4k^2-8k-2=0

Solution for 4k^2-8k-2=0 equation:

Simplifying
4k2 + -8k + -2 = 0

Reorder the terms:
-2 + -8k + 4k2 = 0

Solving
-2 + -8k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4k + 2k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4k + 2k2)' equal to zero and attempt to solve:

Simplifying
-1 + -4k + 2k2 = 0

Solving
-1 + -4k + 2k2 = 0

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

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

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2k + 0.5 + k2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2k + k2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2k + k2 = 0 + 0.5
-2k + k2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2k + k2 = 0.5

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 = 0.5 + 1

Reorder the terms:
1 + -2k + k2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + -2k + k2 = 1.5

Factor a perfect square on the left side:
(k + -1)(k + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(k + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1
k + -1 = 1.224744871

Simplifying
k + -1 = 1.224744871

Reorder the terms:
-1 + k = 1.224744871

Solving
-1 + k = 1.224744871

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 = 1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + k = 1.224744871 + 1
k = 1.224744871 + 1

Combine like terms: 1.224744871 + 1 = 2.224744871
k = 2.224744871

Simplifying
k = 2.224744871

Subproblem 2
k + -1 = -1.224744871

Simplifying
k + -1 = -1.224744871

Reorder the terms:
-1 + k = -1.224744871

Solving
-1 + k = -1.224744871

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 = -1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + k = -1.224744871 + 1
k = -1.224744871 + 1

Combine like terms: -1.224744871 + 1 = -0.224744871
k = -0.224744871

Simplifying
k = -0.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.224744871, -0.224744871}
Solution
k = {2.224744871, -0.224744871}