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Simplifying w(w + 400) = 6000 Reorder the terms: w(400 + w) = 6000 (400 * w + w * w) = 6000 (400w + w2) = 6000 Solving 400w + w2 = 6000 Solving for variable 'w'. Reorder the terms: -6000 + 400w + w2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -6000 + 400w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '6000' to each side of the equation. -6000 + 400w + 6000 + w2 = 0 + 6000 Reorder the terms: -6000 + 6000 + 400w + w2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + 400w + w2 = 0 + 6000 400w + w2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 400w + w2 = 6000 The w term is 400w. Take half its coefficient (200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. 400w + 40000 + w2 = 6000 + 40000 Reorder the terms: 40000 + 400w + w2 = 6000 + 40000 Combine like terms: 6000 + 40000 = 46000 40000 + 400w + w2 = 46000 Factor a perfect square on the left side: (w + 200)(w + 200) = 46000 Calculate the square root of the right side: 214.476105895 Break this problem into two subproblems by setting (w + 200) equal to 214.476105895 and -214.476105895.Subproblem 1
w + 200 = 214.476105895 Simplifying w + 200 = 214.476105895 Reorder the terms: 200 + w = 214.476105895 Solving 200 + w = 214.476105895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + w = 214.476105895 + -200 Combine like terms: 200 + -200 = 0 0 + w = 214.476105895 + -200 w = 214.476105895 + -200 Combine like terms: 214.476105895 + -200 = 14.476105895 w = 14.476105895 Simplifying w = 14.476105895Subproblem 2
w + 200 = -214.476105895 Simplifying w + 200 = -214.476105895 Reorder the terms: 200 + w = -214.476105895 Solving 200 + w = -214.476105895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + w = -214.476105895 + -200 Combine like terms: 200 + -200 = 0 0 + w = -214.476105895 + -200 w = -214.476105895 + -200 Combine like terms: -214.476105895 + -200 = -414.476105895 w = -414.476105895 Simplifying w = -414.476105895Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.476105895, -414.476105895}
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