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Simplifying n2 + -15n + -27 = 0 Reorder the terms: -27 + -15n + n2 = 0 Solving -27 + -15n + 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 + -15n + 27 + n2 = 0 + 27 Reorder the terms: -27 + 27 + -15n + n2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -15n + n2 = 0 + 27 -15n + n2 = 0 + 27 Combine like terms: 0 + 27 = 27 -15n + n2 = 27 The n term is -15n. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15n + 56.25 + n2 = 27 + 56.25 Reorder the terms: 56.25 + -15n + n2 = 27 + 56.25 Combine like terms: 27 + 56.25 = 83.25 56.25 + -15n + n2 = 83.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (n + -7.5) equal to 9.124143795 and -9.124143795.Subproblem 1
n + -7.5 = 9.124143795 Simplifying n + -7.5 = 9.124143795 Reorder the terms: -7.5 + n = 9.124143795 Solving -7.5 + n = 9.124143795 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 9.124143795 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 9.124143795 + 7.5 n = 9.124143795 + 7.5 Combine like terms: 9.124143795 + 7.5 = 16.624143795 n = 16.624143795 Simplifying n = 16.624143795Subproblem 2
n + -7.5 = -9.124143795 Simplifying n + -7.5 = -9.124143795 Reorder the terms: -7.5 + n = -9.124143795 Solving -7.5 + n = -9.124143795 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -9.124143795 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -9.124143795 + 7.5 n = -9.124143795 + 7.5 Combine like terms: -9.124143795 + 7.5 = -1.624143795 n = -1.624143795 Simplifying n = -1.624143795Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.624143795, -1.624143795}
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