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Simplifying n2 + 5 = -8n Reorder the terms: 5 + n2 = -8n Solving 5 + n2 = -8n Solving for variable 'n'. Reorder the terms: 5 + 8n + n2 = -8n + 8n Combine like terms: -8n + 8n = 0 5 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 8n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8n + n2 = 0 + -5 8n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 8n + n2 = -5 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 = -5 + 16 Reorder the terms: 16 + 8n + n2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + 8n + n2 = 11 Factor a perfect square on the left side: (n + 4)(n + 4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + 4) equal to 3.31662479 and -3.31662479.Subproblem 1
n + 4 = 3.31662479 Simplifying n + 4 = 3.31662479 Reorder the terms: 4 + n = 3.31662479 Solving 4 + n = 3.31662479 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 = 3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + n = 3.31662479 + -4 n = 3.31662479 + -4 Combine like terms: 3.31662479 + -4 = -0.68337521 n = -0.68337521 Simplifying n = -0.68337521Subproblem 2
n + 4 = -3.31662479 Simplifying n + 4 = -3.31662479 Reorder the terms: 4 + n = -3.31662479 Solving 4 + n = -3.31662479 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 = -3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + n = -3.31662479 + -4 n = -3.31662479 + -4 Combine like terms: -3.31662479 + -4 = -7.31662479 n = -7.31662479 Simplifying n = -7.31662479Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.68337521, -7.31662479}
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