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Simplifying w(w + 2) = 52 Reorder the terms: w(2 + w) = 52 (2 * w + w * w) = 52 (2w + w2) = 52 Solving 2w + w2 = 52 Solving for variable 'w'. Reorder the terms: -52 + 2w + w2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 2w + 52 + w2 = 0 + 52 Reorder the terms: -52 + 52 + 2w + w2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 2w + w2 = 0 + 52 2w + w2 = 0 + 52 Combine like terms: 0 + 52 = 52 2w + w2 = 52 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 52 + 1 Reorder the terms: 1 + 2w + w2 = 52 + 1 Combine like terms: 52 + 1 = 53 1 + 2w + w2 = 53 Factor a perfect square on the left side: (w + 1)(w + 1) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (w + 1) equal to 7.280109889 and -7.280109889.Subproblem 1
w + 1 = 7.280109889 Simplifying w + 1 = 7.280109889 Reorder the terms: 1 + w = 7.280109889 Solving 1 + w = 7.280109889 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + w = 7.280109889 + -1 w = 7.280109889 + -1 Combine like terms: 7.280109889 + -1 = 6.280109889 w = 6.280109889 Simplifying w = 6.280109889Subproblem 2
w + 1 = -7.280109889 Simplifying w + 1 = -7.280109889 Reorder the terms: 1 + w = -7.280109889 Solving 1 + w = -7.280109889 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + w = -7.280109889 + -1 w = -7.280109889 + -1 Combine like terms: -7.280109889 + -1 = -8.280109889 w = -8.280109889 Simplifying w = -8.280109889Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.280109889, -8.280109889}
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