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Simplifying n2 + 2n + -180 = 0 Reorder the terms: -180 + 2n + n2 = 0 Solving -180 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 2n + 180 + n2 = 0 + 180 Reorder the terms: -180 + 180 + 2n + n2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 2n + n2 = 0 + 180 2n + n2 = 0 + 180 Combine like terms: 0 + 180 = 180 2n + n2 = 180 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 180 + 1 Reorder the terms: 1 + 2n + n2 = 180 + 1 Combine like terms: 180 + 1 = 181 1 + 2n + n2 = 181 Factor a perfect square on the left side: (n + 1)(n + 1) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (n + 1) equal to 13.453624047 and -13.453624047.Subproblem 1
n + 1 = 13.453624047 Simplifying n + 1 = 13.453624047 Reorder the terms: 1 + n = 13.453624047 Solving 1 + n = 13.453624047 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + n = 13.453624047 + -1 n = 13.453624047 + -1 Combine like terms: 13.453624047 + -1 = 12.453624047 n = 12.453624047 Simplifying n = 12.453624047Subproblem 2
n + 1 = -13.453624047 Simplifying n + 1 = -13.453624047 Reorder the terms: 1 + n = -13.453624047 Solving 1 + n = -13.453624047 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + n = -13.453624047 + -1 n = -13.453624047 + -1 Combine like terms: -13.453624047 + -1 = -14.453624047 n = -14.453624047 Simplifying n = -14.453624047Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.453624047, -14.453624047}
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