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Simplifying 85 = W(W + 12) Reorder the terms: 85 = W(12 + W) 85 = (12 * W + W * W) 85 = (12W + W2) Solving 85 = 12W + W2 Solving for variable 'W'. Reorder the terms: 85 + -12W + -1W2 = 12W + -12W + W2 + -1W2 Combine like terms: 12W + -12W = 0 85 + -12W + -1W2 = 0 + W2 + -1W2 85 + -12W + -1W2 = W2 + -1W2 Combine like terms: W2 + -1W2 = 0 85 + -12W + -1W2 = 0 Factor a trinomial. (5 + -1W)(17 + W) = 0Subproblem 1
Set the factor '(5 + -1W)' equal to zero and attempt to solve: Simplifying 5 + -1W = 0 Solving 5 + -1W = 0 Move all terms containing W to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1W = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1W = 0 + -5 -1W = 0 + -5 Combine like terms: 0 + -5 = -5 -1W = -5 Divide each side by '-1'. W = 5 Simplifying W = 5Subproblem 2
Set the factor '(17 + W)' equal to zero and attempt to solve: Simplifying 17 + W = 0 Solving 17 + W = 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 + W = 0 + -17 Combine like terms: 17 + -17 = 0 0 + W = 0 + -17 W = 0 + -17 Combine like terms: 0 + -17 = -17 W = -17 Simplifying W = -17Solution
W = {5, -17}
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