k^2-31-2k=-6-3k-2k

Solution for k^2-31-2k=-6-3k-2k equation:

Simplifying
k2 + -31 + -2k = -6 + -3k + -2k

Reorder the terms:
-31 + -2k + k2 = -6 + -3k + -2k

Combine like terms: -3k + -2k = -5k
-31 + -2k + k2 = -6 + -5k

Solving
-31 + -2k + k2 = -6 + -5k

Solving for variable 'k'.

Reorder the terms:
-31 + 6 + -2k + 5k + k2 = -6 + -5k + 6 + 5k

Combine like terms: -31 + 6 = -25
-25 + -2k + 5k + k2 = -6 + -5k + 6 + 5k

Combine like terms: -2k + 5k = 3k
-25 + 3k + k2 = -6 + -5k + 6 + 5k

Reorder the terms:
-25 + 3k + k2 = -6 + 6 + -5k + 5k

Combine like terms: -6 + 6 = 0
-25 + 3k + k2 = 0 + -5k + 5k
-25 + 3k + k2 = -5k + 5k

Combine like terms: -5k + 5k = 0
-25 + 3k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 3k + 25 + k2 = 0 + 25

Reorder the terms:
-25 + 25 + 3k + k2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 3k + k2 = 0 + 25
3k + k2 = 0 + 25

Combine like terms: 0 + 25 = 25
3k + k2 = 25

The k term is 3k.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3k + 2.25 + k2 = 25 + 2.25

Reorder the terms:
2.25 + 3k + k2 = 25 + 2.25

Combine like terms: 25 + 2.25 = 27.25
2.25 + 3k + k2 = 27.25

Factor a perfect square on the left side:
(k + 1.5)(k + 1.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(k + 1.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
k + 1.5 = 5.220153254

Simplifying
k + 1.5 = 5.220153254

Reorder the terms:
1.5 + k = 5.220153254

Solving
1.5 + k = 5.220153254

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = 5.220153254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = 5.220153254 + -1.5
k = 5.220153254 + -1.5

Combine like terms: 5.220153254 + -1.5 = 3.720153254
k = 3.720153254

Simplifying
k = 3.720153254

Subproblem 2
k + 1.5 = -5.220153254

Simplifying
k + 1.5 = -5.220153254

Reorder the terms:
1.5 + k = -5.220153254

Solving
1.5 + k = -5.220153254

Solving for variable 'k'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + k = -5.220153254 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + k = -5.220153254 + -1.5
k = -5.220153254 + -1.5

Combine like terms: -5.220153254 + -1.5 = -6.720153254
k = -6.720153254

Simplifying
k = -6.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.720153254, -6.720153254}