m^2-22m-12=0

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Solution for m^2-22m-12=0 equation: 


Simplifying
m2 + -22m + -12 = 0

Reorder the terms:
-12 + -22m + m2 = 0

Solving
-12 + -22m + 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 + -22m + 12 + m2 = 0 + 12

Reorder the terms:
-12 + 12 + -22m + m2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -22m + m2 = 0 + 12
-22m + m2 = 0 + 12

Combine like terms: 0 + 12 = 12
-22m + m2 = 12

The m term is -22m.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22m + 121 + m2 = 12 + 121

Reorder the terms:
121 + -22m + m2 = 12 + 121

Combine like terms: 12 + 121 = 133
121 + -22m + m2 = 133

Factor a perfect square on the left side:
(m + -11)(m + -11) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(m + -11) equal to 11.532562595 and -11.532562595.


Subproblem 1
m + -11 = 11.532562595

Simplifying
m + -11 = 11.532562595

Reorder the terms:
-11 + m = 11.532562595

Solving
-11 + m = 11.532562595

Solving for variable 'm'.

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

Add '11' to each side of the equation.
-11 + 11 + m = 11.532562595 + 11

Combine like terms: -11 + 11 = 0
0 + m = 11.532562595 + 11
m = 11.532562595 + 11

Combine like terms: 11.532562595 + 11 = 22.532562595
m = 22.532562595

Simplifying
m = 22.532562595


Subproblem 2
m + -11 = -11.532562595

Simplifying
m + -11 = -11.532562595

Reorder the terms:
-11 + m = -11.532562595

Solving
-11 + m = -11.532562595

Solving for variable 'm'.

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

Add '11' to each side of the equation.
-11 + 11 + m = -11.532562595 + 11

Combine like terms: -11 + 11 = 0
0 + m = -11.532562595 + 11
m = -11.532562595 + 11

Combine like terms: -11.532562595 + 11 = -0.532562595
m = -0.532562595

Simplifying
m = -0.532562595


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {22.532562595, -0.532562595}

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