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Simplifying n2 + 8n + -11 = 5 Reorder the terms: -11 + 8n + n2 = 5 Solving -11 + 8n + n2 = 5 Solving for variable 'n'. Reorder the terms: -11 + -5 + 8n + n2 = 5 + -5 Combine like terms: -11 + -5 = -16 -16 + 8n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -16 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 8n + 16 + n2 = 0 + 16 Reorder the terms: -16 + 16 + 8n + n2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8n + n2 = 0 + 16 8n + n2 = 0 + 16 Combine like terms: 0 + 16 = 16 8n + n2 = 16 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 = 16 + 16 Reorder the terms: 16 + 8n + n2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8n + n2 = 32 Factor a perfect square on the left side: (n + 4)(n + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (n + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
n + 4 = 5.656854249 Simplifying n + 4 = 5.656854249 Reorder the terms: 4 + n = 5.656854249 Solving 4 + n = 5.656854249 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 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + n = 5.656854249 + -4 n = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 n = 1.656854249 Simplifying n = 1.656854249Subproblem 2
n + 4 = -5.656854249 Simplifying n + 4 = -5.656854249 Reorder the terms: 4 + n = -5.656854249 Solving 4 + n = -5.656854249 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 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + n = -5.656854249 + -4 n = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 n = -9.656854249 Simplifying n = -9.656854249Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.656854249, -9.656854249}
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