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Simplifying 3w2 + -370w + -9000 = 0 Reorder the terms: -9000 + -370w + 3w2 = 0 Solving -9000 + -370w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3000 + -123.3333333w + w2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + -123.3333333w + 3000 + w2 = 0 + 3000 Reorder the terms: -3000 + 3000 + -123.3333333w + w2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + -123.3333333w + w2 = 0 + 3000 -123.3333333w + w2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 -123.3333333w + w2 = 3000 The w term is -123.3333333w. Take half its coefficient (-61.66666665). Square it (3802.777776) and add it to both sides. Add '3802.777776' to each side of the equation. -123.3333333w + 3802.777776 + w2 = 3000 + 3802.777776 Reorder the terms: 3802.777776 + -123.3333333w + w2 = 3000 + 3802.777776 Combine like terms: 3000 + 3802.777776 = 6802.777776 3802.777776 + -123.3333333w + w2 = 6802.777776 Factor a perfect square on the left side: (w + -61.66666665)(w + -61.66666665) = 6802.777776 Calculate the square root of the right side: 82.478953534 Break this problem into two subproblems by setting (w + -61.66666665) equal to 82.478953534 and -82.478953534.Subproblem 1
w + -61.66666665 = 82.478953534 Simplifying w + -61.66666665 = 82.478953534 Reorder the terms: -61.66666665 + w = 82.478953534 Solving -61.66666665 + w = 82.478953534 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '61.66666665' to each side of the equation. -61.66666665 + 61.66666665 + w = 82.478953534 + 61.66666665 Combine like terms: -61.66666665 + 61.66666665 = 0.00000000 0.00000000 + w = 82.478953534 + 61.66666665 w = 82.478953534 + 61.66666665 Combine like terms: 82.478953534 + 61.66666665 = 144.145620184 w = 144.145620184 Simplifying w = 144.145620184Subproblem 2
w + -61.66666665 = -82.478953534 Simplifying w + -61.66666665 = -82.478953534 Reorder the terms: -61.66666665 + w = -82.478953534 Solving -61.66666665 + w = -82.478953534 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '61.66666665' to each side of the equation. -61.66666665 + 61.66666665 + w = -82.478953534 + 61.66666665 Combine like terms: -61.66666665 + 61.66666665 = 0.00000000 0.00000000 + w = -82.478953534 + 61.66666665 w = -82.478953534 + 61.66666665 Combine like terms: -82.478953534 + 61.66666665 = -20.812286884 w = -20.812286884 Simplifying w = -20.812286884Solution
The solution to the problem is based on the solutions from the subproblems. w = {144.145620184, -20.812286884}
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