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Simplifying 2w2 + -11w + -27 = 0 Reorder the terms: -27 + -11w + 2w2 = 0 Solving -27 + -11w + 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'. -13.5 + -5.5w + w2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -5.5w + 13.5 + w2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -5.5w + w2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -5.5w + w2 = 0 + 13.5 -5.5w + w2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -5.5w + w2 = 13.5 The w term is -5.5w. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5w + 7.5625 + w2 = 13.5 + 7.5625 Reorder the terms: 7.5625 + -5.5w + w2 = 13.5 + 7.5625 Combine like terms: 13.5 + 7.5625 = 21.0625 7.5625 + -5.5w + w2 = 21.0625 Factor a perfect square on the left side: (w + -2.75)(w + -2.75) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (w + -2.75) equal to 4.589389938 and -4.589389938.Subproblem 1
w + -2.75 = 4.589389938 Simplifying w + -2.75 = 4.589389938 Reorder the terms: -2.75 + w = 4.589389938 Solving -2.75 + w = 4.589389938 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + w = 4.589389938 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = 4.589389938 + 2.75 w = 4.589389938 + 2.75 Combine like terms: 4.589389938 + 2.75 = 7.339389938 w = 7.339389938 Simplifying w = 7.339389938Subproblem 2
w + -2.75 = -4.589389938 Simplifying w + -2.75 = -4.589389938 Reorder the terms: -2.75 + w = -4.589389938 Solving -2.75 + w = -4.589389938 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + w = -4.589389938 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = -4.589389938 + 2.75 w = -4.589389938 + 2.75 Combine like terms: -4.589389938 + 2.75 = -1.839389938 w = -1.839389938 Simplifying w = -1.839389938Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.339389938, -1.839389938}
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