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Simplifying (4q + -1)(q + 5) = 0 Reorder the terms: (-1 + 4q)(q + 5) = 0 Reorder the terms: (-1 + 4q)(5 + q) = 0 Multiply (-1 + 4q) * (5 + q) (-1(5 + q) + 4q * (5 + q)) = 0 ((5 * -1 + q * -1) + 4q * (5 + q)) = 0 ((-5 + -1q) + 4q * (5 + q)) = 0 (-5 + -1q + (5 * 4q + q * 4q)) = 0 (-5 + -1q + (20q + 4q2)) = 0 Combine like terms: -1q + 20q = 19q (-5 + 19q + 4q2) = 0 Solving -5 + 19q + 4q2 = 0 Solving for variable 'q'. Factor a trinomial. (-5 + -1q)(1 + -4q) = 0Subproblem 1
Set the factor '(-5 + -1q)' equal to zero and attempt to solve: Simplifying -5 + -1q = 0 Solving -5 + -1q = 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 + -1q = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1q = 0 + 5 -1q = 0 + 5 Combine like terms: 0 + 5 = 5 -1q = 5 Divide each side by '-1'. q = -5 Simplifying q = -5Subproblem 2
Set the factor '(1 + -4q)' equal to zero and attempt to solve: Simplifying 1 + -4q = 0 Solving 1 + -4q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4q = 0 + -1 -4q = 0 + -1 Combine like terms: 0 + -1 = -1 -4q = -1 Divide each side by '-4'. q = 0.25 Simplifying q = 0.25Solution
q = {-5, 0.25}
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