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Simplifying 2w2 + -11w = 1 Reorder the terms: -11w + 2w2 = 1 Solving -11w + 2w2 = 1 Solving for variable 'w'. Reorder the terms: -1 + -11w + 2w2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -11w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -5.5w + w2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.5w + 0.5 + w2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.5w + w2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.5w + w2 = 0 + 0.5 -5.5w + w2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.5w + w2 = 0.5 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 = 0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5w + w2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + -5.5w + w2 = 8.0625 Factor a perfect square on the left side: (w + -2.75)(w + -2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (w + -2.75) equal to 2.839454173 and -2.839454173.Subproblem 1
w + -2.75 = 2.839454173 Simplifying w + -2.75 = 2.839454173 Reorder the terms: -2.75 + w = 2.839454173 Solving -2.75 + w = 2.839454173 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 = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = 2.839454173 + 2.75 w = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 w = 5.589454173 Simplifying w = 5.589454173Subproblem 2
w + -2.75 = -2.839454173 Simplifying w + -2.75 = -2.839454173 Reorder the terms: -2.75 + w = -2.839454173 Solving -2.75 + w = -2.839454173 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 = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + w = -2.839454173 + 2.75 w = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 w = -0.089454173 Simplifying w = -0.089454173Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.589454173, -0.089454173}
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