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Simplifying n2 + -4n = 1 Reorder the terms: -4n + n2 = 1 Solving -4n + n2 = 1 Solving for variable 'n'. Reorder the terms: -1 + -4n + n2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -4n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4n + n2 = 0 + 1 -4n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4n + n2 = 1 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 1 + 4 Reorder the terms: 4 + -4n + n2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4n + n2 = 5 Factor a perfect square on the left side: (n + -2)(n + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (n + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
n + -2 = 2.236067978 Simplifying n + -2 = 2.236067978 Reorder the terms: -2 + n = 2.236067978 Solving -2 + n = 2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + n = 2.236067978 + 2 n = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 n = 4.236067978 Simplifying n = 4.236067978Subproblem 2
n + -2 = -2.236067978 Simplifying n + -2 = -2.236067978 Reorder the terms: -2 + n = -2.236067978 Solving -2 + n = -2.236067978 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + n = -2.236067978 + 2 n = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 n = -0.236067978 Simplifying n = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.236067978, -0.236067978}
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