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Simplifying n2 + -8n + -488 = 0 Reorder the terms: -488 + -8n + n2 = 0 Solving -488 + -8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '488' to each side of the equation. -488 + -8n + 488 + n2 = 0 + 488 Reorder the terms: -488 + 488 + -8n + n2 = 0 + 488 Combine like terms: -488 + 488 = 0 0 + -8n + n2 = 0 + 488 -8n + n2 = 0 + 488 Combine like terms: 0 + 488 = 488 -8n + n2 = 488 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 = 488 + 16 Reorder the terms: 16 + -8n + n2 = 488 + 16 Combine like terms: 488 + 16 = 504 16 + -8n + n2 = 504 Factor a perfect square on the left side: (n + -4)(n + -4) = 504 Calculate the square root of the right side: 22.449944321 Break this problem into two subproblems by setting (n + -4) equal to 22.449944321 and -22.449944321.Subproblem 1
n + -4 = 22.449944321 Simplifying n + -4 = 22.449944321 Reorder the terms: -4 + n = 22.449944321 Solving -4 + n = 22.449944321 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 = 22.449944321 + 4 Combine like terms: -4 + 4 = 0 0 + n = 22.449944321 + 4 n = 22.449944321 + 4 Combine like terms: 22.449944321 + 4 = 26.449944321 n = 26.449944321 Simplifying n = 26.449944321Subproblem 2
n + -4 = -22.449944321 Simplifying n + -4 = -22.449944321 Reorder the terms: -4 + n = -22.449944321 Solving -4 + n = -22.449944321 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 = -22.449944321 + 4 Combine like terms: -4 + 4 = 0 0 + n = -22.449944321 + 4 n = -22.449944321 + 4 Combine like terms: -22.449944321 + 4 = -18.449944321 n = -18.449944321 Simplifying n = -18.449944321Solution
The solution to the problem is based on the solutions from the subproblems. n = {26.449944321, -18.449944321}
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