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Simplifying n2 + -4 = 8n Reorder the terms: -4 + n2 = 8n Solving -4 + n2 = 8n Solving for variable 'n'. Reorder the terms: -4 + -8n + n2 = 8n + -8n Combine like terms: 8n + -8n = 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 = 8.472135955 n = 8.472135955 Simplifying n = 8.472135955Subproblem 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 = -0.472135955 n = -0.472135955 Simplifying n = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.472135955, -0.472135955}
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