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Simplifying n2 + -2n + -92 = -10 Reorder the terms: -92 + -2n + n2 = -10 Solving -92 + -2n + n2 = -10 Solving for variable 'n'. Reorder the terms: -92 + 10 + -2n + n2 = -10 + 10 Combine like terms: -92 + 10 = -82 -82 + -2n + n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -82 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -2n + 82 + n2 = 0 + 82 Reorder the terms: -82 + 82 + -2n + n2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -2n + n2 = 0 + 82 -2n + n2 = 0 + 82 Combine like terms: 0 + 82 = 82 -2n + n2 = 82 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 82 + 1 Reorder the terms: 1 + -2n + n2 = 82 + 1 Combine like terms: 82 + 1 = 83 1 + -2n + n2 = 83 Factor a perfect square on the left side: (n + -1)(n + -1) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (n + -1) equal to 9.110433579 and -9.110433579.Subproblem 1
n + -1 = 9.110433579 Simplifying n + -1 = 9.110433579 Reorder the terms: -1 + n = 9.110433579 Solving -1 + n = 9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 9.110433579 + 1 Combine like terms: -1 + 1 = 0 0 + n = 9.110433579 + 1 n = 9.110433579 + 1 Combine like terms: 9.110433579 + 1 = 10.110433579 n = 10.110433579 Simplifying n = 10.110433579Subproblem 2
n + -1 = -9.110433579 Simplifying n + -1 = -9.110433579 Reorder the terms: -1 + n = -9.110433579 Solving -1 + n = -9.110433579 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -9.110433579 + 1 Combine like terms: -1 + 1 = 0 0 + n = -9.110433579 + 1 n = -9.110433579 + 1 Combine like terms: -9.110433579 + 1 = -8.110433579 n = -8.110433579 Simplifying n = -8.110433579Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.110433579, -8.110433579}
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