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Simplifying w2 + 2w + 2 = 48 Reorder the terms: 2 + 2w + w2 = 48 Solving 2 + 2w + w2 = 48 Solving for variable 'w'. Reorder the terms: 2 + -48 + 2w + w2 = 48 + -48 Combine like terms: 2 + -48 = -46 -46 + 2w + w2 = 48 + -48 Combine like terms: 48 + -48 = 0 -46 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 2w + 46 + w2 = 0 + 46 Reorder the terms: -46 + 46 + 2w + w2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 2w + w2 = 0 + 46 2w + w2 = 0 + 46 Combine like terms: 0 + 46 = 46 2w + w2 = 46 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 = 46 + 1 Reorder the terms: 1 + 2w + w2 = 46 + 1 Combine like terms: 46 + 1 = 47 1 + 2w + w2 = 47 Factor a perfect square on the left side: (w + 1)(w + 1) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (w + 1) equal to 6.8556546 and -6.8556546.Subproblem 1
w + 1 = 6.8556546 Simplifying w + 1 = 6.8556546 Reorder the terms: 1 + w = 6.8556546 Solving 1 + w = 6.8556546 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 = 6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + w = 6.8556546 + -1 w = 6.8556546 + -1 Combine like terms: 6.8556546 + -1 = 5.8556546 w = 5.8556546 Simplifying w = 5.8556546Subproblem 2
w + 1 = -6.8556546 Simplifying w + 1 = -6.8556546 Reorder the terms: 1 + w = -6.8556546 Solving 1 + w = -6.8556546 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 = -6.8556546 + -1 Combine like terms: 1 + -1 = 0 0 + w = -6.8556546 + -1 w = -6.8556546 + -1 Combine like terms: -6.8556546 + -1 = -7.8556546 w = -7.8556546 Simplifying w = -7.8556546Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.8556546, -7.8556546}
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