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Simplifying 11n2 + -2n + -8 = 0 Reorder the terms: -8 + -2n + 11n2 = 0 Solving -8 + -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'. -0.7272727273 + -0.1818181818n + n2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.1818181818n + 0.7272727273 + n2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.1818181818n + n2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.1818181818n + n2 = 0 + 0.7272727273 -0.1818181818n + n2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.1818181818n + n2 = 0.7272727273 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 = 0.7272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818n + n2 = 0.7272727273 + 0.008264462808 Combine like terms: 0.7272727273 + 0.008264462808 = 0.735537190108 0.008264462808 + -0.1818181818n + n2 = 0.735537190108 Factor a perfect square on the left side: (n + -0.0909090909)(n + -0.0909090909) = 0.735537190108 Calculate the square root of the right side: 0.857634648 Break this problem into two subproblems by setting (n + -0.0909090909) equal to 0.857634648 and -0.857634648.Subproblem 1
n + -0.0909090909 = 0.857634648 Simplifying n + -0.0909090909 = 0.857634648 Reorder the terms: -0.0909090909 + n = 0.857634648 Solving -0.0909090909 + n = 0.857634648 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 = 0.857634648 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + n = 0.857634648 + 0.0909090909 n = 0.857634648 + 0.0909090909 Combine like terms: 0.857634648 + 0.0909090909 = 0.9485437389 n = 0.9485437389 Simplifying n = 0.9485437389Subproblem 2
n + -0.0909090909 = -0.857634648 Simplifying n + -0.0909090909 = -0.857634648 Reorder the terms: -0.0909090909 + n = -0.857634648 Solving -0.0909090909 + n = -0.857634648 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 = -0.857634648 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + n = -0.857634648 + 0.0909090909 n = -0.857634648 + 0.0909090909 Combine like terms: -0.857634648 + 0.0909090909 = -0.7667255571 n = -0.7667255571 Simplifying n = -0.7667255571Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.9485437389, -0.7667255571}
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