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Simplifying n2 + 8n + -73 = -9 Reorder the terms: -73 + 8n + n2 = -9 Solving -73 + 8n + n2 = -9 Solving for variable 'n'. Reorder the terms: -73 + 9 + 8n + n2 = -9 + 9 Combine like terms: -73 + 9 = -64 -64 + 8n + n2 = -9 + 9 Combine like terms: -9 + 9 = 0 -64 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 8n + 64 + n2 = 0 + 64 Reorder the terms: -64 + 64 + 8n + n2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 8n + n2 = 0 + 64 8n + n2 = 0 + 64 Combine like terms: 0 + 64 = 64 8n + n2 = 64 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 = 64 + 16 Reorder the terms: 16 + 8n + n2 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + 8n + n2 = 80 Factor a perfect square on the left side: (n + 4)(n + 4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (n + 4) equal to 8.94427191 and -8.94427191.Subproblem 1
n + 4 = 8.94427191 Simplifying n + 4 = 8.94427191 Reorder the terms: 4 + n = 8.94427191 Solving 4 + n = 8.94427191 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 = 8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + n = 8.94427191 + -4 n = 8.94427191 + -4 Combine like terms: 8.94427191 + -4 = 4.94427191 n = 4.94427191 Simplifying n = 4.94427191Subproblem 2
n + 4 = -8.94427191 Simplifying n + 4 = -8.94427191 Reorder the terms: 4 + n = -8.94427191 Solving 4 + n = -8.94427191 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 = -8.94427191 + -4 Combine like terms: 4 + -4 = 0 0 + n = -8.94427191 + -4 n = -8.94427191 + -4 Combine like terms: -8.94427191 + -4 = -12.94427191 n = -12.94427191 Simplifying n = -12.94427191Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.94427191, -12.94427191}
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