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Simplifying n2 + 8n + -60 = 0 Reorder the terms: -60 + 8n + n2 = 0 Solving -60 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 8n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 8n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 8n + n2 = 0 + 60 8n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 8n + n2 = 60 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 = 60 + 16 Reorder the terms: 16 + 8n + n2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + 8n + n2 = 76 Factor a perfect square on the left side: (n + 4)(n + 4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (n + 4) equal to 8.717797887 and -8.717797887.Subproblem 1
n + 4 = 8.717797887 Simplifying n + 4 = 8.717797887 Reorder the terms: 4 + n = 8.717797887 Solving 4 + n = 8.717797887 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 = 8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + n = 8.717797887 + -4 n = 8.717797887 + -4 Combine like terms: 8.717797887 + -4 = 4.717797887 n = 4.717797887 Simplifying n = 4.717797887Subproblem 2
n + 4 = -8.717797887 Simplifying n + 4 = -8.717797887 Reorder the terms: 4 + n = -8.717797887 Solving 4 + n = -8.717797887 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 = -8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + n = -8.717797887 + -4 n = -8.717797887 + -4 Combine like terms: -8.717797887 + -4 = -12.717797887 n = -12.717797887 Simplifying n = -12.717797887Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.717797887, -12.717797887}
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