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Simplifying w(w + 5) = 238 Reorder the terms: w(5 + w) = 238 (5 * w + w * w) = 238 (5w + w2) = 238 Solving 5w + w2 = 238 Solving for variable 'w'. Reorder the terms: -238 + 5w + w2 = 238 + -238 Combine like terms: 238 + -238 = 0 -238 + 5w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '238' to each side of the equation. -238 + 5w + 238 + w2 = 0 + 238 Reorder the terms: -238 + 238 + 5w + w2 = 0 + 238 Combine like terms: -238 + 238 = 0 0 + 5w + w2 = 0 + 238 5w + w2 = 0 + 238 Combine like terms: 0 + 238 = 238 5w + w2 = 238 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 = 238 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 238 + 6.25 Combine like terms: 238 + 6.25 = 244.25 6.25 + 5w + w2 = 244.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 244.25 Calculate the square root of the right side: 15.628499608 Break this problem into two subproblems by setting (w + 2.5) equal to 15.628499608 and -15.628499608.Subproblem 1
w + 2.5 = 15.628499608 Simplifying w + 2.5 = 15.628499608 Reorder the terms: 2.5 + w = 15.628499608 Solving 2.5 + w = 15.628499608 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 = 15.628499608 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 15.628499608 + -2.5 w = 15.628499608 + -2.5 Combine like terms: 15.628499608 + -2.5 = 13.128499608 w = 13.128499608 Simplifying w = 13.128499608Subproblem 2
w + 2.5 = -15.628499608 Simplifying w + 2.5 = -15.628499608 Reorder the terms: 2.5 + w = -15.628499608 Solving 2.5 + w = -15.628499608 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 = -15.628499608 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -15.628499608 + -2.5 w = -15.628499608 + -2.5 Combine like terms: -15.628499608 + -2.5 = -18.128499608 w = -18.128499608 Simplifying w = -18.128499608Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.128499608, -18.128499608}
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