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Simplifying w2 + (2w + 44) = 46 Reorder the terms: w2 + (44 + 2w) = 46 Remove parenthesis around (44 + 2w) w2 + 44 + 2w = 46 Reorder the terms: 44 + 2w + w2 = 46 Solving 44 + 2w + w2 = 46 Solving for variable 'w'. Reorder the terms: 44 + -46 + 2w + w2 = 46 + -46 Combine like terms: 44 + -46 = -2 -2 + 2w + w2 = 46 + -46 Combine like terms: 46 + -46 = 0 -2 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 2w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 2w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2w + w2 = 0 + 2 2w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 2w + w2 = 2 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 = 2 + 1 Reorder the terms: 1 + 2w + w2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2w + w2 = 3 Factor a perfect square on the left side: (w + 1)(w + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (w + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
w + 1 = 1.732050808 Simplifying w + 1 = 1.732050808 Reorder the terms: 1 + w = 1.732050808 Solving 1 + w = 1.732050808 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 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + w = 1.732050808 + -1 w = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 w = 0.732050808 Simplifying w = 0.732050808Subproblem 2
w + 1 = -1.732050808 Simplifying w + 1 = -1.732050808 Reorder the terms: 1 + w = -1.732050808 Solving 1 + w = -1.732050808 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 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + w = -1.732050808 + -1 w = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 w = -2.732050808 Simplifying w = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.732050808, -2.732050808}
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