m^2+4m-55=0

Solution for m^2+4m-55=0 equation:

Simplifying
m2 + 4m + -55 = 0

Reorder the terms:
-55 + 4m + m2 = 0

Solving
-55 + 4m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 4m + 55 + m2 = 0 + 55

Reorder the terms:
-55 + 55 + 4m + m2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 4m + m2 = 0 + 55
4m + m2 = 0 + 55

Combine like terms: 0 + 55 = 55
4m + m2 = 55

The m term is 4m.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4m + 4 + m2 = 55 + 4

Reorder the terms:
4 + 4m + m2 = 55 + 4

Combine like terms: 55 + 4 = 59
4 + 4m + m2 = 59

Factor a perfect square on the left side:
(m + 2)(m + 2) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(m + 2) equal to 7.681145748 and -7.681145748.

Subproblem 1
m + 2 = 7.681145748

Simplifying
m + 2 = 7.681145748

Reorder the terms:
2 + m = 7.681145748

Solving
2 + m = 7.681145748

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = 7.681145748 + -2

Combine like terms: 2 + -2 = 0
0 + m = 7.681145748 + -2
m = 7.681145748 + -2

Combine like terms: 7.681145748 + -2 = 5.681145748
m = 5.681145748

Simplifying
m = 5.681145748

Subproblem 2
m + 2 = -7.681145748

Simplifying
m + 2 = -7.681145748

Reorder the terms:
2 + m = -7.681145748

Solving
2 + m = -7.681145748

Solving for variable 'm'.

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

Add '-2' to each side of the equation.
2 + -2 + m = -7.681145748 + -2

Combine like terms: 2 + -2 = 0
0 + m = -7.681145748 + -2
m = -7.681145748 + -2

Combine like terms: -7.681145748 + -2 = -9.681145748
m = -9.681145748

Simplifying
m = -9.681145748

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.681145748, -9.681145748}