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Simplifying (w + -200)(w) = 40000 Reorder the terms: (-200 + w)(w) = 40000 Reorder the terms for easier multiplication: w(-200 + w) = 40000 (-200 * w + w * w) = 40000 (-200w + w2) = 40000 Solving -200w + w2 = 40000 Solving for variable 'w'. Reorder the terms: -40000 + -200w + w2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -40000 + -200w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '40000' to each side of the equation. -40000 + -200w + 40000 + w2 = 0 + 40000 Reorder the terms: -40000 + 40000 + -200w + w2 = 0 + 40000 Combine like terms: -40000 + 40000 = 0 0 + -200w + w2 = 0 + 40000 -200w + w2 = 0 + 40000 Combine like terms: 0 + 40000 = 40000 -200w + w2 = 40000 The w term is -200w. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200w + 10000 + w2 = 40000 + 10000 Reorder the terms: 10000 + -200w + w2 = 40000 + 10000 Combine like terms: 40000 + 10000 = 50000 10000 + -200w + w2 = 50000 Factor a perfect square on the left side: (w + -100)(w + -100) = 50000 Calculate the square root of the right side: 223.60679775 Break this problem into two subproblems by setting (w + -100) equal to 223.60679775 and -223.60679775.Subproblem 1
w + -100 = 223.60679775 Simplifying w + -100 = 223.60679775 Reorder the terms: -100 + w = 223.60679775 Solving -100 + w = 223.60679775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + w = 223.60679775 + 100 Combine like terms: -100 + 100 = 0 0 + w = 223.60679775 + 100 w = 223.60679775 + 100 Combine like terms: 223.60679775 + 100 = 323.60679775 w = 323.60679775 Simplifying w = 323.60679775Subproblem 2
w + -100 = -223.60679775 Simplifying w + -100 = -223.60679775 Reorder the terms: -100 + w = -223.60679775 Solving -100 + w = -223.60679775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + w = -223.60679775 + 100 Combine like terms: -100 + 100 = 0 0 + w = -223.60679775 + 100 w = -223.60679775 + 100 Combine like terms: -223.60679775 + 100 = -123.60679775 w = -123.60679775 Simplifying w = -123.60679775Solution
The solution to the problem is based on the solutions from the subproblems. w = {323.60679775, -123.60679775}
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