m(m)=(m+1)+109(109)

Solution for m(m)=(m+1)+109(109) equation:

Simplifying
m(m) = (m + 1) + 109(109)

Multiply m * m
m2 = (m + 1) + 109(109)

Reorder the terms:
m2 = (1 + m) + 109(109)

Remove parenthesis around (1 + m)
m2 = 1 + m + 109(109)

Multiply 109 * 109
m2 = 1 + m + 11881

Reorder the terms:
m2 = 1 + 11881 + m

Combine like terms: 1 + 11881 = 11882
m2 = 11882 + m

Solving
m2 = 11882 + m

Solving for variable 'm'.

Reorder the terms:
-11882 + -1m + m2 = 11882 + m + -11882 + -1m

Reorder the terms:
-11882 + -1m + m2 = 11882 + -11882 + m + -1m

Combine like terms: 11882 + -11882 = 0
-11882 + -1m + m2 = 0 + m + -1m
-11882 + -1m + m2 = m + -1m

Combine like terms: m + -1m = 0
-11882 + -1m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11882' to each side of the equation.
-11882 + -1m + 11882 + m2 = 0 + 11882

Reorder the terms:
-11882 + 11882 + -1m + m2 = 0 + 11882

Combine like terms: -11882 + 11882 = 0
0 + -1m + m2 = 0 + 11882
-1m + m2 = 0 + 11882

Combine like terms: 0 + 11882 = 11882
-1m + m2 = 11882

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 11882 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 11882 + 0.25

Combine like terms: 11882 + 0.25 = 11882.25
0.25 + -1m + m2 = 11882.25

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 11882.25

Calculate the square root of the right side: 109.005733794

Break this problem into two subproblems by setting 
(m + -0.5) equal to 109.005733794 and -109.005733794.

Subproblem 1
m + -0.5 = 109.005733794

Simplifying
m + -0.5 = 109.005733794

Reorder the terms:
-0.5 + m = 109.005733794

Solving
-0.5 + m = 109.005733794

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 109.005733794 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 109.005733794 + 0.5
m = 109.005733794 + 0.5

Combine like terms: 109.005733794 + 0.5 = 109.505733794
m = 109.505733794

Simplifying
m = 109.505733794

Subproblem 2
m + -0.5 = -109.005733794

Simplifying
m + -0.5 = -109.005733794

Reorder the terms:
-0.5 + m = -109.005733794

Solving
-0.5 + m = -109.005733794

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -109.005733794 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -109.005733794 + 0.5
m = -109.005733794 + 0.5

Combine like terms: -109.005733794 + 0.5 = -108.505733794
m = -108.505733794

Simplifying
m = -108.505733794

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {109.505733794, -108.505733794}