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Simplifying (W + 5)(W + 5) + -80 = 0 Reorder the terms: (5 + W)(W + 5) + -80 = 0 Reorder the terms: (5 + W)(5 + W) + -80 = 0 Multiply (5 + W) * (5 + W) (5(5 + W) + W(5 + W)) + -80 = 0 ((5 * 5 + W * 5) + W(5 + W)) + -80 = 0 ((25 + 5W) + W(5 + W)) + -80 = 0 (25 + 5W + (5 * W + W * W)) + -80 = 0 (25 + 5W + (5W + W2)) + -80 = 0 Combine like terms: 5W + 5W = 10W (25 + 10W + W2) + -80 = 0 Reorder the terms: 25 + -80 + 10W + W2 = 0 Combine like terms: 25 + -80 = -55 -55 + 10W + W2 = 0 Solving -55 + 10W + W2 = 0 Solving for variable 'W'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 10W + 55 + W2 = 0 + 55 Reorder the terms: -55 + 55 + 10W + W2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 10W + W2 = 0 + 55 10W + W2 = 0 + 55 Combine like terms: 0 + 55 = 55 10W + W2 = 55 The W term is 10W. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10W + 25 + W2 = 55 + 25 Reorder the terms: 25 + 10W + W2 = 55 + 25 Combine like terms: 55 + 25 = 80 25 + 10W + W2 = 80 Factor a perfect square on the left side: (W + 5)(W + 5) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (W + 5) equal to 8.94427191 and -8.94427191.Subproblem 1
W + 5 = 8.94427191 Simplifying W + 5 = 8.94427191 Reorder the terms: 5 + W = 8.94427191 Solving 5 + W = 8.94427191 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + W = 8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + W = 8.94427191 + -5 W = 8.94427191 + -5 Combine like terms: 8.94427191 + -5 = 3.94427191 W = 3.94427191 Simplifying W = 3.94427191Subproblem 2
W + 5 = -8.94427191 Simplifying W + 5 = -8.94427191 Reorder the terms: 5 + W = -8.94427191 Solving 5 + W = -8.94427191 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + W = -8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + W = -8.94427191 + -5 W = -8.94427191 + -5 Combine like terms: -8.94427191 + -5 = -13.94427191 W = -13.94427191 Simplifying W = -13.94427191Solution
The solution to the problem is based on the solutions from the subproblems. W = {3.94427191, -13.94427191}
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