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Simplifying 0 = -50 + 2w2 + w Reorder the terms: 0 = -50 + w + 2w2 Solving 0 = -50 + w + 2w2 Solving for variable 'w'. Combine like terms: 0 + 50 = 50 50 + -1w + -2w2 = -50 + w + 2w2 + 50 + -1w + -2w2 Reorder the terms: 50 + -1w + -2w2 = -50 + 50 + w + -1w + 2w2 + -2w2 Combine like terms: -50 + 50 = 0 50 + -1w + -2w2 = 0 + w + -1w + 2w2 + -2w2 50 + -1w + -2w2 = w + -1w + 2w2 + -2w2 Combine like terms: w + -1w = 0 50 + -1w + -2w2 = 0 + 2w2 + -2w2 50 + -1w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 50 + -1w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -25 + 0.5w + w2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.5w + 25 + w2 = 0 + 25 Reorder the terms: -25 + 25 + 0.5w + w2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.5w + w2 = 0 + 25 0.5w + w2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.5w + w2 = 25 The w term is 0.5w. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5w + 0.0625 + w2 = 25 + 0.0625 Reorder the terms: 0.0625 + 0.5w + w2 = 25 + 0.0625 Combine like terms: 25 + 0.0625 = 25.0625 0.0625 + 0.5w + w2 = 25.0625 Factor a perfect square on the left side: (w + 0.25)(w + 0.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (w + 0.25) equal to 5.006246099 and -5.006246099.Subproblem 1
w + 0.25 = 5.006246099 Simplifying w + 0.25 = 5.006246099 Reorder the terms: 0.25 + w = 5.006246099 Solving 0.25 + w = 5.006246099 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + w = 5.006246099 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + w = 5.006246099 + -0.25 w = 5.006246099 + -0.25 Combine like terms: 5.006246099 + -0.25 = 4.756246099 w = 4.756246099 Simplifying w = 4.756246099Subproblem 2
w + 0.25 = -5.006246099 Simplifying w + 0.25 = -5.006246099 Reorder the terms: 0.25 + w = -5.006246099 Solving 0.25 + w = -5.006246099 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + w = -5.006246099 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + w = -5.006246099 + -0.25 w = -5.006246099 + -0.25 Combine like terms: -5.006246099 + -0.25 = -5.256246099 w = -5.256246099 Simplifying w = -5.256246099Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.756246099, -5.256246099}
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