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Simplifying 0.3327 = -0.32w2 + 1.32w Reorder the terms: 0.3327 = 1.32w + -0.32w2 Solving 0.3327 = 1.32w + -0.32w2 Solving for variable 'w'. Reorder the terms: 0.3327 + -1.32w + 0.32w2 = 1.32w + -1.32w + -0.32w2 + 0.32w2 Combine like terms: 1.32w + -1.32w = 0.00 0.3327 + -1.32w + 0.32w2 = 0.00 + -0.32w2 + 0.32w2 0.3327 + -1.32w + 0.32w2 = -0.32w2 + 0.32w2 Combine like terms: -0.32w2 + 0.32w2 = 0.00 0.3327 + -1.32w + 0.32w2 = 0.00 Begin completing the square. Divide all terms by 0.32 the coefficient of the squared term: Divide each side by '0.32'. 1.0396875 + -4.125w + w2 = 0 Move the constant term to the right: Add '-1.0396875' to each side of the equation. 1.0396875 + -4.125w + -1.0396875 + w2 = 0 + -1.0396875 Reorder the terms: 1.0396875 + -1.0396875 + -4.125w + w2 = 0 + -1.0396875 Combine like terms: 1.0396875 + -1.0396875 = 0.0000000 0.0000000 + -4.125w + w2 = 0 + -1.0396875 -4.125w + w2 = 0 + -1.0396875 Combine like terms: 0 + -1.0396875 = -1.0396875 -4.125w + w2 = -1.0396875 The w term is -4.125w. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125w + 4.25390625 + w2 = -1.0396875 + 4.25390625 Reorder the terms: 4.25390625 + -4.125w + w2 = -1.0396875 + 4.25390625 Combine like terms: -1.0396875 + 4.25390625 = 3.21421875 4.25390625 + -4.125w + w2 = 3.21421875 Factor a perfect square on the left side: (w + -2.0625)(w + -2.0625) = 3.21421875 Calculate the square root of the right side: 1.792824238 Break this problem into two subproblems by setting (w + -2.0625) equal to 1.792824238 and -1.792824238.Subproblem 1
w + -2.0625 = 1.792824238 Simplifying w + -2.0625 = 1.792824238 Reorder the terms: -2.0625 + w = 1.792824238 Solving -2.0625 + w = 1.792824238 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + w = 1.792824238 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + w = 1.792824238 + 2.0625 w = 1.792824238 + 2.0625 Combine like terms: 1.792824238 + 2.0625 = 3.855324238 w = 3.855324238 Simplifying w = 3.855324238Subproblem 2
w + -2.0625 = -1.792824238 Simplifying w + -2.0625 = -1.792824238 Reorder the terms: -2.0625 + w = -1.792824238 Solving -2.0625 + w = -1.792824238 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + w = -1.792824238 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + w = -1.792824238 + 2.0625 w = -1.792824238 + 2.0625 Combine like terms: -1.792824238 + 2.0625 = 0.269675762 w = 0.269675762 Simplifying w = 0.269675762Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.855324238, 0.269675762}
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