(-2k+8)k=1

Solution for (-2k+8)k=1 equation:

Simplifying
(-2k + 8) * k = 1

Reorder the terms:
(8 + -2k) * k = 1

Reorder the terms for easier multiplication:
k(8 + -2k) = 1
(8 * k + -2k * k) = 1
(8k + -2k2) = 1

Solving
8k + -2k2 = 1

Solving for variable 'k'.

Reorder the terms:
-1 + 8k + -2k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 8k + -2k2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -4k + k2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4k + -0.5 + k2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4k + k2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4k + k2 = 0 + -0.5
-4k + k2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4k + k2 = -0.5

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = -0.5 + 4

Reorder the terms:
4 + -4k + k2 = -0.5 + 4

Combine like terms: -0.5 + 4 = 3.5
4 + -4k + k2 = 3.5

Factor a perfect square on the left side:
(k + -2)(k + -2) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(k + -2) equal to 1.870828693 and -1.870828693.

Subproblem 1
k + -2 = 1.870828693

Simplifying
k + -2 = 1.870828693

Reorder the terms:
-2 + k = 1.870828693

Solving
-2 + k = 1.870828693

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = 1.870828693 + 2

Combine like terms: -2 + 2 = 0
0 + k = 1.870828693 + 2
k = 1.870828693 + 2

Combine like terms: 1.870828693 + 2 = 3.870828693
k = 3.870828693

Simplifying
k = 3.870828693

Subproblem 2
k + -2 = -1.870828693

Simplifying
k + -2 = -1.870828693

Reorder the terms:
-2 + k = -1.870828693

Solving
-2 + k = -1.870828693

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = -1.870828693 + 2

Combine like terms: -2 + 2 = 0
0 + k = -1.870828693 + 2
k = -1.870828693 + 2

Combine like terms: -1.870828693 + 2 = 0.129171307
k = 0.129171307

Simplifying
k = 0.129171307

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.870828693, 0.129171307}