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Simplifying n2 + -6n + -77 = -6 Reorder the terms: -77 + -6n + n2 = -6 Solving -77 + -6n + n2 = -6 Solving for variable 'n'. Reorder the terms: -77 + 6 + -6n + n2 = -6 + 6 Combine like terms: -77 + 6 = -71 -71 + -6n + n2 = -6 + 6 Combine like terms: -6 + 6 = 0 -71 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -6n + 71 + n2 = 0 + 71 Reorder the terms: -71 + 71 + -6n + n2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -6n + n2 = 0 + 71 -6n + n2 = 0 + 71 Combine like terms: 0 + 71 = 71 -6n + n2 = 71 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 71 + 9 Reorder the terms: 9 + -6n + n2 = 71 + 9 Combine like terms: 71 + 9 = 80 9 + -6n + n2 = 80 Factor a perfect square on the left side: (n + -3)(n + -3) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (n + -3) equal to 8.94427191 and -8.94427191.Subproblem 1
n + -3 = 8.94427191 Simplifying n + -3 = 8.94427191 Reorder the terms: -3 + n = 8.94427191 Solving -3 + n = 8.94427191 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + n = 8.94427191 + 3 n = 8.94427191 + 3 Combine like terms: 8.94427191 + 3 = 11.94427191 n = 11.94427191 Simplifying n = 11.94427191Subproblem 2
n + -3 = -8.94427191 Simplifying n + -3 = -8.94427191 Reorder the terms: -3 + n = -8.94427191 Solving -3 + n = -8.94427191 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + n = -8.94427191 + 3 n = -8.94427191 + 3 Combine like terms: -8.94427191 + 3 = -5.94427191 n = -5.94427191 Simplifying n = -5.94427191Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.94427191, -5.94427191}
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