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Simplifying 216 = w(w + 6) Reorder the terms: 216 = w(6 + w) 216 = (6 * w + w * w) 216 = (6w + w2) Solving 216 = 6w + w2 Solving for variable 'w'. Reorder the terms: 216 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 216 + -6w + -1w2 = 0 + w2 + -1w2 216 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 216 + -6w + -1w2 = 0 Factor a trinomial. (12 + -1w)(18 + w) = 0Subproblem 1
Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12Subproblem 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 = {12, -18}
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