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Simplifying 5q(q + 2) = 40 Reorder the terms: 5q(2 + q) = 40 (2 * 5q + q * 5q) = 40 (10q + 5q2) = 40 Solving 10q + 5q2 = 40 Solving for variable 'q'. Reorder the terms: -40 + 10q + 5q2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 10q + 5q2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + 2q + q2) = 0 Factor a trinomial. 5((-4 + -1q)(2 + -1q)) = 0 Ignore the factor 5.Subproblem 1
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 = -4Subproblem 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 = {-4, 2}
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