k^2-8k+6=0

Solution for k^2-8k+6=0 equation:

Simplifying
k2 + -8k + 6 = 0

Reorder the terms:
6 + -8k + k2 = 0

Solving
6 + -8k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -8k + -6 + k2 = 0 + -6

Reorder the terms:
6 + -6 + -8k + k2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -8k + k2 = 0 + -6
-8k + k2 = 0 + -6

Combine like terms: 0 + -6 = -6
-8k + k2 = -6

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

Add '16' to each side of the equation.
-8k + 16 + k2 = -6 + 16

Reorder the terms:
16 + -8k + k2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + -8k + k2 = 10

Factor a perfect square on the left side:
(k + -4)(k + -4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(k + -4) equal to 3.16227766 and -3.16227766.

Subproblem 1
k + -4 = 3.16227766

Simplifying
k + -4 = 3.16227766

Reorder the terms:
-4 + k = 3.16227766

Solving
-4 + k = 3.16227766

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = 3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + k = 3.16227766 + 4
k = 3.16227766 + 4

Combine like terms: 3.16227766 + 4 = 7.16227766
k = 7.16227766

Simplifying
k = 7.16227766

Subproblem 2
k + -4 = -3.16227766

Simplifying
k + -4 = -3.16227766

Reorder the terms:
-4 + k = -3.16227766

Solving
-4 + k = -3.16227766

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + k = -3.16227766 + 4

Combine like terms: -4 + 4 = 0
0 + k = -3.16227766 + 4
k = -3.16227766 + 4

Combine like terms: -3.16227766 + 4 = 0.83772234
k = 0.83772234

Simplifying
k = 0.83772234

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {7.16227766, 0.83772234}