30m^2-11m-4=0

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Solution for 30m^2-11m-4=0 equation: 


Simplifying
30m2 + -11m + -4 = 0

Reorder the terms:
-4 + -11m + 30m2 = 0

Solving
-4 + -11m + 30m2 = 0

Solving for variable 'm'.

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

Divide each side by '30'.
-0.1333333333 + -0.3666666667m + m2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -0.3666666667m + 0.1333333333 + m2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -0.3666666667m + m2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -0.3666666667m + m2 = 0 + 0.1333333333
-0.3666666667m + m2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
-0.3666666667m + m2 = 0.1333333333

The m term is -0.3666666667m.  Take half its coefficient (-0.1833333334).
Square it (0.03361111114) and add it to both sides.

Add '0.03361111114' to each side of the equation.
-0.3666666667m + 0.03361111114 + m2 = 0.1333333333 + 0.03361111114

Reorder the terms:
0.03361111114 + -0.3666666667m + m2 = 0.1333333333 + 0.03361111114

Combine like terms: 0.1333333333 + 0.03361111114 = 0.16694444444
0.03361111114 + -0.3666666667m + m2 = 0.16694444444

Factor a perfect square on the left side:
(m + -0.1833333334)(m + -0.1833333334) = 0.16694444444

Calculate the square root of the right side: 0.408588356

Break this problem into two subproblems by setting 
(m + -0.1833333334) equal to 0.408588356 and -0.408588356.


Subproblem 1
m + -0.1833333334 = 0.408588356

Simplifying
m + -0.1833333334 = 0.408588356

Reorder the terms:
-0.1833333334 + m = 0.408588356

Solving
-0.1833333334 + m = 0.408588356

Solving for variable 'm'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + m = 0.408588356 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + m = 0.408588356 + 0.1833333334
m = 0.408588356 + 0.1833333334

Combine like terms: 0.408588356 + 0.1833333334 = 0.5919216894
m = 0.5919216894

Simplifying
m = 0.5919216894


Subproblem 2
m + -0.1833333334 = -0.408588356

Simplifying
m + -0.1833333334 = -0.408588356

Reorder the terms:
-0.1833333334 + m = -0.408588356

Solving
-0.1833333334 + m = -0.408588356

Solving for variable 'm'.

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

Add '0.1833333334' to each side of the equation.
-0.1833333334 + 0.1833333334 + m = -0.408588356 + 0.1833333334

Combine like terms: -0.1833333334 + 0.1833333334 = 0.0000000000
0.0000000000 + m = -0.408588356 + 0.1833333334
m = -0.408588356 + 0.1833333334

Combine like terms: -0.408588356 + 0.1833333334 = -0.2252550226
m = -0.2252550226

Simplifying
m = -0.2252550226


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.5919216894, -0.2252550226}

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