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Simplifying n2 + -3n + -27 = 0 Reorder the terms: -27 + -3n + n2 = 0 Solving -27 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -3n + 27 + n2 = 0 + 27 Reorder the terms: -27 + 27 + -3n + n2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -3n + n2 = 0 + 27 -3n + n2 = 0 + 27 Combine like terms: 0 + 27 = 27 -3n + n2 = 27 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 27 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 27 + 2.25 Combine like terms: 27 + 2.25 = 29.25 2.25 + -3n + n2 = 29.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (n + -1.5) equal to 5.408326913 and -5.408326913.Subproblem 1
n + -1.5 = 5.408326913 Simplifying n + -1.5 = 5.408326913 Reorder the terms: -1.5 + n = 5.408326913 Solving -1.5 + n = 5.408326913 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 5.408326913 + 1.5 n = 5.408326913 + 1.5 Combine like terms: 5.408326913 + 1.5 = 6.908326913 n = 6.908326913 Simplifying n = 6.908326913Subproblem 2
n + -1.5 = -5.408326913 Simplifying n + -1.5 = -5.408326913 Reorder the terms: -1.5 + n = -5.408326913 Solving -1.5 + n = -5.408326913 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -5.408326913 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -5.408326913 + 1.5 n = -5.408326913 + 1.5 Combine like terms: -5.408326913 + 1.5 = -3.908326913 n = -3.908326913 Simplifying n = -3.908326913Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.908326913, -3.908326913}
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