2m^2-28m+82=0

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Solution for 2m^2-28m+82=0 equation: 


Simplifying
2m2 + -28m + 82 = 0

Reorder the terms:
82 + -28m + 2m2 = 0

Solving
82 + -28m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(41 + -14m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(41 + -14m + m2)' equal to zero and attempt to solve:

Simplifying
41 + -14m + m2 = 0

Solving
41 + -14m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + -14m + -41 + m2 = 0 + -41

Reorder the terms:
41 + -41 + -14m + m2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -14m + m2 = 0 + -41
-14m + m2 = 0 + -41

Combine like terms: 0 + -41 = -41
-14m + m2 = -41

The m term is -14m.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14m + 49 + m2 = -41 + 49

Reorder the terms:
49 + -14m + m2 = -41 + 49

Combine like terms: -41 + 49 = 8
49 + -14m + m2 = 8

Factor a perfect square on the left side:
(m + -7)(m + -7) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(m + -7) equal to 2.828427125 and -2.828427125.


Subproblem 1
m + -7 = 2.828427125

Simplifying
m + -7 = 2.828427125

Reorder the terms:
-7 + m = 2.828427125

Solving
-7 + m = 2.828427125

Solving for variable 'm'.

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

Add '7' to each side of the equation.
-7 + 7 + m = 2.828427125 + 7

Combine like terms: -7 + 7 = 0
0 + m = 2.828427125 + 7
m = 2.828427125 + 7

Combine like terms: 2.828427125 + 7 = 9.828427125
m = 9.828427125

Simplifying
m = 9.828427125


Subproblem 2
m + -7 = -2.828427125

Simplifying
m + -7 = -2.828427125

Reorder the terms:
-7 + m = -2.828427125

Solving
-7 + m = -2.828427125

Solving for variable 'm'.

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

Add '7' to each side of the equation.
-7 + 7 + m = -2.828427125 + 7

Combine like terms: -7 + 7 = 0
0 + m = -2.828427125 + 7
m = -2.828427125 + 7

Combine like terms: -2.828427125 + 7 = 4.171572875
m = 4.171572875

Simplifying
m = 4.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.828427125, 4.171572875}
Solution
m = {9.828427125, 4.171572875}

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