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Simplifying w2 + 2w = 66 Reorder the terms: 2w + w2 = 66 Solving 2w + w2 = 66 Solving for variable 'w'. Reorder the terms: -66 + 2w + w2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 2w + 66 + w2 = 0 + 66 Reorder the terms: -66 + 66 + 2w + w2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 2w + w2 = 0 + 66 2w + w2 = 0 + 66 Combine like terms: 0 + 66 = 66 2w + w2 = 66 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 = 66 + 1 Reorder the terms: 1 + 2w + w2 = 66 + 1 Combine like terms: 66 + 1 = 67 1 + 2w + w2 = 67 Factor a perfect square on the left side: (w + 1)(w + 1) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (w + 1) equal to 8.185352772 and -8.185352772.Subproblem 1
w + 1 = 8.185352772 Simplifying w + 1 = 8.185352772 Reorder the terms: 1 + w = 8.185352772 Solving 1 + w = 8.185352772 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 = 8.185352772 + -1 Combine like terms: 1 + -1 = 0 0 + w = 8.185352772 + -1 w = 8.185352772 + -1 Combine like terms: 8.185352772 + -1 = 7.185352772 w = 7.185352772 Simplifying w = 7.185352772Subproblem 2
w + 1 = -8.185352772 Simplifying w + 1 = -8.185352772 Reorder the terms: 1 + w = -8.185352772 Solving 1 + w = -8.185352772 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 = -8.185352772 + -1 Combine like terms: 1 + -1 = 0 0 + w = -8.185352772 + -1 w = -8.185352772 + -1 Combine like terms: -8.185352772 + -1 = -9.185352772 w = -9.185352772 Simplifying w = -9.185352772Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.185352772, -9.185352772}
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