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Simplifying 18W2 + 33W + 13 = 0 Reorder the terms: 13 + 33W + 18W2 = 0 Solving 13 + 33W + 18W2 = 0 Solving for variable 'W'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.7222222222 + 1.833333333W + W2 = 0 Move the constant term to the right: Add '-0.7222222222' to each side of the equation. 0.7222222222 + 1.833333333W + -0.7222222222 + W2 = 0 + -0.7222222222 Reorder the terms: 0.7222222222 + -0.7222222222 + 1.833333333W + W2 = 0 + -0.7222222222 Combine like terms: 0.7222222222 + -0.7222222222 = 0.0000000000 0.0000000000 + 1.833333333W + W2 = 0 + -0.7222222222 1.833333333W + W2 = 0 + -0.7222222222 Combine like terms: 0 + -0.7222222222 = -0.7222222222 1.833333333W + W2 = -0.7222222222 The W term is 1.833333333W. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333W + 0.8402777775 + W2 = -0.7222222222 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333W + W2 = -0.7222222222 + 0.8402777775 Combine like terms: -0.7222222222 + 0.8402777775 = 0.1180555553 0.8402777775 + 1.833333333W + W2 = 0.1180555553 Factor a perfect square on the left side: (W + 0.9166666665)(W + 0.9166666665) = 0.1180555553 Calculate the square root of the right side: 0.343592135 Break this problem into two subproblems by setting (W + 0.9166666665) equal to 0.343592135 and -0.343592135.Subproblem 1
W + 0.9166666665 = 0.343592135 Simplifying W + 0.9166666665 = 0.343592135 Reorder the terms: 0.9166666665 + W = 0.343592135 Solving 0.9166666665 + W = 0.343592135 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + W = 0.343592135 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + W = 0.343592135 + -0.9166666665 W = 0.343592135 + -0.9166666665 Combine like terms: 0.343592135 + -0.9166666665 = -0.5730745315 W = -0.5730745315 Simplifying W = -0.5730745315Subproblem 2
W + 0.9166666665 = -0.343592135 Simplifying W + 0.9166666665 = -0.343592135 Reorder the terms: 0.9166666665 + W = -0.343592135 Solving 0.9166666665 + W = -0.343592135 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + W = -0.343592135 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + W = -0.343592135 + -0.9166666665 W = -0.343592135 + -0.9166666665 Combine like terms: -0.343592135 + -0.9166666665 = -1.2602588015 W = -1.2602588015 Simplifying W = -1.2602588015Solution
The solution to the problem is based on the solutions from the subproblems. W = {-0.5730745315, -1.2602588015}
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