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Simplifying 2n2 + -11n = -1 Reorder the terms: -11n + 2n2 = -1 Solving -11n + 2n2 = -1 Solving for variable 'n'. Reorder the terms: 1 + -11n + 2n2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -11n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -5.5n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5.5n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5.5n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5.5n + n2 = 0 + -0.5 -5.5n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5.5n + n2 = -0.5 The n term is -5.5n. 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. -5.5n + 7.5625 + n2 = -0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5n + n2 = -0.5 + 7.5625 Combine like terms: -0.5 + 7.5625 = 7.0625 7.5625 + -5.5n + n2 = 7.0625 Factor a perfect square on the left side: (n + -2.75)(n + -2.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (n + -2.75) equal to 2.657536453 and -2.657536453.Subproblem 1
n + -2.75 = 2.657536453 Simplifying n + -2.75 = 2.657536453 Reorder the terms: -2.75 + n = 2.657536453 Solving -2.75 + n = 2.657536453 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = 2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = 2.657536453 + 2.75 n = 2.657536453 + 2.75 Combine like terms: 2.657536453 + 2.75 = 5.407536453 n = 5.407536453 Simplifying n = 5.407536453Subproblem 2
n + -2.75 = -2.657536453 Simplifying n + -2.75 = -2.657536453 Reorder the terms: -2.75 + n = -2.657536453 Solving -2.75 + n = -2.657536453 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = -2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = -2.657536453 + 2.75 n = -2.657536453 + 2.75 Combine like terms: -2.657536453 + 2.75 = 0.092463547 n = 0.092463547 Simplifying n = 0.092463547Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.407536453, 0.092463547}
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