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Simplifying 2w2 + 18w + 36 = 261 Reorder the terms: 36 + 18w + 2w2 = 261 Solving 36 + 18w + 2w2 = 261 Solving for variable 'w'. Reorder the terms: 36 + -261 + 18w + 2w2 = 261 + -261 Combine like terms: 36 + -261 = -225 -225 + 18w + 2w2 = 261 + -261 Combine like terms: 261 + -261 = 0 -225 + 18w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + 9w + w2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 9w + 112.5 + w2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + 9w + w2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 9w + w2 = 0 + 112.5 9w + w2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 9w + w2 = 112.5 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = 112.5 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 112.5 + 20.25 Combine like terms: 112.5 + 20.25 = 132.75 20.25 + 9w + w2 = 132.75 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 132.75 Calculate the square root of the right side: 11.521718622 Break this problem into two subproblems by setting (w + 4.5) equal to 11.521718622 and -11.521718622.Subproblem 1
w + 4.5 = 11.521718622 Simplifying w + 4.5 = 11.521718622 Reorder the terms: 4.5 + w = 11.521718622 Solving 4.5 + w = 11.521718622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 11.521718622 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 11.521718622 + -4.5 w = 11.521718622 + -4.5 Combine like terms: 11.521718622 + -4.5 = 7.021718622 w = 7.021718622 Simplifying w = 7.021718622Subproblem 2
w + 4.5 = -11.521718622 Simplifying w + 4.5 = -11.521718622 Reorder the terms: 4.5 + w = -11.521718622 Solving 4.5 + w = -11.521718622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -11.521718622 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -11.521718622 + -4.5 w = -11.521718622 + -4.5 Combine like terms: -11.521718622 + -4.5 = -16.021718622 w = -16.021718622 Simplifying w = -16.021718622Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.021718622, -16.021718622}
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