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Simplifying w2 + 0.11w + -0.057 = 0 Reorder the terms: -0.057 + 0.11w + w2 = 0 Solving -0.057 + 0.11w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '0.057' to each side of the equation. -0.057 + 0.11w + 0.057 + w2 = 0 + 0.057 Reorder the terms: -0.057 + 0.057 + 0.11w + w2 = 0 + 0.057 Combine like terms: -0.057 + 0.057 = 0.000 0.000 + 0.11w + w2 = 0 + 0.057 0.11w + w2 = 0 + 0.057 Combine like terms: 0 + 0.057 = 0.057 0.11w + w2 = 0.057 The w term is 0.11w. Take half its coefficient (0.055). Square it (0.003025) and add it to both sides. Add '0.003025' to each side of the equation. 0.11w + 0.003025 + w2 = 0.057 + 0.003025 Reorder the terms: 0.003025 + 0.11w + w2 = 0.057 + 0.003025 Combine like terms: 0.057 + 0.003025 = 0.060025 0.003025 + 0.11w + w2 = 0.060025 Factor a perfect square on the left side: (w + 0.055)(w + 0.055) = 0.060025 Calculate the square root of the right side: 0.245 Break this problem into two subproblems by setting (w + 0.055) equal to 0.245 and -0.245.Subproblem 1
w + 0.055 = 0.245 Simplifying w + 0.055 = 0.245 Reorder the terms: 0.055 + w = 0.245 Solving 0.055 + w = 0.245 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + w = 0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + w = 0.245 + -0.055 w = 0.245 + -0.055 Combine like terms: 0.245 + -0.055 = 0.19 w = 0.19 Simplifying w = 0.19Subproblem 2
w + 0.055 = -0.245 Simplifying w + 0.055 = -0.245 Reorder the terms: 0.055 + w = -0.245 Solving 0.055 + w = -0.245 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.055' to each side of the equation. 0.055 + -0.055 + w = -0.245 + -0.055 Combine like terms: 0.055 + -0.055 = 0.000 0.000 + w = -0.245 + -0.055 w = -0.245 + -0.055 Combine like terms: -0.245 + -0.055 = -0.3 w = -0.3 Simplifying w = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.19, -0.3}
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