m^2+8.18182m+10.9091=0

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Solution for m^2+8.18182m+10.9091=0 equation: 


Simplifying
m2 + 8.18182m + 10.9091 = 0

Reorder the terms:
10.9091 + 8.18182m + m2 = 0

Solving
10.9091 + 8.18182m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-10.9091' to each side of the equation.
10.9091 + 8.18182m + -10.9091 + m2 = 0 + -10.9091

Reorder the terms:
10.9091 + -10.9091 + 8.18182m + m2 = 0 + -10.9091

Combine like terms: 10.9091 + -10.9091 = 0.0000
0.0000 + 8.18182m + m2 = 0 + -10.9091
8.18182m + m2 = 0 + -10.9091

Combine like terms: 0 + -10.9091 = -10.9091
8.18182m + m2 = -10.9091

The m term is 8.18182m.  Take half its coefficient (4.09091).
Square it (16.73554463) and add it to both sides.

Add '16.73554463' to each side of the equation.
8.18182m + 16.73554463 + m2 = -10.9091 + 16.73554463

Reorder the terms:
16.73554463 + 8.18182m + m2 = -10.9091 + 16.73554463

Combine like terms: -10.9091 + 16.73554463 = 5.82644463
16.73554463 + 8.18182m + m2 = 5.82644463

Factor a perfect square on the left side:
(m + 4.09091)(m + 4.09091) = 5.82644463

Calculate the square root of the right side: 2.413802939

Break this problem into two subproblems by setting 
(m + 4.09091) equal to 2.413802939 and -2.413802939.


Subproblem 1
m + 4.09091 = 2.413802939

Simplifying
m + 4.09091 = 2.413802939

Reorder the terms:
4.09091 + m = 2.413802939

Solving
4.09091 + m = 2.413802939

Solving for variable 'm'.

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

Add '-4.09091' to each side of the equation.
4.09091 + -4.09091 + m = 2.413802939 + -4.09091

Combine like terms: 4.09091 + -4.09091 = 0.00000
0.00000 + m = 2.413802939 + -4.09091
m = 2.413802939 + -4.09091

Combine like terms: 2.413802939 + -4.09091 = -1.677107061
m = -1.677107061

Simplifying
m = -1.677107061


Subproblem 2
m + 4.09091 = -2.413802939

Simplifying
m + 4.09091 = -2.413802939

Reorder the terms:
4.09091 + m = -2.413802939

Solving
4.09091 + m = -2.413802939

Solving for variable 'm'.

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

Add '-4.09091' to each side of the equation.
4.09091 + -4.09091 + m = -2.413802939 + -4.09091

Combine like terms: 4.09091 + -4.09091 = 0.00000
0.00000 + m = -2.413802939 + -4.09091
m = -2.413802939 + -4.09091

Combine like terms: -2.413802939 + -4.09091 = -6.504712939
m = -6.504712939

Simplifying
m = -6.504712939


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.677107061, -6.504712939}

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