12m^2+7m-1=0

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Solution for 12m^2+7m-1=0 equation: 


Simplifying
12m2 + 7m + -1 = 0

Reorder the terms:
-1 + 7m + 12m2 = 0

Solving
-1 + 7m + 12m2 = 0

Solving for variable 'm'.

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

Divide each side by '12'.
-0.08333333333 + 0.5833333333m + m2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.5833333333m + 0.08333333333 + m2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.5833333333m + m2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.5833333333m + m2 = 0 + 0.08333333333
0.5833333333m + m2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
0.5833333333m + m2 = 0.08333333333

The m term is 0.5833333333m.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333m + 0.08506944446 + m2 = 0.08333333333 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333m + m2 = 0.08333333333 + 0.08506944446

Combine like terms: 0.08333333333 + 0.08506944446 = 0.16840277779
0.08506944446 + 0.5833333333m + m2 = 0.16840277779

Factor a perfect square on the left side:
(m + 0.2916666667)(m + 0.2916666667) = 0.16840277779

Calculate the square root of the right side: 0.410369075

Break this problem into two subproblems by setting 
(m + 0.2916666667) equal to 0.410369075 and -0.410369075.


Subproblem 1
m + 0.2916666667 = 0.410369075

Simplifying
m + 0.2916666667 = 0.410369075

Reorder the terms:
0.2916666667 + m = 0.410369075

Solving
0.2916666667 + m = 0.410369075

Solving for variable 'm'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + m = 0.410369075 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + m = 0.410369075 + -0.2916666667
m = 0.410369075 + -0.2916666667

Combine like terms: 0.410369075 + -0.2916666667 = 0.1187024083
m = 0.1187024083

Simplifying
m = 0.1187024083


Subproblem 2
m + 0.2916666667 = -0.410369075

Simplifying
m + 0.2916666667 = -0.410369075

Reorder the terms:
0.2916666667 + m = -0.410369075

Solving
0.2916666667 + m = -0.410369075

Solving for variable 'm'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + m = -0.410369075 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + m = -0.410369075 + -0.2916666667
m = -0.410369075 + -0.2916666667

Combine like terms: -0.410369075 + -0.2916666667 = -0.7020357417
m = -0.7020357417

Simplifying
m = -0.7020357417


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.1187024083, -0.7020357417}

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