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Simplifying n2 + 1 = 14n Reorder the terms: 1 + n2 = 14n Solving 1 + n2 = 14n Solving for variable 'n'. Reorder the terms: 1 + -14n + n2 = 14n + -14n Combine like terms: 14n + -14n = 0 1 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -14n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -14n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -14n + n2 = 0 + -1 -14n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -14n + n2 = -1 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = -1 + 49 Reorder the terms: 49 + -14n + n2 = -1 + 49 Combine like terms: -1 + 49 = 48 49 + -14n + n2 = 48 Factor a perfect square on the left side: (n + -7)(n + -7) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (n + -7) equal to 6.92820323 and -6.92820323.Subproblem 1
n + -7 = 6.92820323 Simplifying n + -7 = 6.92820323 Reorder the terms: -7 + n = 6.92820323 Solving -7 + n = 6.92820323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + n = 6.92820323 + 7 n = 6.92820323 + 7 Combine like terms: 6.92820323 + 7 = 13.92820323 n = 13.92820323 Simplifying n = 13.92820323Subproblem 2
n + -7 = -6.92820323 Simplifying n + -7 = -6.92820323 Reorder the terms: -7 + n = -6.92820323 Solving -7 + n = -6.92820323 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -6.92820323 + 7 Combine like terms: -7 + 7 = 0 0 + n = -6.92820323 + 7 n = -6.92820323 + 7 Combine like terms: -6.92820323 + 7 = 0.07179677 n = 0.07179677 Simplifying n = 0.07179677Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.92820323, 0.07179677}
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