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Simplifying 11n2 + 4n = 2 Reorder the terms: 4n + 11n2 = 2 Solving 4n + 11n2 = 2 Solving for variable 'n'. Reorder the terms: -2 + 4n + 11n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 4n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + 0.3636363636n + n2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.3636363636n + 0.1818181818 + n2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 0.3636363636n + n2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 0.3636363636n + n2 = 0 + 0.1818181818 0.3636363636n + n2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 0.3636363636n + n2 = 0.1818181818 The n term is 0.3636363636n. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636n + 0.03305785123 + n2 = 0.1818181818 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636n + n2 = 0.1818181818 + 0.03305785123 Combine like terms: 0.1818181818 + 0.03305785123 = 0.21487603303 0.03305785123 + 0.3636363636n + n2 = 0.21487603303 Factor a perfect square on the left side: (n + 0.1818181818)(n + 0.1818181818) = 0.21487603303 Calculate the square root of the right side: 0.463547228 Break this problem into two subproblems by setting (n + 0.1818181818) equal to 0.463547228 and -0.463547228.Subproblem 1
n + 0.1818181818 = 0.463547228 Simplifying n + 0.1818181818 = 0.463547228 Reorder the terms: 0.1818181818 + n = 0.463547228 Solving 0.1818181818 + n = 0.463547228 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + n = 0.463547228 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + n = 0.463547228 + -0.1818181818 n = 0.463547228 + -0.1818181818 Combine like terms: 0.463547228 + -0.1818181818 = 0.2817290462 n = 0.2817290462 Simplifying n = 0.2817290462Subproblem 2
n + 0.1818181818 = -0.463547228 Simplifying n + 0.1818181818 = -0.463547228 Reorder the terms: 0.1818181818 + n = -0.463547228 Solving 0.1818181818 + n = -0.463547228 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + n = -0.463547228 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + n = -0.463547228 + -0.1818181818 n = -0.463547228 + -0.1818181818 Combine like terms: -0.463547228 + -0.1818181818 = -0.6453654098 n = -0.6453654098 Simplifying n = -0.6453654098Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.2817290462, -0.6453654098}
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