9k^2+8k+1=0

Solution for 9k^2+8k+1=0 equation:

Simplifying
9k2 + 8k + 1 = 0

Reorder the terms:
1 + 8k + 9k2 = 0

Solving
1 + 8k + 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'.
0.1111111111 + 0.8888888889k + k2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 0.8888888889k + -0.1111111111 + k2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 0.8888888889k + k2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 0.8888888889k + k2 = 0 + -0.1111111111
0.8888888889k + k2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
0.8888888889k + k2 = -0.1111111111

The k term is 0.8888888889k.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889k + 0.1975308642 + k2 = -0.1111111111 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889k + k2 = -0.1111111111 + 0.1975308642

Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531
0.1975308642 + 0.8888888889k + k2 = 0.0864197531

Factor a perfect square on the left side:
(k + 0.4444444445)(k + 0.4444444445) = 0.0864197531

Calculate the square root of the right side: 0.293972368

Break this problem into two subproblems by setting 
(k + 0.4444444445) equal to 0.293972368 and -0.293972368.

Subproblem 1
k + 0.4444444445 = 0.293972368

Simplifying
k + 0.4444444445 = 0.293972368

Reorder the terms:
0.4444444445 + k = 0.293972368

Solving
0.4444444445 + k = 0.293972368

Solving for variable 'k'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + k = 0.293972368 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + k = 0.293972368 + -0.4444444445
k = 0.293972368 + -0.4444444445

Combine like terms: 0.293972368 + -0.4444444445 = -0.1504720765
k = -0.1504720765

Simplifying
k = -0.1504720765

Subproblem 2
k + 0.4444444445 = -0.293972368

Simplifying
k + 0.4444444445 = -0.293972368

Reorder the terms:
0.4444444445 + k = -0.293972368

Solving
0.4444444445 + k = -0.293972368

Solving for variable 'k'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + k = -0.293972368 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + k = -0.293972368 + -0.4444444445
k = -0.293972368 + -0.4444444445

Combine like terms: -0.293972368 + -0.4444444445 = -0.7384168125
k = -0.7384168125

Simplifying
k = -0.7384168125

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.1504720765, -0.7384168125}