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Simplifying 200W2 + W + -20 = 0 Reorder the terms: -20 + W + 200W2 = 0 Solving -20 + W + 200W2 = 0 Solving for variable 'W'. Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. -0.1 + 0.005W + W2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.005W + 0.1 + W2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.005W + W2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.005W + W2 = 0 + 0.1 0.005W + W2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.005W + W2 = 0.1 The W term is W. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.005W + 0.25 + W2 = 0.1 + 0.25 Reorder the terms: 0.25 + 0.005W + W2 = 0.1 + 0.25 Combine like terms: 0.1 + 0.25 = 0.35 0.25 + 0.005W + W2 = 0.35 Factor a perfect square on the left side: (W + 0.5)(W + 0.5) = 0.35 Calculate the square root of the right side: 0.591607978 Break this problem into two subproblems by setting (W + 0.5) equal to 0.591607978 and -0.591607978.Subproblem 1
W + 0.5 = 0.591607978 Simplifying W + 0.5 = 0.591607978 Reorder the terms: 0.5 + W = 0.591607978 Solving 0.5 + W = 0.591607978 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + W = 0.591607978 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = 0.591607978 + -0.5 W = 0.591607978 + -0.5 Combine like terms: 0.591607978 + -0.5 = 0.091607978 W = 0.091607978 Simplifying W = 0.091607978Subproblem 2
W + 0.5 = -0.591607978 Simplifying W + 0.5 = -0.591607978 Reorder the terms: 0.5 + W = -0.591607978 Solving 0.5 + W = -0.591607978 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + W = -0.591607978 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + W = -0.591607978 + -0.5 W = -0.591607978 + -0.5 Combine like terms: -0.591607978 + -0.5 = -1.091607978 W = -1.091607978 Simplifying W = -1.091607978Solution
The solution to the problem is based on the solutions from the subproblems. W = {0.091607978, -1.091607978}
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