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Simplifying w2 + 111w = 104000 Reorder the terms: 111w + w2 = 104000 Solving 111w + w2 = 104000 Solving for variable 'w'. Reorder the terms: -104000 + 111w + w2 = 104000 + -104000 Combine like terms: 104000 + -104000 = 0 -104000 + 111w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '104000' to each side of the equation. -104000 + 111w + 104000 + w2 = 0 + 104000 Reorder the terms: -104000 + 104000 + 111w + w2 = 0 + 104000 Combine like terms: -104000 + 104000 = 0 0 + 111w + w2 = 0 + 104000 111w + w2 = 0 + 104000 Combine like terms: 0 + 104000 = 104000 111w + w2 = 104000 The w term is 111w. Take half its coefficient (55.5). Square it (3080.25) and add it to both sides. Add '3080.25' to each side of the equation. 111w + 3080.25 + w2 = 104000 + 3080.25 Reorder the terms: 3080.25 + 111w + w2 = 104000 + 3080.25 Combine like terms: 104000 + 3080.25 = 107080.25 3080.25 + 111w + w2 = 107080.25 Factor a perfect square on the left side: (w + 55.5)(w + 55.5) = 107080.25 Calculate the square root of the right side: 327.231187389 Break this problem into two subproblems by setting (w + 55.5) equal to 327.231187389 and -327.231187389.Subproblem 1
w + 55.5 = 327.231187389 Simplifying w + 55.5 = 327.231187389 Reorder the terms: 55.5 + w = 327.231187389 Solving 55.5 + w = 327.231187389 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + w = 327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + w = 327.231187389 + -55.5 w = 327.231187389 + -55.5 Combine like terms: 327.231187389 + -55.5 = 271.731187389 w = 271.731187389 Simplifying w = 271.731187389Subproblem 2
w + 55.5 = -327.231187389 Simplifying w + 55.5 = -327.231187389 Reorder the terms: 55.5 + w = -327.231187389 Solving 55.5 + w = -327.231187389 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-55.5' to each side of the equation. 55.5 + -55.5 + w = -327.231187389 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + w = -327.231187389 + -55.5 w = -327.231187389 + -55.5 Combine like terms: -327.231187389 + -55.5 = -382.731187389 w = -382.731187389 Simplifying w = -382.731187389Solution
The solution to the problem is based on the solutions from the subproblems. w = {271.731187389, -382.731187389}
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