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Simplifying w2 + 13w + 17.25 = 399 Reorder the terms: 17.25 + 13w + w2 = 399 Solving 17.25 + 13w + w2 = 399 Solving for variable 'w'. Reorder the terms: 17.25 + -399 + 13w + w2 = 399 + -399 Combine like terms: 17.25 + -399 = -381.75 -381.75 + 13w + w2 = 399 + -399 Combine like terms: 399 + -399 = 0 -381.75 + 13w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '381.75' to each side of the equation. -381.75 + 13w + 381.75 + w2 = 0 + 381.75 Reorder the terms: -381.75 + 381.75 + 13w + w2 = 0 + 381.75 Combine like terms: -381.75 + 381.75 = 0.00 0.00 + 13w + w2 = 0 + 381.75 13w + w2 = 0 + 381.75 Combine like terms: 0 + 381.75 = 381.75 13w + w2 = 381.75 The w term is 13w. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13w + 42.25 + w2 = 381.75 + 42.25 Reorder the terms: 42.25 + 13w + w2 = 381.75 + 42.25 Combine like terms: 381.75 + 42.25 = 424 42.25 + 13w + w2 = 424 Factor a perfect square on the left side: (w + 6.5)(w + 6.5) = 424 Calculate the square root of the right side: 20.591260282 Break this problem into two subproblems by setting (w + 6.5) equal to 20.591260282 and -20.591260282.Subproblem 1
w + 6.5 = 20.591260282 Simplifying w + 6.5 = 20.591260282 Reorder the terms: 6.5 + w = 20.591260282 Solving 6.5 + w = 20.591260282 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = 20.591260282 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = 20.591260282 + -6.5 w = 20.591260282 + -6.5 Combine like terms: 20.591260282 + -6.5 = 14.091260282 w = 14.091260282 Simplifying w = 14.091260282Subproblem 2
w + 6.5 = -20.591260282 Simplifying w + 6.5 = -20.591260282 Reorder the terms: 6.5 + w = -20.591260282 Solving 6.5 + w = -20.591260282 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = -20.591260282 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = -20.591260282 + -6.5 w = -20.591260282 + -6.5 Combine like terms: -20.591260282 + -6.5 = -27.091260282 w = -27.091260282 Simplifying w = -27.091260282Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.091260282, -27.091260282}
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