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Simplifying 40000 = 200w + w2 Solving 40000 = 200w + w2 Solving for variable 'w'. Reorder the terms: 40000 + -200w + -1w2 = 200w + -200w + w2 + -1w2 Combine like terms: 200w + -200w = 0 40000 + -200w + -1w2 = 0 + w2 + -1w2 40000 + -200w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 40000 + -200w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40000 + 200w + w2 = 0 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 = 123.60679775 w = 123.60679775 Simplifying w = 123.60679775Subproblem 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 = -323.60679775 w = -323.60679775 Simplifying w = -323.60679775Solution
The solution to the problem is based on the solutions from the subproblems. w = {123.60679775, -323.60679775}
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