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Simplifying 75w + -2w2 = 600 Solving 75w + -2w2 = 600 Solving for variable 'w'. Reorder the terms: -600 + 75w + -2w2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 75w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 300 + -37.5w + w2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -37.5w + -300 + w2 = 0 + -300 Reorder the terms: 300 + -300 + -37.5w + w2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -37.5w + w2 = 0 + -300 -37.5w + w2 = 0 + -300 Combine like terms: 0 + -300 = -300 -37.5w + w2 = -300 The w term is -37.5w. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5w + 351.5625 + w2 = -300 + 351.5625 Reorder the terms: 351.5625 + -37.5w + w2 = -300 + 351.5625 Combine like terms: -300 + 351.5625 = 51.5625 351.5625 + -37.5w + w2 = 51.5625 Factor a perfect square on the left side: (w + -18.75)(w + -18.75) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (w + -18.75) equal to 7.180703308 and -7.180703308.Subproblem 1
w + -18.75 = 7.180703308 Simplifying w + -18.75 = 7.180703308 Reorder the terms: -18.75 + w = 7.180703308 Solving -18.75 + w = 7.180703308 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + w = 7.180703308 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + w = 7.180703308 + 18.75 w = 7.180703308 + 18.75 Combine like terms: 7.180703308 + 18.75 = 25.930703308 w = 25.930703308 Simplifying w = 25.930703308Subproblem 2
w + -18.75 = -7.180703308 Simplifying w + -18.75 = -7.180703308 Reorder the terms: -18.75 + w = -7.180703308 Solving -18.75 + w = -7.180703308 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + w = -7.180703308 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + w = -7.180703308 + 18.75 w = -7.180703308 + 18.75 Combine like terms: -7.180703308 + 18.75 = 11.569296692 w = 11.569296692 Simplifying w = 11.569296692Solution
The solution to the problem is based on the solutions from the subproblems. w = {25.930703308, 11.569296692}
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