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Simplifying w(w + 4) = 6000 Reorder the terms: w(4 + w) = 6000 (4 * w + w * w) = 6000 (4w + w2) = 6000 Solving 4w + w2 = 6000 Solving for variable 'w'. Reorder the terms: -6000 + 4w + w2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -6000 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '6000' to each side of the equation. -6000 + 4w + 6000 + w2 = 0 + 6000 Reorder the terms: -6000 + 6000 + 4w + w2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + 4w + w2 = 0 + 6000 4w + w2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 4w + w2 = 6000 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 6000 + 4 Reorder the terms: 4 + 4w + w2 = 6000 + 4 Combine like terms: 6000 + 4 = 6004 4 + 4w + w2 = 6004 Factor a perfect square on the left side: (w + 2)(w + 2) = 6004 Calculate the square root of the right side: 77.485482511 Break this problem into two subproblems by setting (w + 2) equal to 77.485482511 and -77.485482511.Subproblem 1
w + 2 = 77.485482511 Simplifying w + 2 = 77.485482511 Reorder the terms: 2 + w = 77.485482511 Solving 2 + w = 77.485482511 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 77.485482511 + -2 Combine like terms: 2 + -2 = 0 0 + w = 77.485482511 + -2 w = 77.485482511 + -2 Combine like terms: 77.485482511 + -2 = 75.485482511 w = 75.485482511 Simplifying w = 75.485482511Subproblem 2
w + 2 = -77.485482511 Simplifying w + 2 = -77.485482511 Reorder the terms: 2 + w = -77.485482511 Solving 2 + w = -77.485482511 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -77.485482511 + -2 Combine like terms: 2 + -2 = 0 0 + w = -77.485482511 + -2 w = -77.485482511 + -2 Combine like terms: -77.485482511 + -2 = -79.485482511 w = -79.485482511 Simplifying w = -79.485482511Solution
The solution to the problem is based on the solutions from the subproblems. w = {75.485482511, -79.485482511}
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