m(11+m)=8

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Solution for m(11+m)=8 equation: 


Simplifying
m(11 + m) = 8
(11 * m + m * m) = 8
(11m + m2) = 8

Solving
11m + m2 = 8

Solving for variable 'm'.

Reorder the terms:
-8 + 11m + m2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 11m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 11m + 8 + m2 = 0 + 8

Reorder the terms:
-8 + 8 + 11m + m2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 11m + m2 = 0 + 8
11m + m2 = 0 + 8

Combine like terms: 0 + 8 = 8
11m + m2 = 8

The m term is 11m.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11m + 30.25 + m2 = 8 + 30.25

Reorder the terms:
30.25 + 11m + m2 = 8 + 30.25

Combine like terms: 8 + 30.25 = 38.25
30.25 + 11m + m2 = 38.25

Factor a perfect square on the left side:
(m + 5.5)(m + 5.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(m + 5.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
m + 5.5 = 6.184658438

Simplifying
m + 5.5 = 6.184658438

Reorder the terms:
5.5 + m = 6.184658438

Solving
5.5 + m = 6.184658438

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = 6.184658438 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = 6.184658438 + -5.5
m = 6.184658438 + -5.5

Combine like terms: 6.184658438 + -5.5 = 0.684658438
m = 0.684658438

Simplifying
m = 0.684658438


Subproblem 2
m + 5.5 = -6.184658438

Simplifying
m + 5.5 = -6.184658438

Reorder the terms:
5.5 + m = -6.184658438

Solving
5.5 + m = -6.184658438

Solving for variable 'm'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + m = -6.184658438 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + m = -6.184658438 + -5.5
m = -6.184658438 + -5.5

Combine like terms: -6.184658438 + -5.5 = -11.684658438
m = -11.684658438

Simplifying
m = -11.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.684658438, -11.684658438}

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