m^2-8=2m(m+4)

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Solution for m^2-8=2m(m+4) equation: 


Simplifying
m2 + -8 = 2m(m + 4)

Reorder the terms:
-8 + m2 = 2m(m + 4)

Reorder the terms:
-8 + m2 = 2m(4 + m)
-8 + m2 = (4 * 2m + m * 2m)
-8 + m2 = (8m + 2m2)

Solving
-8 + m2 = 8m + 2m2

Solving for variable 'm'.

Reorder the terms:
-8 + -8m + m2 + -2m2 = 8m + 2m2 + -8m + -2m2

Combine like terms: m2 + -2m2 = -1m2
-8 + -8m + -1m2 = 8m + 2m2 + -8m + -2m2

Reorder the terms:
-8 + -8m + -1m2 = 8m + -8m + 2m2 + -2m2

Combine like terms: 8m + -8m = 0
-8 + -8m + -1m2 = 0 + 2m2 + -2m2
-8 + -8m + -1m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
-8 + -8m + -1m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 8m + m2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 8m + m2)' equal to zero and attempt to solve:

Simplifying
8 + 8m + m2 = 0

Solving
8 + 8m + m2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The m term is 8m.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8m + 16 + m2 = -8 + 16

Reorder the terms:
16 + 8m + m2 = -8 + 16

Combine like terms: -8 + 16 = 8
16 + 8m + m2 = 8

Factor a perfect square on the left side:
(m + 4)(m + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(m + 4) equal to 2.828427125 and -2.828427125.


Subproblem 1
m + 4 = 2.828427125

Simplifying
m + 4 = 2.828427125

Reorder the terms:
4 + m = 2.828427125

Solving
4 + m = 2.828427125

Solving for variable 'm'.

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

Add '-4' to each side of the equation.
4 + -4 + m = 2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + m = 2.828427125 + -4
m = 2.828427125 + -4

Combine like terms: 2.828427125 + -4 = -1.171572875
m = -1.171572875

Simplifying
m = -1.171572875


Subproblem 2
m + 4 = -2.828427125

Simplifying
m + 4 = -2.828427125

Reorder the terms:
4 + m = -2.828427125

Solving
4 + m = -2.828427125

Solving for variable 'm'.

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

Add '-4' to each side of the equation.
4 + -4 + m = -2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + m = -2.828427125 + -4
m = -2.828427125 + -4

Combine like terms: -2.828427125 + -4 = -6.828427125
m = -6.828427125

Simplifying
m = -6.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.171572875, -6.828427125}
Solution
m = {-1.171572875, -6.828427125}

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