2m^2-24m+52=0

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Solution for 2m^2-24m+52=0 equation: 


Simplifying
2m2 + -24m + 52 = 0

Reorder the terms:
52 + -24m + 2m2 = 0

Solving
52 + -24m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(26 + -12m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(26 + -12m + m2)' equal to zero and attempt to solve:

Simplifying
26 + -12m + m2 = 0

Solving
26 + -12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -12m + -26 + m2 = 0 + -26

Reorder the terms:
26 + -26 + -12m + m2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -12m + m2 = 0 + -26
-12m + m2 = 0 + -26

Combine like terms: 0 + -26 = -26
-12m + m2 = -26

The m term is -12m.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12m + 36 + m2 = -26 + 36

Reorder the terms:
36 + -12m + m2 = -26 + 36

Combine like terms: -26 + 36 = 10
36 + -12m + m2 = 10

Factor a perfect square on the left side:
(m + -6)(m + -6) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(m + -6) equal to 3.16227766 and -3.16227766.


Subproblem 1
m + -6 = 3.16227766

Simplifying
m + -6 = 3.16227766

Reorder the terms:
-6 + m = 3.16227766

Solving
-6 + m = 3.16227766

Solving for variable 'm'.

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

Add '6' to each side of the equation.
-6 + 6 + m = 3.16227766 + 6

Combine like terms: -6 + 6 = 0
0 + m = 3.16227766 + 6
m = 3.16227766 + 6

Combine like terms: 3.16227766 + 6 = 9.16227766
m = 9.16227766

Simplifying
m = 9.16227766


Subproblem 2
m + -6 = -3.16227766

Simplifying
m + -6 = -3.16227766

Reorder the terms:
-6 + m = -3.16227766

Solving
-6 + m = -3.16227766

Solving for variable 'm'.

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

Add '6' to each side of the equation.
-6 + 6 + m = -3.16227766 + 6

Combine like terms: -6 + 6 = 0
0 + m = -3.16227766 + 6
m = -3.16227766 + 6

Combine like terms: -3.16227766 + 6 = 2.83772234
m = 2.83772234

Simplifying
m = 2.83772234


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.16227766, 2.83772234}
Solution
m = {9.16227766, 2.83772234}

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