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Simplifying 306 = w2 + w Reorder the terms: 306 = w + w2 Solving 306 = w + w2 Solving for variable 'w'. Reorder the terms: 306 + -1w + -1w2 = w + -1w + w2 + -1w2 Combine like terms: w + -1w = 0 306 + -1w + -1w2 = 0 + w2 + -1w2 306 + -1w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 306 + -1w + -1w2 = 0 Factor a trinomial. (17 + -1w)(18 + w) = 0Subproblem 1
Set the factor '(17 + -1w)' equal to zero and attempt to solve: Simplifying 17 + -1w = 0 Solving 17 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1w = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1w = 0 + -17 -1w = 0 + -17 Combine like terms: 0 + -17 = -17 -1w = -17 Divide each side by '-1'. w = 17 Simplifying w = 17Subproblem 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 = {17, -18}
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