n^2-8n+4=0

Solution for n^2-8n+4=0 equation:

Simplifying
n2 + -8n + 4 = 0

Reorder the terms:
4 + -8n + n2 = 0

Solving
4 + -8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + -8n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8n + n2 = 0 + -4
-8n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8n + n2 = -4

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 = -4 + 16

Reorder the terms:
16 + -8n + n2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8n + n2 = 12

Factor a perfect square on the left side:
(n + -4)(n + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(n + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1
n + -4 = 3.464101615

Simplifying
n + -4 = 3.464101615

Reorder the terms:
-4 + n = 3.464101615

Solving
-4 + n = 3.464101615

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 = 3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + n = 3.464101615 + 4
n = 3.464101615 + 4

Combine like terms: 3.464101615 + 4 = 7.464101615
n = 7.464101615

Simplifying
n = 7.464101615

Subproblem 2
n + -4 = -3.464101615

Simplifying
n + -4 = -3.464101615

Reorder the terms:
-4 + n = -3.464101615

Solving
-4 + n = -3.464101615

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 = -3.464101615 + 4

Combine like terms: -4 + 4 = 0
0 + n = -3.464101615 + 4
n = -3.464101615 + 4

Combine like terms: -3.464101615 + 4 = 0.535898385
n = 0.535898385

Simplifying
n = 0.535898385

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.464101615, 0.535898385}