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Simplifying n2 + -11n + -14 = 0 Reorder the terms: -14 + -11n + n2 = 0 Solving -14 + -11n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -11n + 14 + n2 = 0 + 14 Reorder the terms: -14 + 14 + -11n + n2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -11n + n2 = 0 + 14 -11n + n2 = 0 + 14 Combine like terms: 0 + 14 = 14 -11n + n2 = 14 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = 14 + 30.25 Reorder the terms: 30.25 + -11n + n2 = 14 + 30.25 Combine like terms: 14 + 30.25 = 44.25 30.25 + -11n + n2 = 44.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (n + -5.5) equal to 6.652067348 and -6.652067348.Subproblem 1
n + -5.5 = 6.652067348 Simplifying n + -5.5 = 6.652067348 Reorder the terms: -5.5 + n = 6.652067348 Solving -5.5 + n = 6.652067348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 6.652067348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 6.652067348 + 5.5 n = 6.652067348 + 5.5 Combine like terms: 6.652067348 + 5.5 = 12.152067348 n = 12.152067348 Simplifying n = 12.152067348Subproblem 2
n + -5.5 = -6.652067348 Simplifying n + -5.5 = -6.652067348 Reorder the terms: -5.5 + n = -6.652067348 Solving -5.5 + n = -6.652067348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -6.652067348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -6.652067348 + 5.5 n = -6.652067348 + 5.5 Combine like terms: -6.652067348 + 5.5 = -1.152067348 n = -1.152067348 Simplifying n = -1.152067348Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.152067348, -1.152067348}
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