k^2-31-2k=-6

Solution for k^2-31-2k=-6 equation:

Simplifying
k2 + -31 + -2k = -6

Reorder the terms:
-31 + -2k + k2 = -6

Solving
-31 + -2k + k2 = -6

Solving for variable 'k'.

Reorder the terms:
-31 + 6 + -2k + k2 = -6 + 6

Combine like terms: -31 + 6 = -25
-25 + -2k + k2 = -6 + 6

Combine like terms: -6 + 6 = 0
-25 + -2k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -2k + 25 + k2 = 0 + 25

Reorder the terms:
-25 + 25 + -2k + k2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2k + k2 = 0 + 25
-2k + k2 = 0 + 25

Combine like terms: 0 + 25 = 25
-2k + k2 = 25

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 = 25 + 1

Reorder the terms:
1 + -2k + k2 = 25 + 1

Combine like terms: 25 + 1 = 26
1 + -2k + k2 = 26

Factor a perfect square on the left side:
(k + -1)(k + -1) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(k + -1) equal to 5.099019514 and -5.099019514.

Subproblem 1
k + -1 = 5.099019514

Simplifying
k + -1 = 5.099019514

Reorder the terms:
-1 + k = 5.099019514

Solving
-1 + k = 5.099019514

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 = 5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + k = 5.099019514 + 1
k = 5.099019514 + 1

Combine like terms: 5.099019514 + 1 = 6.099019514
k = 6.099019514

Simplifying
k = 6.099019514

Subproblem 2
k + -1 = -5.099019514

Simplifying
k + -1 = -5.099019514

Reorder the terms:
-1 + k = -5.099019514

Solving
-1 + k = -5.099019514

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 = -5.099019514 + 1

Combine like terms: -1 + 1 = 0
0 + k = -5.099019514 + 1
k = -5.099019514 + 1

Combine like terms: -5.099019514 + 1 = -4.099019514
k = -4.099019514

Simplifying
k = -4.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {6.099019514, -4.099019514}