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Simplifying 11n2 + -16 + -2n = 0 Reorder the terms: -16 + -2n + 11n2 = 0 Solving -16 + -2n + 11n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.454545455 + -0.1818181818n + n2 = 0 Move the constant term to the right: Add '1.454545455' to each side of the equation. -1.454545455 + -0.1818181818n + 1.454545455 + n2 = 0 + 1.454545455 Reorder the terms: -1.454545455 + 1.454545455 + -0.1818181818n + n2 = 0 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + -0.1818181818n + n2 = 0 + 1.454545455 -0.1818181818n + n2 = 0 + 1.454545455 Combine like terms: 0 + 1.454545455 = 1.454545455 -0.1818181818n + n2 = 1.454545455 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 = 1.454545455 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818n + n2 = 1.454545455 + 0.008264462808 Combine like terms: 1.454545455 + 0.008264462808 = 1.462809917808 0.008264462808 + -0.1818181818n + n2 = 1.462809917808 Factor a perfect square on the left side: (n + -0.0909090909)(n + -0.0909090909) = 1.462809917808 Calculate the square root of the right side: 1.209466791 Break this problem into two subproblems by setting (n + -0.0909090909) equal to 1.209466791 and -1.209466791.Subproblem 1
n + -0.0909090909 = 1.209466791 Simplifying n + -0.0909090909 = 1.209466791 Reorder the terms: -0.0909090909 + n = 1.209466791 Solving -0.0909090909 + n = 1.209466791 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 = 1.209466791 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + n = 1.209466791 + 0.0909090909 n = 1.209466791 + 0.0909090909 Combine like terms: 1.209466791 + 0.0909090909 = 1.3003758819 n = 1.3003758819 Simplifying n = 1.3003758819Subproblem 2
n + -0.0909090909 = -1.209466791 Simplifying n + -0.0909090909 = -1.209466791 Reorder the terms: -0.0909090909 + n = -1.209466791 Solving -0.0909090909 + n = -1.209466791 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 = -1.209466791 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + n = -1.209466791 + 0.0909090909 n = -1.209466791 + 0.0909090909 Combine like terms: -1.209466791 + 0.0909090909 = -1.1185577001 n = -1.1185577001 Simplifying n = -1.1185577001Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.3003758819, -1.1185577001}
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