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Simplifying n2 + -8n + -52 = 9 Reorder the terms: -52 + -8n + n2 = 9 Solving -52 + -8n + n2 = 9 Solving for variable 'n'. Reorder the terms: -52 + -9 + -8n + n2 = 9 + -9 Combine like terms: -52 + -9 = -61 -61 + -8n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -61 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + -8n + 61 + n2 = 0 + 61 Reorder the terms: -61 + 61 + -8n + n2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -8n + n2 = 0 + 61 -8n + n2 = 0 + 61 Combine like terms: 0 + 61 = 61 -8n + n2 = 61 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 = 61 + 16 Reorder the terms: 16 + -8n + n2 = 61 + 16 Combine like terms: 61 + 16 = 77 16 + -8n + n2 = 77 Factor a perfect square on the left side: (n + -4)(n + -4) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (n + -4) equal to 8.774964387 and -8.774964387.Subproblem 1
n + -4 = 8.774964387 Simplifying n + -4 = 8.774964387 Reorder the terms: -4 + n = 8.774964387 Solving -4 + n = 8.774964387 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 = 8.774964387 + 4 Combine like terms: -4 + 4 = 0 0 + n = 8.774964387 + 4 n = 8.774964387 + 4 Combine like terms: 8.774964387 + 4 = 12.774964387 n = 12.774964387 Simplifying n = 12.774964387Subproblem 2
n + -4 = -8.774964387 Simplifying n + -4 = -8.774964387 Reorder the terms: -4 + n = -8.774964387 Solving -4 + n = -8.774964387 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 = -8.774964387 + 4 Combine like terms: -4 + 4 = 0 0 + n = -8.774964387 + 4 n = -8.774964387 + 4 Combine like terms: -8.774964387 + 4 = -4.774964387 n = -4.774964387 Simplifying n = -4.774964387Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.774964387, -4.774964387}
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