4m^2-40m-56=0

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Solution for 4m^2-40m-56=0 equation: 


Simplifying
4m2 + -40m + -56 = 0

Reorder the terms:
-56 + -40m + 4m2 = 0

Solving
-56 + -40m + 4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -10m + m2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + -10m + m2)' equal to zero and attempt to solve:

Simplifying
-14 + -10m + m2 = 0

Solving
-14 + -10m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -10m + 14 + m2 = 0 + 14

Reorder the terms:
-14 + 14 + -10m + m2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -10m + m2 = 0 + 14
-10m + m2 = 0 + 14

Combine like terms: 0 + 14 = 14
-10m + m2 = 14

The m term is -10m.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10m + 25 + m2 = 14 + 25

Reorder the terms:
25 + -10m + m2 = 14 + 25

Combine like terms: 14 + 25 = 39
25 + -10m + m2 = 39

Factor a perfect square on the left side:
(m + -5)(m + -5) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(m + -5) equal to 6.244997998 and -6.244997998.


Subproblem 1
m + -5 = 6.244997998

Simplifying
m + -5 = 6.244997998

Reorder the terms:
-5 + m = 6.244997998

Solving
-5 + m = 6.244997998

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = 6.244997998 + 5

Combine like terms: -5 + 5 = 0
0 + m = 6.244997998 + 5
m = 6.244997998 + 5

Combine like terms: 6.244997998 + 5 = 11.244997998
m = 11.244997998

Simplifying
m = 11.244997998


Subproblem 2
m + -5 = -6.244997998

Simplifying
m + -5 = -6.244997998

Reorder the terms:
-5 + m = -6.244997998

Solving
-5 + m = -6.244997998

Solving for variable 'm'.

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

Add '5' to each side of the equation.
-5 + 5 + m = -6.244997998 + 5

Combine like terms: -5 + 5 = 0
0 + m = -6.244997998 + 5
m = -6.244997998 + 5

Combine like terms: -6.244997998 + 5 = -1.244997998
m = -1.244997998

Simplifying
m = -1.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {11.244997998, -1.244997998}
Solution
m = {11.244997998, -1.244997998}

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