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Simplifying 2w2 + w + 0.25 = 88.25 Reorder the terms: 0.25 + w + 2w2 = 88.25 Solving 0.25 + w + 2w2 = 88.25 Solving for variable 'w'. Reorder the terms: 0.25 + -88.25 + w + 2w2 = 88.25 + -88.25 Combine like terms: 0.25 + -88.25 = -88 -88 + w + 2w2 = 88.25 + -88.25 Combine like terms: 88.25 + -88.25 = 0.00 -88 + w + 2w2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -44 + 0.5w + w2 = 0.00 Move the constant term to the right: Add '44' to each side of the equation. -44 + 0.5w + 44 + w2 = 0.00 + 44 Reorder the terms: -44 + 44 + 0.5w + w2 = 0.00 + 44 Combine like terms: -44 + 44 = 0 0 + 0.5w + w2 = 0.00 + 44 0.5w + w2 = 0.00 + 44 Combine like terms: 0.00 + 44 = 44 0.5w + w2 = 44 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5w + 0.25 + w2 = 44 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + 0.5w + w2 = 44.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (w + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
w + 0.5 = 6.652067348 Simplifying w + 0.5 = 6.652067348 Reorder the terms: 0.5 + w = 6.652067348 Solving 0.5 + w = 6.652067348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 6.652067348 + -0.5 w = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 w = 6.152067348 Simplifying w = 6.152067348Subproblem 2
w + 0.5 = -6.652067348 Simplifying w + 0.5 = -6.652067348 Reorder the terms: 0.5 + w = -6.652067348 Solving 0.5 + w = -6.652067348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -6.652067348 + -0.5 w = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 w = -7.152067348 Simplifying w = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.152067348, -7.152067348}
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