9m^2+27m+1=0

Solution for 9m^2+27m+1=0 equation:

Simplifying
9m2 + 27m + 1 = 0

Reorder the terms:
1 + 27m + 9m2 = 0

Solving
1 + 27m + 9m2 = 0

Solving for variable 'm'.

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

Divide each side by '9'.
0.1111111111 + 3m + m2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 3m + -0.1111111111 + m2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 3m + m2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 3m + m2 = 0 + -0.1111111111
3m + m2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
3m + m2 = -0.1111111111

The m term is 3m.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3m + 2.25 + m2 = -0.1111111111 + 2.25

Reorder the terms:
2.25 + 3m + m2 = -0.1111111111 + 2.25

Combine like terms: -0.1111111111 + 2.25 = 2.1388888889
2.25 + 3m + m2 = 2.1388888889

Factor a perfect square on the left side:
(m + 1.5)(m + 1.5) = 2.1388888889

Calculate the square root of the right side: 1.462494065

Break this problem into two subproblems by setting 
(m + 1.5) equal to 1.462494065 and -1.462494065.

Subproblem 1
m + 1.5 = 1.462494065

Simplifying
m + 1.5 = 1.462494065

Reorder the terms:
1.5 + m = 1.462494065

Solving
1.5 + m = 1.462494065

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = 1.462494065 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = 1.462494065 + -1.5
m = 1.462494065 + -1.5

Combine like terms: 1.462494065 + -1.5 = -0.037505935
m = -0.037505935

Simplifying
m = -0.037505935

Subproblem 2
m + 1.5 = -1.462494065

Simplifying
m + 1.5 = -1.462494065

Reorder the terms:
1.5 + m = -1.462494065

Solving
1.5 + m = -1.462494065

Solving for variable 'm'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + m = -1.462494065 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + m = -1.462494065 + -1.5
m = -1.462494065 + -1.5

Combine like terms: -1.462494065 + -1.5 = -2.962494065
m = -2.962494065

Simplifying
m = -2.962494065

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.037505935, -2.962494065}