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Simplifying n2 + -10n + -11 = 11 Reorder the terms: -11 + -10n + n2 = 11 Solving -11 + -10n + n2 = 11 Solving for variable 'n'. Reorder the terms: -11 + -11 + -10n + n2 = 11 + -11 Combine like terms: -11 + -11 = -22 -22 + -10n + n2 = 11 + -11 Combine like terms: 11 + -11 = 0 -22 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -10n + 22 + n2 = 0 + 22 Reorder the terms: -22 + 22 + -10n + n2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -10n + n2 = 0 + 22 -10n + n2 = 0 + 22 Combine like terms: 0 + 22 = 22 -10n + n2 = 22 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 = 22 + 25 Reorder the terms: 25 + -10n + n2 = 22 + 25 Combine like terms: 22 + 25 = 47 25 + -10n + n2 = 47 Factor a perfect square on the left side: (n + -5)(n + -5) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (n + -5) equal to 6.8556546 and -6.8556546.Subproblem 1
n + -5 = 6.8556546 Simplifying n + -5 = 6.8556546 Reorder the terms: -5 + n = 6.8556546 Solving -5 + n = 6.8556546 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 = 6.8556546 + 5 Combine like terms: -5 + 5 = 0 0 + n = 6.8556546 + 5 n = 6.8556546 + 5 Combine like terms: 6.8556546 + 5 = 11.8556546 n = 11.8556546 Simplifying n = 11.8556546Subproblem 2
n + -5 = -6.8556546 Simplifying n + -5 = -6.8556546 Reorder the terms: -5 + n = -6.8556546 Solving -5 + n = -6.8556546 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 = -6.8556546 + 5 Combine like terms: -5 + 5 = 0 0 + n = -6.8556546 + 5 n = -6.8556546 + 5 Combine like terms: -6.8556546 + 5 = -1.8556546 n = -1.8556546 Simplifying n = -1.8556546Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.8556546, -1.8556546}
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