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Simplifying n(n + 2) = 220 Reorder the terms: n(2 + n) = 220 (2 * n + n * n) = 220 (2n + n2) = 220 Solving 2n + n2 = 220 Solving for variable 'n'. Reorder the terms: -220 + 2n + n2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + 2n + 220 + n2 = 0 + 220 Reorder the terms: -220 + 220 + 2n + n2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + 2n + n2 = 0 + 220 2n + n2 = 0 + 220 Combine like terms: 0 + 220 = 220 2n + n2 = 220 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 = 220 + 1 Reorder the terms: 1 + 2n + n2 = 220 + 1 Combine like terms: 220 + 1 = 221 1 + 2n + n2 = 221 Factor a perfect square on the left side: (n + 1)(n + 1) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (n + 1) equal to 14.866068747 and -14.866068747.Subproblem 1
n + 1 = 14.866068747 Simplifying n + 1 = 14.866068747 Reorder the terms: 1 + n = 14.866068747 Solving 1 + n = 14.866068747 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 = 14.866068747 + -1 Combine like terms: 1 + -1 = 0 0 + n = 14.866068747 + -1 n = 14.866068747 + -1 Combine like terms: 14.866068747 + -1 = 13.866068747 n = 13.866068747 Simplifying n = 13.866068747Subproblem 2
n + 1 = -14.866068747 Simplifying n + 1 = -14.866068747 Reorder the terms: 1 + n = -14.866068747 Solving 1 + n = -14.866068747 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 = -14.866068747 + -1 Combine like terms: 1 + -1 = 0 0 + n = -14.866068747 + -1 n = -14.866068747 + -1 Combine like terms: -14.866068747 + -1 = -15.866068747 n = -15.866068747 Simplifying n = -15.866068747Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.866068747, -15.866068747}
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