4k^2-8k-16=0

Solution for 4k^2-8k-16=0 equation:

Simplifying
4k2 + -8k + -16 = 0

Reorder the terms:
-16 + -8k + 4k2 = 0

Solving
-16 + -8k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-4 + -2k + k2 = 0

Solving
-4 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2k + 4 + k2 = 0 + 4

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

Combine like terms: -4 + 4 = 0
0 + -2k + k2 = 0 + 4
-2k + k2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2k + k2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2k + k2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2k + k2 = 5

Factor a perfect square on the left side:
(k + -1)(k + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(k + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
k + -1 = 2.236067978

Simplifying
k + -1 = 2.236067978

Reorder the terms:
-1 + k = 2.236067978

Solving
-1 + k = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + k = 2.236067978 + 1
k = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
k = 3.236067978

Simplifying
k = 3.236067978

Subproblem 2
k + -1 = -2.236067978

Simplifying
k + -1 = -2.236067978

Reorder the terms:
-1 + k = -2.236067978

Solving
-1 + k = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + k = -2.236067978 + 1
k = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
k = -1.236067978

Simplifying
k = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.236067978, -1.236067978}
Solution
k = {3.236067978, -1.236067978}