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Simplifying 6w2 + -11w + -26 = 0 Reorder the terms: -26 + -11w + 6w2 = 0 Solving -26 + -11w + 6w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.333333333 + -1.833333333w + w2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -1.833333333w + 4.333333333 + w2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -1.833333333w + w2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -1.833333333w + w2 = 0 + 4.333333333 -1.833333333w + w2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -1.833333333w + w2 = 4.333333333 The w term is -1.833333333w. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333w + 0.8402777775 + w2 = 4.333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333w + w2 = 4.333333333 + 0.8402777775 Combine like terms: 4.333333333 + 0.8402777775 = 5.1736111105 0.8402777775 + -1.833333333w + w2 = 5.1736111105 Factor a perfect square on the left side: (w + -0.9166666665)(w + -0.9166666665) = 5.1736111105 Calculate the square root of the right side: 2.274557344 Break this problem into two subproblems by setting (w + -0.9166666665) equal to 2.274557344 and -2.274557344.Subproblem 1
w + -0.9166666665 = 2.274557344 Simplifying w + -0.9166666665 = 2.274557344 Reorder the terms: -0.9166666665 + w = 2.274557344 Solving -0.9166666665 + w = 2.274557344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + w = 2.274557344 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + w = 2.274557344 + 0.9166666665 w = 2.274557344 + 0.9166666665 Combine like terms: 2.274557344 + 0.9166666665 = 3.1912240105 w = 3.1912240105 Simplifying w = 3.1912240105Subproblem 2
w + -0.9166666665 = -2.274557344 Simplifying w + -0.9166666665 = -2.274557344 Reorder the terms: -0.9166666665 + w = -2.274557344 Solving -0.9166666665 + w = -2.274557344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + w = -2.274557344 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + w = -2.274557344 + 0.9166666665 w = -2.274557344 + 0.9166666665 Combine like terms: -2.274557344 + 0.9166666665 = -1.3578906775 w = -1.3578906775 Simplifying w = -1.3578906775Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.1912240105, -1.3578906775}
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