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Simplifying n2 + -8n + -79 = 6 Reorder the terms: -79 + -8n + n2 = 6 Solving -79 + -8n + n2 = 6 Solving for variable 'n'. Reorder the terms: -79 + -6 + -8n + n2 = 6 + -6 Combine like terms: -79 + -6 = -85 -85 + -8n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -85 + -8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -8n + 85 + n2 = 0 + 85 Reorder the terms: -85 + 85 + -8n + n2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -8n + n2 = 0 + 85 -8n + n2 = 0 + 85 Combine like terms: 0 + 85 = 85 -8n + n2 = 85 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 = 85 + 16 Reorder the terms: 16 + -8n + n2 = 85 + 16 Combine like terms: 85 + 16 = 101 16 + -8n + n2 = 101 Factor a perfect square on the left side: (n + -4)(n + -4) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (n + -4) equal to 10.049875621 and -10.049875621.Subproblem 1
n + -4 = 10.049875621 Simplifying n + -4 = 10.049875621 Reorder the terms: -4 + n = 10.049875621 Solving -4 + n = 10.049875621 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 = 10.049875621 + 4 Combine like terms: -4 + 4 = 0 0 + n = 10.049875621 + 4 n = 10.049875621 + 4 Combine like terms: 10.049875621 + 4 = 14.049875621 n = 14.049875621 Simplifying n = 14.049875621Subproblem 2
n + -4 = -10.049875621 Simplifying n + -4 = -10.049875621 Reorder the terms: -4 + n = -10.049875621 Solving -4 + n = -10.049875621 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 = -10.049875621 + 4 Combine like terms: -4 + 4 = 0 0 + n = -10.049875621 + 4 n = -10.049875621 + 4 Combine like terms: -10.049875621 + 4 = -6.049875621 n = -6.049875621 Simplifying n = -6.049875621Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.049875621, -6.049875621}
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