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Simplifying n2 + 8n + -32 = 0 Reorder the terms: -32 + 8n + n2 = 0 Solving -32 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 8n + 32 + n2 = 0 + 32 Reorder the terms: -32 + 32 + 8n + n2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 8n + n2 = 0 + 32 8n + n2 = 0 + 32 Combine like terms: 0 + 32 = 32 8n + n2 = 32 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 = 32 + 16 Reorder the terms: 16 + 8n + n2 = 32 + 16 Combine like terms: 32 + 16 = 48 16 + 8n + n2 = 48 Factor a perfect square on the left side: (n + 4)(n + 4) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (n + 4) equal to 6.92820323 and -6.92820323.Subproblem 1
n + 4 = 6.92820323 Simplifying n + 4 = 6.92820323 Reorder the terms: 4 + n = 6.92820323 Solving 4 + n = 6.92820323 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 = 6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + n = 6.92820323 + -4 n = 6.92820323 + -4 Combine like terms: 6.92820323 + -4 = 2.92820323 n = 2.92820323 Simplifying n = 2.92820323Subproblem 2
n + 4 = -6.92820323 Simplifying n + 4 = -6.92820323 Reorder the terms: 4 + n = -6.92820323 Solving 4 + n = -6.92820323 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 = -6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + n = -6.92820323 + -4 n = -6.92820323 + -4 Combine like terms: -6.92820323 + -4 = -10.92820323 n = -10.92820323 Simplifying n = -10.92820323Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.92820323, -10.92820323}
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