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Simplifying 11n2 = -9n + 5 Reorder the terms: 11n2 = 5 + -9n Solving 11n2 = 5 + -9n Solving for variable 'n'. Reorder the terms: -5 + 9n + 11n2 = 5 + -9n + -5 + 9n Reorder the terms: -5 + 9n + 11n2 = 5 + -5 + -9n + 9n Combine like terms: 5 + -5 = 0 -5 + 9n + 11n2 = 0 + -9n + 9n -5 + 9n + 11n2 = -9n + 9n Combine like terms: -9n + 9n = 0 -5 + 9n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + 0.8181818182n + n2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + 0.8181818182n + 0.4545454545 + n2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + 0.8181818182n + n2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + 0.8181818182n + n2 = 0 + 0.4545454545 0.8181818182n + n2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 0.8181818182n + n2 = 0.4545454545 The n term is 0.8181818182n. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182n + 0.1673553719 + n2 = 0.4545454545 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182n + n2 = 0.4545454545 + 0.1673553719 Combine like terms: 0.4545454545 + 0.1673553719 = 0.6219008264 0.1673553719 + 0.8181818182n + n2 = 0.6219008264 Factor a perfect square on the left side: (n + 0.4090909091)(n + 0.4090909091) = 0.6219008264 Calculate the square root of the right side: 0.78860689 Break this problem into two subproblems by setting (n + 0.4090909091) equal to 0.78860689 and -0.78860689.Subproblem 1
n + 0.4090909091 = 0.78860689 Simplifying n + 0.4090909091 = 0.78860689 Reorder the terms: 0.4090909091 + n = 0.78860689 Solving 0.4090909091 + n = 0.78860689 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + n = 0.78860689 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + n = 0.78860689 + -0.4090909091 n = 0.78860689 + -0.4090909091 Combine like terms: 0.78860689 + -0.4090909091 = 0.3795159809 n = 0.3795159809 Simplifying n = 0.3795159809Subproblem 2
n + 0.4090909091 = -0.78860689 Simplifying n + 0.4090909091 = -0.78860689 Reorder the terms: 0.4090909091 + n = -0.78860689 Solving 0.4090909091 + n = -0.78860689 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + n = -0.78860689 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + n = -0.78860689 + -0.4090909091 n = -0.78860689 + -0.4090909091 Combine like terms: -0.78860689 + -0.4090909091 = -1.1976977991 n = -1.1976977991 Simplifying n = -1.1976977991Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.3795159809, -1.1976977991}
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