4m^2-13m-27=0

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Solution for 4m^2-13m-27=0 equation: 


Simplifying
4m2 + -13m + -27 = 0

Reorder the terms:
-27 + -13m + 4m2 = 0

Solving
-27 + -13m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
-6.75 + -3.25m + m2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + -3.25m + 6.75 + m2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + -3.25m + m2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + -3.25m + m2 = 0 + 6.75
-3.25m + m2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
-3.25m + m2 = 6.75

The m term is -3.25m.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25m + 2.640625 + m2 = 6.75 + 2.640625

Reorder the terms:
2.640625 + -3.25m + m2 = 6.75 + 2.640625

Combine like terms: 6.75 + 2.640625 = 9.390625
2.640625 + -3.25m + m2 = 9.390625

Factor a perfect square on the left side:
(m + -1.625)(m + -1.625) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(m + -1.625) equal to 3.064412668 and -3.064412668.


Subproblem 1
m + -1.625 = 3.064412668

Simplifying
m + -1.625 = 3.064412668

Reorder the terms:
-1.625 + m = 3.064412668

Solving
-1.625 + m = 3.064412668

Solving for variable 'm'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + m = 3.064412668 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + m = 3.064412668 + 1.625
m = 3.064412668 + 1.625

Combine like terms: 3.064412668 + 1.625 = 4.689412668
m = 4.689412668

Simplifying
m = 4.689412668


Subproblem 2
m + -1.625 = -3.064412668

Simplifying
m + -1.625 = -3.064412668

Reorder the terms:
-1.625 + m = -3.064412668

Solving
-1.625 + m = -3.064412668

Solving for variable 'm'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + m = -3.064412668 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + m = -3.064412668 + 1.625
m = -3.064412668 + 1.625

Combine like terms: -3.064412668 + 1.625 = -1.439412668
m = -1.439412668

Simplifying
m = -1.439412668


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.689412668, -1.439412668}

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