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Simplifying 2w2 + 18w + -25 = 0 Reorder the terms: -25 + 18w + 2w2 = 0 Solving -25 + 18w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 9w + w2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 9w + 12.5 + w2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 9w + w2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 9w + w2 = 0 + 12.5 9w + w2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 9w + w2 = 12.5 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 = 12.5 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 12.5 + 20.25 Combine like terms: 12.5 + 20.25 = 32.75 20.25 + 9w + w2 = 32.75 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 32.75 Calculate the square root of the right side: 5.722761571 Break this problem into two subproblems by setting (w + 4.5) equal to 5.722761571 and -5.722761571.Subproblem 1
w + 4.5 = 5.722761571 Simplifying w + 4.5 = 5.722761571 Reorder the terms: 4.5 + w = 5.722761571 Solving 4.5 + w = 5.722761571 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 = 5.722761571 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 5.722761571 + -4.5 w = 5.722761571 + -4.5 Combine like terms: 5.722761571 + -4.5 = 1.222761571 w = 1.222761571 Simplifying w = 1.222761571Subproblem 2
w + 4.5 = -5.722761571 Simplifying w + 4.5 = -5.722761571 Reorder the terms: 4.5 + w = -5.722761571 Solving 4.5 + w = -5.722761571 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 = -5.722761571 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -5.722761571 + -4.5 w = -5.722761571 + -4.5 Combine like terms: -5.722761571 + -4.5 = -10.222761571 w = -10.222761571 Simplifying w = -10.222761571Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.222761571, -10.222761571}
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