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Simplifying w2 + 8w = 320 Reorder the terms: 8w + w2 = 320 Solving 8w + w2 = 320 Solving for variable 'w'. Reorder the terms: -320 + 8w + w2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 8w + 320 + w2 = 0 + 320 Reorder the terms: -320 + 320 + 8w + w2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 8w + w2 = 0 + 320 8w + w2 = 0 + 320 Combine like terms: 0 + 320 = 320 8w + w2 = 320 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 320 + 16 Reorder the terms: 16 + 8w + w2 = 320 + 16 Combine like terms: 320 + 16 = 336 16 + 8w + w2 = 336 Factor a perfect square on the left side: (w + 4)(w + 4) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (w + 4) equal to 18.33030278 and -18.33030278.Subproblem 1
w + 4 = 18.33030278 Simplifying w + 4 = 18.33030278 Reorder the terms: 4 + w = 18.33030278 Solving 4 + w = 18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 18.33030278 + -4 Combine like terms: 4 + -4 = 0 0 + w = 18.33030278 + -4 w = 18.33030278 + -4 Combine like terms: 18.33030278 + -4 = 14.33030278 w = 14.33030278 Simplifying w = 14.33030278Subproblem 2
w + 4 = -18.33030278 Simplifying w + 4 = -18.33030278 Reorder the terms: 4 + w = -18.33030278 Solving 4 + w = -18.33030278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -18.33030278 + -4 Combine like terms: 4 + -4 = 0 0 + w = -18.33030278 + -4 w = -18.33030278 + -4 Combine like terms: -18.33030278 + -4 = -22.33030278 w = -22.33030278 Simplifying w = -22.33030278Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.33030278, -22.33030278}
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