2m^2+8m+4=36

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Solution for 2m^2+8m+4=36 equation: 


Simplifying
2m2 + 8m + 4 = 36

Reorder the terms:
4 + 8m + 2m2 = 36

Solving
4 + 8m + 2m2 = 36

Solving for variable 'm'.

Reorder the terms:
4 + -36 + 8m + 2m2 = 36 + -36

Combine like terms: 4 + -36 = -32
-32 + 8m + 2m2 = 36 + -36

Combine like terms: 36 + -36 = 0
-32 + 8m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 4m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + 4m + m2)' equal to zero and attempt to solve:

Simplifying
-16 + 4m + m2 = 0

Solving
-16 + 4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4m + 16 + m2 = 0 + 16

Reorder the terms:
-16 + 16 + 4m + m2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4m + m2 = 0 + 16
4m + m2 = 0 + 16

Combine like terms: 0 + 16 = 16
4m + m2 = 16

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 = 16 + 4

Reorder the terms:
4 + 4m + m2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4m + m2 = 20

Factor a perfect square on the left side:
(m + 2)(m + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(m + 2) equal to 4.472135955 and -4.472135955.


Subproblem 1
m + 2 = 4.472135955

Simplifying
m + 2 = 4.472135955

Reorder the terms:
2 + m = 4.472135955

Solving
2 + m = 4.472135955

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 = 4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + m = 4.472135955 + -2
m = 4.472135955 + -2

Combine like terms: 4.472135955 + -2 = 2.472135955
m = 2.472135955

Simplifying
m = 2.472135955


Subproblem 2
m + 2 = -4.472135955

Simplifying
m + 2 = -4.472135955

Reorder the terms:
2 + m = -4.472135955

Solving
2 + m = -4.472135955

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 = -4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + m = -4.472135955 + -2
m = -4.472135955 + -2

Combine like terms: -4.472135955 + -2 = -6.472135955
m = -6.472135955

Simplifying
m = -6.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.472135955, -6.472135955}
Solution
m = {2.472135955, -6.472135955}

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