-2k^2-24k+64=0

Solution for -2k^2-24k+64=0 equation:

Simplifying
-2k2 + -24k + 64 = 0

Reorder the terms:
64 + -24k + -2k2 = 0

Solving
64 + -24k + -2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -12k + -1k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(32 + -12k + -1k2)' equal to zero and attempt to solve:

Simplifying
32 + -12k + -1k2 = 0

Solving
32 + -12k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-32 + 12k + k2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 12k + 32 + k2 = 0 + 32

Reorder the terms:
-32 + 32 + 12k + k2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 12k + k2 = 0 + 32
12k + k2 = 0 + 32

Combine like terms: 0 + 32 = 32
12k + k2 = 32

The k term is 12k.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12k + 36 + k2 = 32 + 36

Reorder the terms:
36 + 12k + k2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + 12k + k2 = 68

Factor a perfect square on the left side:
(k + 6)(k + 6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(k + 6) equal to 8.246211251 and -8.246211251.

Subproblem 1
k + 6 = 8.246211251

Simplifying
k + 6 = 8.246211251

Reorder the terms:
6 + k = 8.246211251

Solving
6 + k = 8.246211251

Solving for variable 'k'.

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

Add '-6' to each side of the equation.
6 + -6 + k = 8.246211251 + -6

Combine like terms: 6 + -6 = 0
0 + k = 8.246211251 + -6
k = 8.246211251 + -6

Combine like terms: 8.246211251 + -6 = 2.246211251
k = 2.246211251

Simplifying
k = 2.246211251

Subproblem 2
k + 6 = -8.246211251

Simplifying
k + 6 = -8.246211251

Reorder the terms:
6 + k = -8.246211251

Solving
6 + k = -8.246211251

Solving for variable 'k'.

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

Add '-6' to each side of the equation.
6 + -6 + k = -8.246211251 + -6

Combine like terms: 6 + -6 = 0
0 + k = -8.246211251 + -6
k = -8.246211251 + -6

Combine like terms: -8.246211251 + -6 = -14.246211251
k = -14.246211251

Simplifying
k = -14.246211251

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.246211251, -14.246211251}
Solution
k = {2.246211251, -14.246211251}