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Simplifying (2q + -1)(5q + 2) = 0 Reorder the terms: (-1 + 2q)(5q + 2) = 0 Reorder the terms: (-1 + 2q)(2 + 5q) = 0 Multiply (-1 + 2q) * (2 + 5q) (-1(2 + 5q) + 2q * (2 + 5q)) = 0 ((2 * -1 + 5q * -1) + 2q * (2 + 5q)) = 0 ((-2 + -5q) + 2q * (2 + 5q)) = 0 (-2 + -5q + (2 * 2q + 5q * 2q)) = 0 (-2 + -5q + (4q + 10q2)) = 0 Combine like terms: -5q + 4q = -1q (-2 + -1q + 10q2) = 0 Solving -2 + -1q + 10q2 = 0 Solving for variable 'q'. Factor a trinomial. (-2 + -5q)(1 + -2q) = 0Subproblem 1
Set the factor '(-2 + -5q)' equal to zero and attempt to solve: Simplifying -2 + -5q = 0 Solving -2 + -5q = 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 + -5q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5q = 0 + 2 -5q = 0 + 2 Combine like terms: 0 + 2 = 2 -5q = 2 Divide each side by '-5'. q = -0.4 Simplifying q = -0.4Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve: Simplifying 1 + -2q = 0 Solving 1 + -2q = 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 + -2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2q = 0 + -1 -2q = 0 + -1 Combine like terms: 0 + -1 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5Solution
q = {-0.4, 0.5}
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