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Simplifying w2 + w + -28266 = 0 Reorder the terms: -28266 + w + w2 = 0 Solving -28266 + w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '28266' to each side of the equation. -28266 + w + 28266 + w2 = 0 + 28266 Reorder the terms: -28266 + 28266 + w + w2 = 0 + 28266 Combine like terms: -28266 + 28266 = 0 0 + w + w2 = 0 + 28266 w + w2 = 0 + 28266 Combine like terms: 0 + 28266 = 28266 w + w2 = 28266 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. w + 0.25 + w2 = 28266 + 0.25 Reorder the terms: 0.25 + w + w2 = 28266 + 0.25 Combine like terms: 28266 + 0.25 = 28266.25 0.25 + w + w2 = 28266.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 28266.25 Calculate the square root of the right side: 168.125697025 Break this problem into two subproblems by setting (w + 0.5) equal to 168.125697025 and -168.125697025.Subproblem 1
w + 0.5 = 168.125697025 Simplifying w + 0.5 = 168.125697025 Reorder the terms: 0.5 + w = 168.125697025 Solving 0.5 + w = 168.125697025 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 = 168.125697025 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 168.125697025 + -0.5 w = 168.125697025 + -0.5 Combine like terms: 168.125697025 + -0.5 = 167.625697025 w = 167.625697025 Simplifying w = 167.625697025Subproblem 2
w + 0.5 = -168.125697025 Simplifying w + 0.5 = -168.125697025 Reorder the terms: 0.5 + w = -168.125697025 Solving 0.5 + w = -168.125697025 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 = -168.125697025 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -168.125697025 + -0.5 w = -168.125697025 + -0.5 Combine like terms: -168.125697025 + -0.5 = -168.625697025 w = -168.625697025 Simplifying w = -168.625697025Solution
The solution to the problem is based on the solutions from the subproblems. w = {167.625697025, -168.625697025}
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