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Simplifying (5w + -9)(1 + -1w) = 0 Reorder the terms: (-9 + 5w)(1 + -1w) = 0 Multiply (-9 + 5w) * (1 + -1w) (-9(1 + -1w) + 5w * (1 + -1w)) = 0 ((1 * -9 + -1w * -9) + 5w * (1 + -1w)) = 0 ((-9 + 9w) + 5w * (1 + -1w)) = 0 (-9 + 9w + (1 * 5w + -1w * 5w)) = 0 (-9 + 9w + (5w + -5w2)) = 0 Combine like terms: 9w + 5w = 14w (-9 + 14w + -5w2) = 0 Solving -9 + 14w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + 5w)(1 + -1w) = 0Subproblem 1
Set the factor '(-9 + 5w)' equal to zero and attempt to solve: Simplifying -9 + 5w = 0 Solving -9 + 5w = 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 + 5w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5w = 0 + 9 5w = 0 + 9 Combine like terms: 0 + 9 = 9 5w = 9 Divide each side by '5'. w = 1.8 Simplifying w = 1.8Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {1.8, 1}
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