4k^2+8k-5=-6

Solution for 4k^2+8k-5=-6 equation:

Simplifying
4k2 + 8k + -5 = -6

Reorder the terms:
-5 + 8k + 4k2 = -6

Solving
-5 + 8k + 4k2 = -6

Solving for variable 'k'.

Reorder the terms:
-5 + 6 + 8k + 4k2 = -6 + 6

Combine like terms: -5 + 6 = 1
1 + 8k + 4k2 = -6 + 6

Combine like terms: -6 + 6 = 0
1 + 8k + 4k2 = 0

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

Divide each side by '4'.
0.25 + 2k + k2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2k + -0.25 + k2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2k + k2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2k + k2 = 0 + -0.25
2k + k2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2k + k2 = -0.25

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 = -0.25 + 1

Reorder the terms:
1 + 2k + k2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + 2k + k2 = 0.75

Factor a perfect square on the left side:
(k + 1)(k + 1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(k + 1) equal to 0.866025404 and -0.866025404.

Subproblem 1
k + 1 = 0.866025404

Simplifying
k + 1 = 0.866025404

Reorder the terms:
1 + k = 0.866025404

Solving
1 + k = 0.866025404

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 = 0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0.866025404 + -1
k = 0.866025404 + -1

Combine like terms: 0.866025404 + -1 = -0.133974596
k = -0.133974596

Simplifying
k = -0.133974596

Subproblem 2
k + 1 = -0.866025404

Simplifying
k + 1 = -0.866025404

Reorder the terms:
1 + k = -0.866025404

Solving
1 + k = -0.866025404

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 = -0.866025404 + -1

Combine like terms: 1 + -1 = 0
0 + k = -0.866025404 + -1
k = -0.866025404 + -1

Combine like terms: -0.866025404 + -1 = -1.866025404
k = -1.866025404

Simplifying
k = -1.866025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.133974596, -1.866025404}