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Simplifying n2 + 2n + -264 = 0 Reorder the terms: -264 + 2n + n2 = 0 Solving -264 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '264' to each side of the equation. -264 + 2n + 264 + n2 = 0 + 264 Reorder the terms: -264 + 264 + 2n + n2 = 0 + 264 Combine like terms: -264 + 264 = 0 0 + 2n + n2 = 0 + 264 2n + n2 = 0 + 264 Combine like terms: 0 + 264 = 264 2n + n2 = 264 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 = 264 + 1 Reorder the terms: 1 + 2n + n2 = 264 + 1 Combine like terms: 264 + 1 = 265 1 + 2n + n2 = 265 Factor a perfect square on the left side: (n + 1)(n + 1) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (n + 1) equal to 16.278820596 and -16.278820596.Subproblem 1
n + 1 = 16.278820596 Simplifying n + 1 = 16.278820596 Reorder the terms: 1 + n = 16.278820596 Solving 1 + n = 16.278820596 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 = 16.278820596 + -1 Combine like terms: 1 + -1 = 0 0 + n = 16.278820596 + -1 n = 16.278820596 + -1 Combine like terms: 16.278820596 + -1 = 15.278820596 n = 15.278820596 Simplifying n = 15.278820596Subproblem 2
n + 1 = -16.278820596 Simplifying n + 1 = -16.278820596 Reorder the terms: 1 + n = -16.278820596 Solving 1 + n = -16.278820596 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 = -16.278820596 + -1 Combine like terms: 1 + -1 = 0 0 + n = -16.278820596 + -1 n = -16.278820596 + -1 Combine like terms: -16.278820596 + -1 = -17.278820596 n = -17.278820596 Simplifying n = -17.278820596Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.278820596, -17.278820596}
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