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Simplifying (2 + -1w)(2w + -9) = 0 Reorder the terms: (2 + -1w)(-9 + 2w) = 0 Multiply (2 + -1w) * (-9 + 2w) (2(-9 + 2w) + -1w * (-9 + 2w)) = 0 ((-9 * 2 + 2w * 2) + -1w * (-9 + 2w)) = 0 ((-18 + 4w) + -1w * (-9 + 2w)) = 0 (-18 + 4w + (-9 * -1w + 2w * -1w)) = 0 (-18 + 4w + (9w + -2w2)) = 0 Combine like terms: 4w + 9w = 13w (-18 + 13w + -2w2) = 0 Solving -18 + 13w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + 2w)(2 + -1w) = 0Subproblem 1
Set the factor '(-9 + 2w)' equal to zero and attempt to solve: Simplifying -9 + 2w = 0 Solving -9 + 2w = 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 + 2w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2w = 0 + 9 2w = 0 + 9 Combine like terms: 0 + 9 = 9 2w = 9 Divide each side by '2'. w = 4.5 Simplifying w = 4.5Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {4.5, 2}
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