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Simplifying (5w + -1)(9 + w) = 0 Reorder the terms: (-1 + 5w)(9 + w) = 0 Multiply (-1 + 5w) * (9 + w) (-1(9 + w) + 5w * (9 + w)) = 0 ((9 * -1 + w * -1) + 5w * (9 + w)) = 0 ((-9 + -1w) + 5w * (9 + w)) = 0 (-9 + -1w + (9 * 5w + w * 5w)) = 0 (-9 + -1w + (45w + 5w2)) = 0 Combine like terms: -1w + 45w = 44w (-9 + 44w + 5w2) = 0 Solving -9 + 44w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(1 + -5w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2Solution
w = {-9, 0.2}
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