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Simplifying n2 + -6n + 9 = 5 Reorder the terms: 9 + -6n + n2 = 5 Solving 9 + -6n + n2 = 5 Solving for variable 'n'. Reorder the terms: 9 + -5 + -6n + n2 = 5 + -5 Combine like terms: 9 + -5 = 4 4 + -6n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 4 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + -6n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6n + n2 = 0 + -4 -6n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6n + n2 = -4 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = -4 + 9 Reorder the terms: 9 + -6n + n2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6n + n2 = 5 Factor a perfect square on the left side: (n + -3)(n + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (n + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
n + -3 = 2.236067978 Simplifying n + -3 = 2.236067978 Reorder the terms: -3 + n = 2.236067978 Solving -3 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + n = 2.236067978 + 3 n = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 n = 5.236067978 Simplifying n = 5.236067978Subproblem 2
n + -3 = -2.236067978 Simplifying n + -3 = -2.236067978 Reorder the terms: -3 + n = -2.236067978 Solving -3 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + n = -2.236067978 + 3 n = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 n = 0.763932022 Simplifying n = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.236067978, 0.763932022}
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