6-7k-k^2=0

Solution for 6-7k-k^2=0 equation:

Simplifying
6 + -7k + -1k2 = 0

Solving
6 + -7k + -1k2 = 0

Solving for variable 'k'.

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

Divide each side by '-1'.
-6 + 7k + k2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7k + 6 + k2 = 0 + 6

Reorder the terms:
-6 + 6 + 7k + k2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7k + k2 = 0 + 6
7k + k2 = 0 + 6

Combine like terms: 0 + 6 = 6
7k + k2 = 6

The k term is 7k.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7k + 12.25 + k2 = 6 + 12.25

Reorder the terms:
12.25 + 7k + k2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7k + k2 = 18.25

Factor a perfect square on the left side:
(k + 3.5)(k + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(k + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
k + 3.5 = 4.272001873

Simplifying
k + 3.5 = 4.272001873

Reorder the terms:
3.5 + k = 4.272001873

Solving
3.5 + k = 4.272001873

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = 4.272001873 + -3.5
k = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
k = 0.772001873

Simplifying
k = 0.772001873

Subproblem 2
k + 3.5 = -4.272001873

Simplifying
k + 3.5 = -4.272001873

Reorder the terms:
3.5 + k = -4.272001873

Solving
3.5 + k = -4.272001873

Solving for variable 'k'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + k = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + k = -4.272001873 + -3.5
k = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
k = -7.772001873

Simplifying
k = -7.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.772001873, -7.772001873}