0=k^2-12k-43

Solution for 0=k^2-12k-43 equation:

Simplifying
0 = k2 + -12k + -43

Reorder the terms:
0 = -43 + -12k + k2

Solving
0 = -43 + -12k + k2

Solving for variable 'k'.

Combine like terms: 0 + 43 = 43
43 + 12k + -1k2 = -43 + -12k + k2 + 43 + 12k + -1k2

Reorder the terms:
43 + 12k + -1k2 = -43 + 43 + -12k + 12k + k2 + -1k2

Combine like terms: -43 + 43 = 0
43 + 12k + -1k2 = 0 + -12k + 12k + k2 + -1k2
43 + 12k + -1k2 = -12k + 12k + k2 + -1k2

Combine like terms: -12k + 12k = 0
43 + 12k + -1k2 = 0 + k2 + -1k2
43 + 12k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
43 + 12k + -1k2 = 0

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

Divide each side by '-1'.
-43 + -12k + k2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -12k + 43 + k2 = 0 + 43

Reorder the terms:
-43 + 43 + -12k + k2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -12k + k2 = 0 + 43
-12k + k2 = 0 + 43

Combine like terms: 0 + 43 = 43
-12k + k2 = 43

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 = 43 + 36

Reorder the terms:
36 + -12k + k2 = 43 + 36

Combine like terms: 43 + 36 = 79
36 + -12k + k2 = 79

Factor a perfect square on the left side:
(k + -6)(k + -6) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(k + -6) equal to 8.888194417 and -8.888194417.

Subproblem 1
k + -6 = 8.888194417

Simplifying
k + -6 = 8.888194417

Reorder the terms:
-6 + k = 8.888194417

Solving
-6 + k = 8.888194417

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 = 8.888194417 + 6

Combine like terms: -6 + 6 = 0
0 + k = 8.888194417 + 6
k = 8.888194417 + 6

Combine like terms: 8.888194417 + 6 = 14.888194417
k = 14.888194417

Simplifying
k = 14.888194417

Subproblem 2
k + -6 = -8.888194417

Simplifying
k + -6 = -8.888194417

Reorder the terms:
-6 + k = -8.888194417

Solving
-6 + k = -8.888194417

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 = -8.888194417 + 6

Combine like terms: -6 + 6 = 0
0 + k = -8.888194417 + 6
k = -8.888194417 + 6

Combine like terms: -8.888194417 + 6 = -2.888194417
k = -2.888194417

Simplifying
k = -2.888194417

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {14.888194417, -2.888194417}