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Simplifying n(n + 2) = 118 Reorder the terms: n(2 + n) = 118 (2 * n + n * n) = 118 (2n + n2) = 118 Solving 2n + n2 = 118 Solving for variable 'n'. Reorder the terms: -118 + 2n + n2 = 118 + -118 Combine like terms: 118 + -118 = 0 -118 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 2n + 118 + n2 = 0 + 118 Reorder the terms: -118 + 118 + 2n + n2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 2n + n2 = 0 + 118 2n + n2 = 0 + 118 Combine like terms: 0 + 118 = 118 2n + n2 = 118 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 = 118 + 1 Reorder the terms: 1 + 2n + n2 = 118 + 1 Combine like terms: 118 + 1 = 119 1 + 2n + n2 = 119 Factor a perfect square on the left side: (n + 1)(n + 1) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (n + 1) equal to 10.908712115 and -10.908712115.Subproblem 1
n + 1 = 10.908712115 Simplifying n + 1 = 10.908712115 Reorder the terms: 1 + n = 10.908712115 Solving 1 + n = 10.908712115 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 = 10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + n = 10.908712115 + -1 n = 10.908712115 + -1 Combine like terms: 10.908712115 + -1 = 9.908712115 n = 9.908712115 Simplifying n = 9.908712115Subproblem 2
n + 1 = -10.908712115 Simplifying n + 1 = -10.908712115 Reorder the terms: 1 + n = -10.908712115 Solving 1 + n = -10.908712115 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 = -10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + n = -10.908712115 + -1 n = -10.908712115 + -1 Combine like terms: -10.908712115 + -1 = -11.908712115 n = -11.908712115 Simplifying n = -11.908712115Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.908712115, -11.908712115}
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