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Simplifying n2 + -10n + 11 = 0 Reorder the terms: 11 + -10n + n2 = 0 Solving 11 + -10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -10n + -11 + n2 = 0 + -11 Reorder the terms: 11 + -11 + -10n + n2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10n + n2 = 0 + -11 -10n + n2 = 0 + -11 Combine like terms: 0 + -11 = -11 -10n + n2 = -11 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 = -11 + 25 Reorder the terms: 25 + -10n + n2 = -11 + 25 Combine like terms: -11 + 25 = 14 25 + -10n + n2 = 14 Factor a perfect square on the left side: (n + -5)(n + -5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + -5) equal to 3.741657387 and -3.741657387.Subproblem 1
n + -5 = 3.741657387 Simplifying n + -5 = 3.741657387 Reorder the terms: -5 + n = 3.741657387 Solving -5 + n = 3.741657387 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 = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + n = 3.741657387 + 5 n = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 n = 8.741657387 Simplifying n = 8.741657387Subproblem 2
n + -5 = -3.741657387 Simplifying n + -5 = -3.741657387 Reorder the terms: -5 + n = -3.741657387 Solving -5 + n = -3.741657387 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 = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + n = -3.741657387 + 5 n = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 n = 1.258342613 Simplifying n = 1.258342613Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.741657387, 1.258342613}
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