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Simplifying 11n2 + -2 = -2n Reorder the terms: -2 + 11n2 = -2n Solving -2 + 11n2 = -2n Solving for variable 'n'. Reorder the terms: -2 + 2n + 11n2 = -2n + 2n Combine like terms: -2n + 2n = 0 -2 + 2n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + 0.1818181818n + n2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818n + 0.1818181818 + n2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 0.1818181818n + n2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 0.1818181818n + n2 = 0 + 0.1818181818 0.1818181818n + n2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 0.1818181818n + n2 = 0.1818181818 The n term is 0.1818181818n. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818n + 0.008264462808 + n2 = 0.1818181818 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818n + n2 = 0.1818181818 + 0.008264462808 Combine like terms: 0.1818181818 + 0.008264462808 = 0.190082644608 0.008264462808 + 0.1818181818n + n2 = 0.190082644608 Factor a perfect square on the left side: (n + 0.0909090909)(n + 0.0909090909) = 0.190082644608 Calculate the square root of the right side: 0.435984684 Break this problem into two subproblems by setting (n + 0.0909090909) equal to 0.435984684 and -0.435984684.Subproblem 1
n + 0.0909090909 = 0.435984684 Simplifying n + 0.0909090909 = 0.435984684 Reorder the terms: 0.0909090909 + n = 0.435984684 Solving 0.0909090909 + n = 0.435984684 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + n = 0.435984684 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + n = 0.435984684 + -0.0909090909 n = 0.435984684 + -0.0909090909 Combine like terms: 0.435984684 + -0.0909090909 = 0.3450755931 n = 0.3450755931 Simplifying n = 0.3450755931Subproblem 2
n + 0.0909090909 = -0.435984684 Simplifying n + 0.0909090909 = -0.435984684 Reorder the terms: 0.0909090909 + n = -0.435984684 Solving 0.0909090909 + n = -0.435984684 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + n = -0.435984684 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + n = -0.435984684 + -0.0909090909 n = -0.435984684 + -0.0909090909 Combine like terms: -0.435984684 + -0.0909090909 = -0.5268937749 n = -0.5268937749 Simplifying n = -0.5268937749Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.3450755931, -0.5268937749}
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