3k^2+18k+4=0

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Solution for 3k^2+18k+4=0 equation: 


Simplifying
3k2 + 18k + 4 = 0

Reorder the terms:
4 + 18k + 3k2 = 0

Solving
4 + 18k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
1.333333333 + 6k + k2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 6k + -1.333333333 + k2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 6k + k2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 6k + k2 = 0 + -1.333333333
6k + k2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
6k + k2 = -1.333333333

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = -1.333333333 + 9

Reorder the terms:
9 + 6k + k2 = -1.333333333 + 9

Combine like terms: -1.333333333 + 9 = 7.666666667
9 + 6k + k2 = 7.666666667

Factor a perfect square on the left side:
(k + 3)(k + 3) = 7.666666667

Calculate the square root of the right side: 2.768874621

Break this problem into two subproblems by setting 
(k + 3) equal to 2.768874621 and -2.768874621.


Subproblem 1
k + 3 = 2.768874621

Simplifying
k + 3 = 2.768874621

Reorder the terms:
3 + k = 2.768874621

Solving
3 + k = 2.768874621

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 2.768874621 + -3

Combine like terms: 3 + -3 = 0
0 + k = 2.768874621 + -3
k = 2.768874621 + -3

Combine like terms: 2.768874621 + -3 = -0.231125379
k = -0.231125379

Simplifying
k = -0.231125379


Subproblem 2
k + 3 = -2.768874621

Simplifying
k + 3 = -2.768874621

Reorder the terms:
3 + k = -2.768874621

Solving
3 + k = -2.768874621

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -2.768874621 + -3

Combine like terms: 3 + -3 = 0
0 + k = -2.768874621 + -3
k = -2.768874621 + -3

Combine like terms: -2.768874621 + -3 = -5.768874621
k = -5.768874621

Simplifying
k = -5.768874621


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.231125379, -5.768874621}

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