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Simplifying n2 + 8n + -92 = 0 Reorder the terms: -92 + 8n + n2 = 0 Solving -92 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 8n + 92 + n2 = 0 + 92 Reorder the terms: -92 + 92 + 8n + n2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 8n + n2 = 0 + 92 8n + n2 = 0 + 92 Combine like terms: 0 + 92 = 92 8n + n2 = 92 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = 92 + 16 Reorder the terms: 16 + 8n + n2 = 92 + 16 Combine like terms: 92 + 16 = 108 16 + 8n + n2 = 108 Factor a perfect square on the left side: (n + 4)(n + 4) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (n + 4) equal to 10.392304845 and -10.392304845.Subproblem 1
n + 4 = 10.392304845 Simplifying n + 4 = 10.392304845 Reorder the terms: 4 + n = 10.392304845 Solving 4 + n = 10.392304845 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 10.392304845 + -4 Combine like terms: 4 + -4 = 0 0 + n = 10.392304845 + -4 n = 10.392304845 + -4 Combine like terms: 10.392304845 + -4 = 6.392304845 n = 6.392304845 Simplifying n = 6.392304845Subproblem 2
n + 4 = -10.392304845 Simplifying n + 4 = -10.392304845 Reorder the terms: 4 + n = -10.392304845 Solving 4 + n = -10.392304845 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -10.392304845 + -4 Combine like terms: 4 + -4 = 0 0 + n = -10.392304845 + -4 n = -10.392304845 + -4 Combine like terms: -10.392304845 + -4 = -14.392304845 n = -14.392304845 Simplifying n = -14.392304845Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.392304845, -14.392304845}
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