5k^2-10k-16=0

Solution for 5k^2-10k-16=0 equation:

Simplifying
5k2 + -10k + -16 = 0

Reorder the terms:
-16 + -10k + 5k2 = 0

Solving
-16 + -10k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
-3.2 + -2k + k2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -2k + 3.2 + k2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -2k + k2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -2k + k2 = 0 + 3.2
-2k + k2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-2k + k2 = 3.2

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 = 3.2 + 1

Reorder the terms:
1 + -2k + k2 = 3.2 + 1

Combine like terms: 3.2 + 1 = 4.2
1 + -2k + k2 = 4.2

Factor a perfect square on the left side:
(k + -1)(k + -1) = 4.2

Calculate the square root of the right side: 2.049390153

Break this problem into two subproblems by setting 
(k + -1) equal to 2.049390153 and -2.049390153.

Subproblem 1
k + -1 = 2.049390153

Simplifying
k + -1 = 2.049390153

Reorder the terms:
-1 + k = 2.049390153

Solving
-1 + k = 2.049390153

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 = 2.049390153 + 1

Combine like terms: -1 + 1 = 0
0 + k = 2.049390153 + 1
k = 2.049390153 + 1

Combine like terms: 2.049390153 + 1 = 3.049390153
k = 3.049390153

Simplifying
k = 3.049390153

Subproblem 2
k + -1 = -2.049390153

Simplifying
k + -1 = -2.049390153

Reorder the terms:
-1 + k = -2.049390153

Solving
-1 + k = -2.049390153

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 = -2.049390153 + 1

Combine like terms: -1 + 1 = 0
0 + k = -2.049390153 + 1
k = -2.049390153 + 1

Combine like terms: -2.049390153 + 1 = -1.049390153
k = -1.049390153

Simplifying
k = -1.049390153

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.049390153, -1.049390153}