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Simplifying w2 + 2w = 47 Reorder the terms: 2w + w2 = 47 Solving 2w + w2 = 47 Solving for variable 'w'. Reorder the terms: -47 + 2w + w2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2w + 47 + w2 = 0 + 47 Reorder the terms: -47 + 47 + 2w + w2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2w + w2 = 0 + 47 2w + w2 = 0 + 47 Combine like terms: 0 + 47 = 47 2w + w2 = 47 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 = 47 + 1 Reorder the terms: 1 + 2w + w2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2w + w2 = 48 Factor a perfect square on the left side: (w + 1)(w + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (w + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
w + 1 = 6.92820323 Simplifying w + 1 = 6.92820323 Reorder the terms: 1 + w = 6.92820323 Solving 1 + w = 6.92820323 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 = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + w = 6.92820323 + -1 w = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 w = 5.92820323 Simplifying w = 5.92820323Subproblem 2
w + 1 = -6.92820323 Simplifying w + 1 = -6.92820323 Reorder the terms: 1 + w = -6.92820323 Solving 1 + w = -6.92820323 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 = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + w = -6.92820323 + -1 w = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 w = -7.92820323 Simplifying w = -7.92820323Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.92820323, -7.92820323}
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