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Simplifying 228 = (w + 7) * w Reorder the terms: 228 = (7 + w) * w Reorder the terms for easier multiplication: 228 = w(7 + w) 228 = (7 * w + w * w) 228 = (7w + w2) Solving 228 = 7w + w2 Solving for variable 'w'. Reorder the terms: 228 + -7w + -1w2 = 7w + -7w + w2 + -1w2 Combine like terms: 7w + -7w = 0 228 + -7w + -1w2 = 0 + w2 + -1w2 228 + -7w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 228 + -7w + -1w2 = 0 Factor a trinomial. (12 + -1w)(19 + 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 '(19 + w)' equal to zero and attempt to solve: Simplifying 19 + w = 0 Solving 19 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + w = 0 + -19 Combine like terms: 19 + -19 = 0 0 + w = 0 + -19 w = 0 + -19 Combine like terms: 0 + -19 = -19 w = -19 Simplifying w = -19Solution
w = {12, -19}
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