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Simplifying 2w2 + 5w + -364 = 0 Reorder the terms: -364 + 5w + 2w2 = 0 Solving -364 + 5w + 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'. -182 + 2.5w + w2 = 0 Move the constant term to the right: Add '182' to each side of the equation. -182 + 2.5w + 182 + w2 = 0 + 182 Reorder the terms: -182 + 182 + 2.5w + w2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 2.5w + w2 = 0 + 182 2.5w + w2 = 0 + 182 Combine like terms: 0 + 182 = 182 2.5w + w2 = 182 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = 182 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = 182 + 1.5625 Combine like terms: 182 + 1.5625 = 183.5625 1.5625 + 2.5w + w2 = 183.5625 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = 183.5625 Calculate the square root of the right side: 13.548523905 Break this problem into two subproblems by setting (w + 1.25) equal to 13.548523905 and -13.548523905.Subproblem 1
w + 1.25 = 13.548523905 Simplifying w + 1.25 = 13.548523905 Reorder the terms: 1.25 + w = 13.548523905 Solving 1.25 + w = 13.548523905 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 13.548523905 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 13.548523905 + -1.25 w = 13.548523905 + -1.25 Combine like terms: 13.548523905 + -1.25 = 12.298523905 w = 12.298523905 Simplifying w = 12.298523905Subproblem 2
w + 1.25 = -13.548523905 Simplifying w + 1.25 = -13.548523905 Reorder the terms: 1.25 + w = -13.548523905 Solving 1.25 + w = -13.548523905 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -13.548523905 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -13.548523905 + -1.25 w = -13.548523905 + -1.25 Combine like terms: -13.548523905 + -1.25 = -14.798523905 w = -14.798523905 Simplifying w = -14.798523905Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.298523905, -14.798523905}
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