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Simplifying w(w + 5) = 7056 Reorder the terms: w(5 + w) = 7056 (5 * w + w * w) = 7056 (5w + w2) = 7056 Solving 5w + w2 = 7056 Solving for variable 'w'. Reorder the terms: -7056 + 5w + w2 = 7056 + -7056 Combine like terms: 7056 + -7056 = 0 -7056 + 5w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '7056' to each side of the equation. -7056 + 5w + 7056 + w2 = 0 + 7056 Reorder the terms: -7056 + 7056 + 5w + w2 = 0 + 7056 Combine like terms: -7056 + 7056 = 0 0 + 5w + w2 = 0 + 7056 5w + w2 = 0 + 7056 Combine like terms: 0 + 7056 = 7056 5w + w2 = 7056 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 7056 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 7056 + 6.25 Combine like terms: 7056 + 6.25 = 7062.25 6.25 + 5w + w2 = 7062.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 7062.25 Calculate the square root of the right side: 84.037194146 Break this problem into two subproblems by setting (w + 2.5) equal to 84.037194146 and -84.037194146.Subproblem 1
w + 2.5 = 84.037194146 Simplifying w + 2.5 = 84.037194146 Reorder the terms: 2.5 + w = 84.037194146 Solving 2.5 + w = 84.037194146 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 84.037194146 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 84.037194146 + -2.5 w = 84.037194146 + -2.5 Combine like terms: 84.037194146 + -2.5 = 81.537194146 w = 81.537194146 Simplifying w = 81.537194146Subproblem 2
w + 2.5 = -84.037194146 Simplifying w + 2.5 = -84.037194146 Reorder the terms: 2.5 + w = -84.037194146 Solving 2.5 + w = -84.037194146 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -84.037194146 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -84.037194146 + -2.5 w = -84.037194146 + -2.5 Combine like terms: -84.037194146 + -2.5 = -86.537194146 w = -86.537194146 Simplifying w = -86.537194146Solution
The solution to the problem is based on the solutions from the subproblems. w = {81.537194146, -86.537194146}
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