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Simplifying n2 + -10n + 22 = 2 Reorder the terms: 22 + -10n + n2 = 2 Solving 22 + -10n + n2 = 2 Solving for variable 'n'. Reorder the terms: 22 + -2 + -10n + n2 = 2 + -2 Combine like terms: 22 + -2 = 20 20 + -10n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 20 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10n + -20 + n2 = 0 + -20 Reorder the terms: 20 + -20 + -10n + n2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10n + n2 = 0 + -20 -10n + n2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10n + n2 = -20 The n term is -10n. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10n + 25 + n2 = -20 + 25 Reorder the terms: 25 + -10n + n2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + -10n + n2 = 5 Factor a perfect square on the left side: (n + -5)(n + -5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (n + -5) equal to 2.236067978 and -2.236067978.Subproblem 1
n + -5 = 2.236067978 Simplifying n + -5 = 2.236067978 Reorder the terms: -5 + n = 2.236067978 Solving -5 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + n = 2.236067978 + 5 n = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 n = 7.236067978 Simplifying n = 7.236067978Subproblem 2
n + -5 = -2.236067978 Simplifying n + -5 = -2.236067978 Reorder the terms: -5 + n = -2.236067978 Solving -5 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + n = -2.236067978 + 5 n = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 n = 2.763932022 Simplifying n = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.236067978, 2.763932022}
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