3m^2+12m+1=0

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Solution for 3m^2+12m+1=0 equation: 


Simplifying
3m2 + 12m + 1 = 0

Reorder the terms:
1 + 12m + 3m2 = 0

Solving
1 + 12m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
0.3333333333 + 4m + m2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 4m + -0.3333333333 + m2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 4m + m2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 4m + m2 = 0 + -0.3333333333
4m + m2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
4m + m2 = -0.3333333333

The m term is 4m.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4m + 4 + m2 = -0.3333333333 + 4

Reorder the terms:
4 + 4m + m2 = -0.3333333333 + 4

Combine like terms: -0.3333333333 + 4 = 3.6666666667
4 + 4m + m2 = 3.6666666667

Factor a perfect square on the left side:
(m + 2)(m + 2) = 3.6666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(m + 2) equal to 1.914854216 and -1.914854216.


Subproblem 1
m + 2 = 1.914854216

Simplifying
m + 2 = 1.914854216

Reorder the terms:
2 + m = 1.914854216

Solving
2 + m = 1.914854216

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = 1.914854216 + -2

Combine like terms: 2 + -2 = 0
0 + m = 1.914854216 + -2
m = 1.914854216 + -2

Combine like terms: 1.914854216 + -2 = -0.085145784
m = -0.085145784

Simplifying
m = -0.085145784


Subproblem 2
m + 2 = -1.914854216

Simplifying
m + 2 = -1.914854216

Reorder the terms:
2 + m = -1.914854216

Solving
2 + m = -1.914854216

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = -1.914854216 + -2

Combine like terms: 2 + -2 = 0
0 + m = -1.914854216 + -2
m = -1.914854216 + -2

Combine like terms: -1.914854216 + -2 = -3.914854216
m = -3.914854216

Simplifying
m = -3.914854216


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.085145784, -3.914854216}

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