N^2-2=8N

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Solution for N^2-2=8N equation: 


Simplifying
N2 + -2 = 8N

Reorder the terms:
-2 + N2 = 8N

Solving
-2 + N2 = 8N

Solving for variable 'N'.

Reorder the terms:
-2 + -8N + N2 = 8N + -8N

Combine like terms: 8N + -8N = 0
-2 + -8N + N2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8N + 2 + N2 = 0 + 2

Reorder the terms:
-2 + 2 + -8N + N2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8N + N2 = 0 + 2
-8N + N2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8N + N2 = 2

The N term is -8N.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8N + 16 + N2 = 2 + 16

Reorder the terms:
16 + -8N + N2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8N + N2 = 18

Factor a perfect square on the left side:
(N + -4)(N + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(N + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
N + -4 = 4.242640687

Simplifying
N + -4 = 4.242640687

Reorder the terms:
-4 + N = 4.242640687

Solving
-4 + N = 4.242640687

Solving for variable 'N'.

Move all terms containing N to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + N = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + N = 4.242640687 + 4
N = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
N = 8.242640687

Simplifying
N = 8.242640687


Subproblem 2
N + -4 = -4.242640687

Simplifying
N + -4 = -4.242640687

Reorder the terms:
-4 + N = -4.242640687

Solving
-4 + N = -4.242640687

Solving for variable 'N'.

Move all terms containing N to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + N = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + N = -4.242640687 + 4
N = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
N = -0.242640687

Simplifying
N = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {8.242640687, -0.242640687}

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