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Simplifying 2w2 + 1.5w + -314.50 = 0 Reorder the terms: -314.50 + 1.5w + 2w2 = 0 Solving -314.50 + 1.5w + 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'. -157.25 + 0.75w + w2 = 0 Move the constant term to the right: Add '157.25' to each side of the equation. -157.25 + 0.75w + 157.25 + w2 = 0 + 157.25 Reorder the terms: -157.25 + 157.25 + 0.75w + w2 = 0 + 157.25 Combine like terms: -157.25 + 157.25 = 0.00 0.00 + 0.75w + w2 = 0 + 157.25 0.75w + w2 = 0 + 157.25 Combine like terms: 0 + 157.25 = 157.25 0.75w + w2 = 157.25 The w term is 0.75w. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75w + 0.140625 + w2 = 157.25 + 0.140625 Reorder the terms: 0.140625 + 0.75w + w2 = 157.25 + 0.140625 Combine like terms: 157.25 + 0.140625 = 157.390625 0.140625 + 0.75w + w2 = 157.390625 Factor a perfect square on the left side: (w + 0.375)(w + 0.375) = 157.390625 Calculate the square root of the right side: 12.545542037 Break this problem into two subproblems by setting (w + 0.375) equal to 12.545542037 and -12.545542037.Subproblem 1
w + 0.375 = 12.545542037 Simplifying w + 0.375 = 12.545542037 Reorder the terms: 0.375 + w = 12.545542037 Solving 0.375 + w = 12.545542037 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + w = 12.545542037 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + w = 12.545542037 + -0.375 w = 12.545542037 + -0.375 Combine like terms: 12.545542037 + -0.375 = 12.170542037 w = 12.170542037 Simplifying w = 12.170542037Subproblem 2
w + 0.375 = -12.545542037 Simplifying w + 0.375 = -12.545542037 Reorder the terms: 0.375 + w = -12.545542037 Solving 0.375 + w = -12.545542037 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + w = -12.545542037 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + w = -12.545542037 + -0.375 w = -12.545542037 + -0.375 Combine like terms: -12.545542037 + -0.375 = -12.920542037 w = -12.920542037 Simplifying w = -12.920542037Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.170542037, -12.920542037}
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