4k^2-8k-24=0

Solution for 4k^2-8k-24=0 equation:

Simplifying
4k2 + -8k + -24 = 0

Reorder the terms:
-24 + -8k + 4k2 = 0

Solving
-24 + -8k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -2k + k2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -2k + k2)' equal to zero and attempt to solve:

Simplifying
-6 + -2k + k2 = 0

Solving
-6 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2k + 6 + k2 = 0 + 6

Reorder the terms:
-6 + 6 + -2k + k2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2k + k2 = 0 + 6
-2k + k2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2k + k2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2k + k2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2k + k2 = 7

Factor a perfect square on the left side:
(k + -1)(k + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(k + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
k + -1 = 2.645751311

Simplifying
k + -1 = 2.645751311

Reorder the terms:
-1 + k = 2.645751311

Solving
-1 + k = 2.645751311

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + k = 2.645751311 + 1
k = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
k = 3.645751311

Simplifying
k = 3.645751311

Subproblem 2
k + -1 = -2.645751311

Simplifying
k + -1 = -2.645751311

Reorder the terms:
-1 + k = -2.645751311

Solving
-1 + k = -2.645751311

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + k = -2.645751311 + 1
k = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
k = -1.645751311

Simplifying
k = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.645751311, -1.645751311}
Solution
k = {3.645751311, -1.645751311}