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Simplifying n2 + 2n + -2016 = 0 Reorder the terms: -2016 + 2n + n2 = 0 Solving -2016 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2016' to each side of the equation. -2016 + 2n + 2016 + n2 = 0 + 2016 Reorder the terms: -2016 + 2016 + 2n + n2 = 0 + 2016 Combine like terms: -2016 + 2016 = 0 0 + 2n + n2 = 0 + 2016 2n + n2 = 0 + 2016 Combine like terms: 0 + 2016 = 2016 2n + n2 = 2016 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 = 2016 + 1 Reorder the terms: 1 + 2n + n2 = 2016 + 1 Combine like terms: 2016 + 1 = 2017 1 + 2n + n2 = 2017 Factor a perfect square on the left side: (n + 1)(n + 1) = 2017 Calculate the square root of the right side: 44.911023146 Break this problem into two subproblems by setting (n + 1) equal to 44.911023146 and -44.911023146.Subproblem 1
n + 1 = 44.911023146 Simplifying n + 1 = 44.911023146 Reorder the terms: 1 + n = 44.911023146 Solving 1 + n = 44.911023146 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 = 44.911023146 + -1 Combine like terms: 1 + -1 = 0 0 + n = 44.911023146 + -1 n = 44.911023146 + -1 Combine like terms: 44.911023146 + -1 = 43.911023146 n = 43.911023146 Simplifying n = 43.911023146Subproblem 2
n + 1 = -44.911023146 Simplifying n + 1 = -44.911023146 Reorder the terms: 1 + n = -44.911023146 Solving 1 + n = -44.911023146 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 = -44.911023146 + -1 Combine like terms: 1 + -1 = 0 0 + n = -44.911023146 + -1 n = -44.911023146 + -1 Combine like terms: -44.911023146 + -1 = -45.911023146 n = -45.911023146 Simplifying n = -45.911023146Solution
The solution to the problem is based on the solutions from the subproblems. n = {43.911023146, -45.911023146}
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