m^2-8m-12=0

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Solution for m^2-8m-12=0 equation: 


Simplifying
m2 + -8m + -12 = 0

Reorder the terms:
-12 + -8m + m2 = 0

Solving
-12 + -8m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8m + 12 + m2 = 0 + 12

Reorder the terms:
-12 + 12 + -8m + m2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8m + m2 = 0 + 12
-8m + m2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8m + m2 = 12

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 = 12 + 16

Reorder the terms:
16 + -8m + m2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8m + m2 = 28

Factor a perfect square on the left side:
(m + -4)(m + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(m + -4) equal to 5.291502622 and -5.291502622.


Subproblem 1
m + -4 = 5.291502622

Simplifying
m + -4 = 5.291502622

Reorder the terms:
-4 + m = 5.291502622

Solving
-4 + m = 5.291502622

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 = 5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + m = 5.291502622 + 4
m = 5.291502622 + 4

Combine like terms: 5.291502622 + 4 = 9.291502622
m = 9.291502622

Simplifying
m = 9.291502622


Subproblem 2
m + -4 = -5.291502622

Simplifying
m + -4 = -5.291502622

Reorder the terms:
-4 + m = -5.291502622

Solving
-4 + m = -5.291502622

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 = -5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + m = -5.291502622 + 4
m = -5.291502622 + 4

Combine like terms: -5.291502622 + 4 = -1.291502622
m = -1.291502622

Simplifying
m = -1.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {9.291502622, -1.291502622}

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