + -1q2 Reorder the terms: -100 + -25q + -1q2 = 100 + -100 + 25q + -25q + q2 + -1q2 Combine like terms: 100 + -100 = 0 -100 + -25q + -1q2 = 0 + 25q + -25q + q2 + -1q2 -100 + -25q + -1q2 = 25q + -25q + q2 + -1q2 Combine like terms: 25q + -25q = 0 -100 + -25q + -1q2 = 0 + q2 + -1q2 -100 + -25q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 -100 + -25q + -1q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 25q + q2) = 0 Factor a trinomial. -1((20 + q)(5 + q)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + q)' equal to zero and attempt to solve: Simplifying 20 + q = 0 Solving 20 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + q = 0 + -20 Combine like terms: 20 + -20 = 0 0 + q = 0 + -20 q = 0 + -20 Combine like terms: 0 + -20 = -20 q = -20 Simplifying q = -20Subproblem 2
Set the factor '(5 + q)' equal to zero and attempt to solve: Simplifying 5 + q = 0 Solving 5 + q = 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 + q = 0 + -5 Combine like terms: 5 + -5 = 0 0 + q = 0 + -5 q = 0 + -5 Combine like terms: 0 + -5 = -5 q = -5 Simplifying q = -5Solution
q = {-20, -5}
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