-5k^2-5k+2=-4

Solution for -5k^2-5k+2=-4 equation:

Simplifying
-5k2 + -5k + 2 = -4

Reorder the terms:
2 + -5k + -5k2 = -4

Solving
2 + -5k + -5k2 = -4

Solving for variable 'k'.

Reorder the terms:
2 + 4 + -5k + -5k2 = -4 + 4

Combine like terms: 2 + 4 = 6
6 + -5k + -5k2 = -4 + 4

Combine like terms: -4 + 4 = 0
6 + -5k + -5k2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + k + k2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + k + 1.2 + k2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + k + k2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + k + k2 = 0 + 1.2
k + k2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
k + k2 = 1.2

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + k2 = 1.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + k2 = 1.2 + 0.25

Combine like terms: 1.2 + 0.25 = 1.45
1.25 + k2 = 1.45

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 1.45

Calculate the square root of the right side: 1.204159458

Break this problem into two subproblems by setting 
(k + 0.5) equal to 1.204159458 and -1.204159458.

Subproblem 1
k + 0.5 = 1.204159458

Simplifying
k + 0.5 = 1.204159458

Reorder the terms:
0.5 + k = 1.204159458

Solving
0.5 + k = 1.204159458

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = 1.204159458 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = 1.204159458 + -0.5
k = 1.204159458 + -0.5

Combine like terms: 1.204159458 + -0.5 = 0.704159458
k = 0.704159458

Simplifying
k = 0.704159458

Subproblem 2
k + 0.5 = -1.204159458

Simplifying
k + 0.5 = -1.204159458

Reorder the terms:
0.5 + k = -1.204159458

Solving
0.5 + k = -1.204159458

Solving for variable 'k'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + k = -1.204159458 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + k = -1.204159458 + -0.5
k = -1.204159458 + -0.5

Combine like terms: -1.204159458 + -0.5 = -1.704159458
k = -1.704159458

Simplifying
k = -1.704159458

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.704159458, -1.704159458}