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Simplifying n2 + -1n + -2468 = 0 Reorder the terms: -2468 + -1n + n2 = 0 Solving -2468 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2468' to each side of the equation. -2468 + -1n + 2468 + n2 = 0 + 2468 Reorder the terms: -2468 + 2468 + -1n + n2 = 0 + 2468 Combine like terms: -2468 + 2468 = 0 0 + -1n + n2 = 0 + 2468 -1n + n2 = 0 + 2468 Combine like terms: 0 + 2468 = 2468 -1n + n2 = 2468 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 2468 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 2468 + 0.25 Combine like terms: 2468 + 0.25 = 2468.25 0.25 + -1n + n2 = 2468.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2468.25 Calculate the square root of the right side: 49.681485485 Break this problem into two subproblems by setting (n + -0.5) equal to 49.681485485 and -49.681485485.Subproblem 1
n + -0.5 = 49.681485485 Simplifying n + -0.5 = 49.681485485 Reorder the terms: -0.5 + n = 49.681485485 Solving -0.5 + n = 49.681485485 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 49.681485485 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 49.681485485 + 0.5 n = 49.681485485 + 0.5 Combine like terms: 49.681485485 + 0.5 = 50.181485485 n = 50.181485485 Simplifying n = 50.181485485Subproblem 2
n + -0.5 = -49.681485485 Simplifying n + -0.5 = -49.681485485 Reorder the terms: -0.5 + n = -49.681485485 Solving -0.5 + n = -49.681485485 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -49.681485485 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -49.681485485 + 0.5 n = -49.681485485 + 0.5 Combine like terms: -49.681485485 + 0.5 = -49.181485485 n = -49.181485485 Simplifying n = -49.181485485Solution
The solution to the problem is based on the solutions from the subproblems. n = {50.181485485, -49.181485485}
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