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Simplifying n2 + -6n + 6 = 5n + 5 Reorder the terms: 6 + -6n + n2 = 5n + 5 Reorder the terms: 6 + -6n + n2 = 5 + 5n Solving 6 + -6n + n2 = 5 + 5n Solving for variable 'n'. Reorder the terms: 6 + -5 + -6n + -5n + n2 = 5 + 5n + -5 + -5n Combine like terms: 6 + -5 = 1 1 + -6n + -5n + n2 = 5 + 5n + -5 + -5n Combine like terms: -6n + -5n = -11n 1 + -11n + n2 = 5 + 5n + -5 + -5n Reorder the terms: 1 + -11n + n2 = 5 + -5 + 5n + -5n Combine like terms: 5 + -5 = 0 1 + -11n + n2 = 0 + 5n + -5n 1 + -11n + n2 = 5n + -5n Combine like terms: 5n + -5n = 0 1 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -11n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11n + n2 = 0 + -1 -11n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11n + n2 = -1 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 = -1 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11n + n2 = 29.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (n + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
n + -5.5 = 5.408326913 Simplifying n + -5.5 = 5.408326913 Reorder the terms: -5.5 + n = 5.408326913 Solving -5.5 + n = 5.408326913 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 = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 5.408326913 + 5.5 n = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 n = 10.908326913 Simplifying n = 10.908326913Subproblem 2
n + -5.5 = -5.408326913 Simplifying n + -5.5 = -5.408326913 Reorder the terms: -5.5 + n = -5.408326913 Solving -5.5 + n = -5.408326913 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 = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -5.408326913 + 5.5 n = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 n = 0.091673087 Simplifying n = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.908326913, 0.091673087}
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