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Simplifying n2 + -27n + 168 = 0 Reorder the terms: 168 + -27n + n2 = 0 Solving 168 + -27n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-168' to each side of the equation. 168 + -27n + -168 + n2 = 0 + -168 Reorder the terms: 168 + -168 + -27n + n2 = 0 + -168 Combine like terms: 168 + -168 = 0 0 + -27n + n2 = 0 + -168 -27n + n2 = 0 + -168 Combine like terms: 0 + -168 = -168 -27n + n2 = -168 The n term is -27n. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27n + 182.25 + n2 = -168 + 182.25 Reorder the terms: 182.25 + -27n + n2 = -168 + 182.25 Combine like terms: -168 + 182.25 = 14.25 182.25 + -27n + n2 = 14.25 Factor a perfect square on the left side: (n + -13.5)(n + -13.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (n + -13.5) equal to 3.774917218 and -3.774917218.Subproblem 1
n + -13.5 = 3.774917218 Simplifying n + -13.5 = 3.774917218 Reorder the terms: -13.5 + n = 3.774917218 Solving -13.5 + n = 3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + n = 3.774917218 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + n = 3.774917218 + 13.5 n = 3.774917218 + 13.5 Combine like terms: 3.774917218 + 13.5 = 17.274917218 n = 17.274917218 Simplifying n = 17.274917218Subproblem 2
n + -13.5 = -3.774917218 Simplifying n + -13.5 = -3.774917218 Reorder the terms: -13.5 + n = -3.774917218 Solving -13.5 + n = -3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + n = -3.774917218 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + n = -3.774917218 + 13.5 n = -3.774917218 + 13.5 Combine like terms: -3.774917218 + 13.5 = 9.725082782 n = 9.725082782 Simplifying n = 9.725082782Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.274917218, 9.725082782}
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