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Simplifying n2 + -18n + 81 = 5 Reorder the terms: 81 + -18n + n2 = 5 Solving 81 + -18n + n2 = 5 Solving for variable 'n'. Reorder the terms: 81 + -5 + -18n + n2 = 5 + -5 Combine like terms: 81 + -5 = 76 76 + -18n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 76 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + -18n + -76 + n2 = 0 + -76 Reorder the terms: 76 + -76 + -18n + n2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + -18n + n2 = 0 + -76 -18n + n2 = 0 + -76 Combine like terms: 0 + -76 = -76 -18n + n2 = -76 The n term is -18n. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18n + 81 + n2 = -76 + 81 Reorder the terms: 81 + -18n + n2 = -76 + 81 Combine like terms: -76 + 81 = 5 81 + -18n + n2 = 5 Factor a perfect square on the left side: (n + -9)(n + -9) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (n + -9) equal to 2.236067978 and -2.236067978.Subproblem 1
n + -9 = 2.236067978 Simplifying n + -9 = 2.236067978 Reorder the terms: -9 + n = 2.236067978 Solving -9 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = 2.236067978 + 9 Combine like terms: -9 + 9 = 0 0 + n = 2.236067978 + 9 n = 2.236067978 + 9 Combine like terms: 2.236067978 + 9 = 11.236067978 n = 11.236067978 Simplifying n = 11.236067978Subproblem 2
n + -9 = -2.236067978 Simplifying n + -9 = -2.236067978 Reorder the terms: -9 + n = -2.236067978 Solving -9 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + n = -2.236067978 + 9 Combine like terms: -9 + 9 = 0 0 + n = -2.236067978 + 9 n = -2.236067978 + 9 Combine like terms: -2.236067978 + 9 = 6.763932022 n = 6.763932022 Simplifying n = 6.763932022Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.236067978, 6.763932022}
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