N^2-2N-22=0

Solution for N^2-2N-22=0 equation:

Simplifying
N2 + -2N + -22 = 0

Reorder the terms:
-22 + -2N + N2 = 0

Solving
-22 + -2N + N2 = 0

Solving for variable 'N'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -2N + 22 + N2 = 0 + 22

Reorder the terms:
-22 + 22 + -2N + N2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -2N + N2 = 0 + 22
-2N + N2 = 0 + 22

Combine like terms: 0 + 22 = 22
-2N + N2 = 22

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 = 22 + 1

Reorder the terms:
1 + -2N + N2 = 22 + 1

Combine like terms: 22 + 1 = 23
1 + -2N + N2 = 23

Factor a perfect square on the left side:
(N + -1)(N + -1) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(N + -1) equal to 4.795831523 and -4.795831523.

Subproblem 1
N + -1 = 4.795831523

Simplifying
N + -1 = 4.795831523

Reorder the terms:
-1 + N = 4.795831523

Solving
-1 + N = 4.795831523

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 = 4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + N = 4.795831523 + 1
N = 4.795831523 + 1

Combine like terms: 4.795831523 + 1 = 5.795831523
N = 5.795831523

Simplifying
N = 5.795831523

Subproblem 2
N + -1 = -4.795831523

Simplifying
N + -1 = -4.795831523

Reorder the terms:
-1 + N = -4.795831523

Solving
-1 + N = -4.795831523

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 = -4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + N = -4.795831523 + 1
N = -4.795831523 + 1

Combine like terms: -4.795831523 + 1 = -3.795831523
N = -3.795831523

Simplifying
N = -3.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {5.795831523, -3.795831523}