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Simplifying n2 + 16n + -92 = -9 Reorder the terms: -92 + 16n + n2 = -9 Solving -92 + 16n + n2 = -9 Solving for variable 'n'. Reorder the terms: -92 + 9 + 16n + n2 = -9 + 9 Combine like terms: -92 + 9 = -83 -83 + 16n + n2 = -9 + 9 Combine like terms: -9 + 9 = 0 -83 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + 16n + 83 + n2 = 0 + 83 Reorder the terms: -83 + 83 + 16n + n2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + 16n + n2 = 0 + 83 16n + n2 = 0 + 83 Combine like terms: 0 + 83 = 83 16n + n2 = 83 The n term is 16n. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16n + 64 + n2 = 83 + 64 Reorder the terms: 64 + 16n + n2 = 83 + 64 Combine like terms: 83 + 64 = 147 64 + 16n + n2 = 147 Factor a perfect square on the left side: (n + 8)(n + 8) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (n + 8) equal to 12.124355653 and -12.124355653.Subproblem 1
n + 8 = 12.124355653 Simplifying n + 8 = 12.124355653 Reorder the terms: 8 + n = 12.124355653 Solving 8 + n = 12.124355653 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 12.124355653 + -8 Combine like terms: 8 + -8 = 0 0 + n = 12.124355653 + -8 n = 12.124355653 + -8 Combine like terms: 12.124355653 + -8 = 4.124355653 n = 4.124355653 Simplifying n = 4.124355653Subproblem 2
n + 8 = -12.124355653 Simplifying n + 8 = -12.124355653 Reorder the terms: 8 + n = -12.124355653 Solving 8 + n = -12.124355653 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = -12.124355653 + -8 Combine like terms: 8 + -8 = 0 0 + n = -12.124355653 + -8 n = -12.124355653 + -8 Combine like terms: -12.124355653 + -8 = -20.124355653 n = -20.124355653 Simplifying n = -20.124355653Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.124355653, -20.124355653}
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