8k^2-16k-16=0

Solution for 8k^2-16k-16=0 equation:

Simplifying
8k2 + -16k + -16 = 0

Reorder the terms:
-16 + -16k + 8k2 = 0

Solving
-16 + -16k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -2k + k2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-2 + -2k + k2)' equal to zero and attempt to solve:

Simplifying
-2 + -2k + k2 = 0

Solving
-2 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -2k + k2 = 0 + 2

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

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

The k term is -2k.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2k + 1 + k2 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + -2k + k2 = 3

Factor a perfect square on the left side:
(k + -1)(k + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
k + -1 = 1.732050808

Simplifying
k + -1 = 1.732050808

Reorder the terms:
-1 + k = 1.732050808

Solving
-1 + k = 1.732050808

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + k = 1.732050808 + 1
k = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
k = 2.732050808

Simplifying
k = 2.732050808

Subproblem 2
k + -1 = -1.732050808

Simplifying
k + -1 = -1.732050808

Reorder the terms:
-1 + k = -1.732050808

Solving
-1 + k = -1.732050808

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + k = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + k = -1.732050808 + 1
k = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
k = -0.732050808

Simplifying
k = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.732050808, -0.732050808}
Solution
k = {2.732050808, -0.732050808}