9k^2+12k+1=0

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Solution for 9k^2+12k+1=0 equation: 


Simplifying
9k2 + 12k + 1 = 0

Reorder the terms:
1 + 12k + 9k2 = 0

Solving
1 + 12k + 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 + 1.333333333k + k2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 1.333333333k + -0.1111111111 + k2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 1.333333333k + k2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 1.333333333k + k2 = 0 + -0.1111111111
1.333333333k + k2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
1.333333333k + k2 = -0.1111111111

The k term is 1.333333333k.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333k + 0.4444444442 + k2 = -0.1111111111 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333k + k2 = -0.1111111111 + 0.4444444442

Combine like terms: -0.1111111111 + 0.4444444442 = 0.3333333331
0.4444444442 + 1.333333333k + k2 = 0.3333333331

Factor a perfect square on the left side:
(k + 0.6666666665)(k + 0.6666666665) = 0.3333333331

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(k + 0.6666666665) equal to 0.577350269 and -0.577350269.


Subproblem 1
k + 0.6666666665 = 0.577350269

Simplifying
k + 0.6666666665 = 0.577350269

Reorder the terms:
0.6666666665 + k = 0.577350269

Solving
0.6666666665 + k = 0.577350269

Solving for variable 'k'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + k = 0.577350269 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + k = 0.577350269 + -0.6666666665
k = 0.577350269 + -0.6666666665

Combine like terms: 0.577350269 + -0.6666666665 = -0.0893163975
k = -0.0893163975

Simplifying
k = -0.0893163975


Subproblem 2
k + 0.6666666665 = -0.577350269

Simplifying
k + 0.6666666665 = -0.577350269

Reorder the terms:
0.6666666665 + k = -0.577350269

Solving
0.6666666665 + k = -0.577350269

Solving for variable 'k'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + k = -0.577350269 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + k = -0.577350269 + -0.6666666665
k = -0.577350269 + -0.6666666665

Combine like terms: -0.577350269 + -0.6666666665 = -1.2440169355
k = -1.2440169355

Simplifying
k = -1.2440169355


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.0893163975, -1.2440169355}

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