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Simplifying w2 + -5w = 18 + 2w Reorder the terms: -5w + w2 = 18 + 2w Solving -5w + w2 = 18 + 2w Solving for variable 'w'. Reorder the terms: -18 + -5w + -2w + w2 = 18 + 2w + -18 + -2w Combine like terms: -5w + -2w = -7w -18 + -7w + w2 = 18 + 2w + -18 + -2w Reorder the terms: -18 + -7w + w2 = 18 + -18 + 2w + -2w Combine like terms: 18 + -18 = 0 -18 + -7w + w2 = 0 + 2w + -2w -18 + -7w + w2 = 2w + -2w Combine like terms: 2w + -2w = 0 -18 + -7w + w2 = 0 Factor a trinomial. (-2 + -1w)(9 + -1w) = 0Subproblem 1
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 = -2Subproblem 2
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 = 9Solution
w = {-2, 9}
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