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Simplifying 11n2 + -1n + -56 = 0 Reorder the terms: -56 + -1n + 11n2 = 0 Solving -56 + -1n + 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'. -5.090909091 + -0.09090909091n + n2 = 0 Move the constant term to the right: Add '5.090909091' to each side of the equation. -5.090909091 + -0.09090909091n + 5.090909091 + n2 = 0 + 5.090909091 Reorder the terms: -5.090909091 + 5.090909091 + -0.09090909091n + n2 = 0 + 5.090909091 Combine like terms: -5.090909091 + 5.090909091 = 0.000000000 0.000000000 + -0.09090909091n + n2 = 0 + 5.090909091 -0.09090909091n + n2 = 0 + 5.090909091 Combine like terms: 0 + 5.090909091 = 5.090909091 -0.09090909091n + n2 = 5.090909091 The n term is -0.09090909091n. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091n + 0.002066115703 + n2 = 5.090909091 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091n + n2 = 5.090909091 + 0.002066115703 Combine like terms: 5.090909091 + 0.002066115703 = 5.092975206703 0.002066115703 + -0.09090909091n + n2 = 5.092975206703 Factor a perfect square on the left side: (n + -0.04545454546)(n + -0.04545454546) = 5.092975206703 Calculate the square root of the right side: 2.256762107 Break this problem into two subproblems by setting (n + -0.04545454546) equal to 2.256762107 and -2.256762107.Subproblem 1
n + -0.04545454546 = 2.256762107 Simplifying n + -0.04545454546 = 2.256762107 Reorder the terms: -0.04545454546 + n = 2.256762107 Solving -0.04545454546 + n = 2.256762107 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + n = 2.256762107 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + n = 2.256762107 + 0.04545454546 n = 2.256762107 + 0.04545454546 Combine like terms: 2.256762107 + 0.04545454546 = 2.30221665246 n = 2.30221665246 Simplifying n = 2.30221665246Subproblem 2
n + -0.04545454546 = -2.256762107 Simplifying n + -0.04545454546 = -2.256762107 Reorder the terms: -0.04545454546 + n = -2.256762107 Solving -0.04545454546 + n = -2.256762107 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + n = -2.256762107 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + n = -2.256762107 + 0.04545454546 n = -2.256762107 + 0.04545454546 Combine like terms: -2.256762107 + 0.04545454546 = -2.21130756154 n = -2.21130756154 Simplifying n = -2.21130756154Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.30221665246, -2.21130756154}
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