2(m^2-6m+9)=16

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Solution for 2(m^2-6m+9)=16 equation: 


Simplifying
2(m2 + -6m + 9) = 16

Reorder the terms:
2(9 + -6m + m2) = 16
(9 * 2 + -6m * 2 + m2 * 2) = 16
(18 + -12m + 2m2) = 16

Solving
18 + -12m + 2m2 = 16

Solving for variable 'm'.

Reorder the terms:
18 + -16 + -12m + 2m2 = 16 + -16

Combine like terms: 18 + -16 = 2
2 + -12m + 2m2 = 16 + -16

Combine like terms: 16 + -16 = 0
2 + -12m + 2m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
1 + -6m + m2 = 0

Solving
1 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + -6m + m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6m + m2 = 0 + -1
-6m + m2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6m + m2 = -1

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = -1 + 9

Reorder the terms:
9 + -6m + m2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + -6m + m2 = 8

Factor a perfect square on the left side:
(m + -3)(m + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(m + -3) equal to 2.828427125 and -2.828427125.


Subproblem 1
m + -3 = 2.828427125

Simplifying
m + -3 = 2.828427125

Reorder the terms:
-3 + m = 2.828427125

Solving
-3 + m = 2.828427125

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + m = 2.828427125 + 3
m = 2.828427125 + 3

Combine like terms: 2.828427125 + 3 = 5.828427125
m = 5.828427125

Simplifying
m = 5.828427125


Subproblem 2
m + -3 = -2.828427125

Simplifying
m + -3 = -2.828427125

Reorder the terms:
-3 + m = -2.828427125

Solving
-3 + m = -2.828427125

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + m = -2.828427125 + 3
m = -2.828427125 + 3

Combine like terms: -2.828427125 + 3 = 0.171572875
m = 0.171572875

Simplifying
m = 0.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.828427125, 0.171572875}
Solution
m = {5.828427125, 0.171572875}

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