9k^2-5k-8=0

Solution for 9k^2-5k-8=0 equation:

Simplifying
9k2 + -5k + -8 = 0

Reorder the terms:
-8 + -5k + 9k2 = 0

Solving
-8 + -5k + 9k2 = 0

Solving for variable 'k'.

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

Divide each side by '9'.
-0.8888888889 + -0.5555555556k + k2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -0.5555555556k + 0.8888888889 + k2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -0.5555555556k + k2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -0.5555555556k + k2 = 0 + 0.8888888889
-0.5555555556k + k2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-0.5555555556k + k2 = 0.8888888889

The k term is -0.5555555556k.  Take half its coefficient (-0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
-0.5555555556k + 0.07716049384 + k2 = 0.8888888889 + 0.07716049384

Reorder the terms:
0.07716049384 + -0.5555555556k + k2 = 0.8888888889 + 0.07716049384

Combine like terms: 0.8888888889 + 0.07716049384 = 0.96604938274
0.07716049384 + -0.5555555556k + k2 = 0.96604938274

Factor a perfect square on the left side:
(k + -0.2777777778)(k + -0.2777777778) = 0.96604938274

Calculate the square root of the right side: 0.982878112

Break this problem into two subproblems by setting 
(k + -0.2777777778) equal to 0.982878112 and -0.982878112.

Subproblem 1
k + -0.2777777778 = 0.982878112

Simplifying
k + -0.2777777778 = 0.982878112

Reorder the terms:
-0.2777777778 + k = 0.982878112

Solving
-0.2777777778 + k = 0.982878112

Solving for variable 'k'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + k = 0.982878112 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + k = 0.982878112 + 0.2777777778
k = 0.982878112 + 0.2777777778

Combine like terms: 0.982878112 + 0.2777777778 = 1.2606558898
k = 1.2606558898

Simplifying
k = 1.2606558898

Subproblem 2
k + -0.2777777778 = -0.982878112

Simplifying
k + -0.2777777778 = -0.982878112

Reorder the terms:
-0.2777777778 + k = -0.982878112

Solving
-0.2777777778 + k = -0.982878112

Solving for variable 'k'.

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

Add '0.2777777778' to each side of the equation.
-0.2777777778 + 0.2777777778 + k = -0.982878112 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + k = -0.982878112 + 0.2777777778
k = -0.982878112 + 0.2777777778

Combine like terms: -0.982878112 + 0.2777777778 = -0.7051003342
k = -0.7051003342

Simplifying
k = -0.7051003342

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.2606558898, -0.7051003342}