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Simplifying 234 = (w + 5)(w) Reorder the terms: 234 = (5 + w)(w) Reorder the terms for easier multiplication: 234 = w(5 + w) 234 = (5 * w + w * w) 234 = (5w + w2) Solving 234 = 5w + w2 Solving for variable 'w'. Reorder the terms: 234 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 234 + -5w + -1w2 = 0 + w2 + -1w2 234 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 234 + -5w + -1w2 = 0 Factor a trinomial. (13 + -1w)(18 + w) = 0Subproblem 1
Set the factor '(13 + -1w)' equal to zero and attempt to solve: Simplifying 13 + -1w = 0 Solving 13 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1w = 0 + -13 -1w = 0 + -13 Combine like terms: 0 + -13 = -13 -1w = -13 Divide each side by '-1'. w = 13 Simplifying w = 13Subproblem 2
Set the factor '(18 + w)' equal to zero and attempt to solve: Simplifying 18 + w = 0 Solving 18 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + w = 0 + -18 Combine like terms: 18 + -18 = 0 0 + w = 0 + -18 w = 0 + -18 Combine like terms: 0 + -18 = -18 w = -18 Simplifying w = -18Solution
w = {13, -18}
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