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Simplifying n2 + 8n + -2 = 2 Reorder the terms: -2 + 8n + n2 = 2 Solving -2 + 8n + n2 = 2 Solving for variable 'n'. Reorder the terms: -2 + -2 + 8n + n2 = 2 + -2 Combine like terms: -2 + -2 = -4 -4 + 8n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -4 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 8n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + 8n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8n + n2 = 0 + 4 8n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 8n + n2 = 4 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 = 4 + 16 Reorder the terms: 16 + 8n + n2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8n + n2 = 20 Factor a perfect square on the left side: (n + 4)(n + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (n + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
n + 4 = 4.472135955 Simplifying n + 4 = 4.472135955 Reorder the terms: 4 + n = 4.472135955 Solving 4 + n = 4.472135955 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 = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + n = 4.472135955 + -4 n = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 n = 0.472135955 Simplifying n = 0.472135955Subproblem 2
n + 4 = -4.472135955 Simplifying n + 4 = -4.472135955 Reorder the terms: 4 + n = -4.472135955 Solving 4 + n = -4.472135955 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 = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + n = -4.472135955 + -4 n = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 n = -8.472135955 Simplifying n = -8.472135955Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.472135955, -8.472135955}
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