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Simplifying n2 + 6n + -82 = 0 Reorder the terms: -82 + 6n + n2 = 0 Solving -82 + 6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 6n + 82 + n2 = 0 + 82 Reorder the terms: -82 + 82 + 6n + n2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 6n + n2 = 0 + 82 6n + n2 = 0 + 82 Combine like terms: 0 + 82 = 82 6n + n2 = 82 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 = 82 + 9 Reorder the terms: 9 + 6n + n2 = 82 + 9 Combine like terms: 82 + 9 = 91 9 + 6n + n2 = 91 Factor a perfect square on the left side: (n + 3)(n + 3) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (n + 3) equal to 9.539392014 and -9.539392014.Subproblem 1
n + 3 = 9.539392014 Simplifying n + 3 = 9.539392014 Reorder the terms: 3 + n = 9.539392014 Solving 3 + n = 9.539392014 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 = 9.539392014 + -3 Combine like terms: 3 + -3 = 0 0 + n = 9.539392014 + -3 n = 9.539392014 + -3 Combine like terms: 9.539392014 + -3 = 6.539392014 n = 6.539392014 Simplifying n = 6.539392014Subproblem 2
n + 3 = -9.539392014 Simplifying n + 3 = -9.539392014 Reorder the terms: 3 + n = -9.539392014 Solving 3 + n = -9.539392014 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 = -9.539392014 + -3 Combine like terms: 3 + -3 = 0 0 + n = -9.539392014 + -3 n = -9.539392014 + -3 Combine like terms: -9.539392014 + -3 = -12.539392014 n = -12.539392014 Simplifying n = -12.539392014Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.539392014, -12.539392014}
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