2m^2+27m-4=0

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Solution for 2m^2+27m-4=0 equation: 


Simplifying
2m2 + 27m + -4 = 0

Reorder the terms:
-4 + 27m + 2m2 = 0

Solving
-4 + 27m + 2m2 = 0

Solving for variable 'm'.

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

Divide each side by '2'.
-2 + 13.5m + m2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 13.5m + 2 + m2 = 0 + 2

Reorder the terms:
-2 + 2 + 13.5m + m2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 13.5m + m2 = 0 + 2
13.5m + m2 = 0 + 2

Combine like terms: 0 + 2 = 2
13.5m + m2 = 2

The m term is 13.5m.  Take half its coefficient (6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
13.5m + 45.5625 + m2 = 2 + 45.5625

Reorder the terms:
45.5625 + 13.5m + m2 = 2 + 45.5625

Combine like terms: 2 + 45.5625 = 47.5625
45.5625 + 13.5m + m2 = 47.5625

Factor a perfect square on the left side:
(m + 6.75)(m + 6.75) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(m + 6.75) equal to 6.896557112 and -6.896557112.


Subproblem 1
m + 6.75 = 6.896557112

Simplifying
m + 6.75 = 6.896557112

Reorder the terms:
6.75 + m = 6.896557112

Solving
6.75 + m = 6.896557112

Solving for variable 'm'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + m = 6.896557112 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + m = 6.896557112 + -6.75
m = 6.896557112 + -6.75

Combine like terms: 6.896557112 + -6.75 = 0.146557112
m = 0.146557112

Simplifying
m = 0.146557112


Subproblem 2
m + 6.75 = -6.896557112

Simplifying
m + 6.75 = -6.896557112

Reorder the terms:
6.75 + m = -6.896557112

Solving
6.75 + m = -6.896557112

Solving for variable 'm'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + m = -6.896557112 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + m = -6.896557112 + -6.75
m = -6.896557112 + -6.75

Combine like terms: -6.896557112 + -6.75 = -13.646557112
m = -13.646557112

Simplifying
m = -13.646557112


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.146557112, -13.646557112}

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