m^2-20m=-33

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Solution for m^2-20m=-33 equation: 


Simplifying
m2 + -20m = -33

Reorder the terms:
-20m + m2 = -33

Solving
-20m + m2 = -33

Solving for variable 'm'.

Reorder the terms:
33 + -20m + m2 = -33 + 33

Combine like terms: -33 + 33 = 0
33 + -20m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + -20m + -33 + m2 = 0 + -33

Reorder the terms:
33 + -33 + -20m + m2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -20m + m2 = 0 + -33
-20m + m2 = 0 + -33

Combine like terms: 0 + -33 = -33
-20m + m2 = -33

The m term is -20m.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20m + 100 + m2 = -33 + 100

Reorder the terms:
100 + -20m + m2 = -33 + 100

Combine like terms: -33 + 100 = 67
100 + -20m + m2 = 67

Factor a perfect square on the left side:
(m + -10)(m + -10) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(m + -10) equal to 8.185352772 and -8.185352772.


Subproblem 1
m + -10 = 8.185352772

Simplifying
m + -10 = 8.185352772

Reorder the terms:
-10 + m = 8.185352772

Solving
-10 + m = 8.185352772

Solving for variable 'm'.

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

Add '10' to each side of the equation.
-10 + 10 + m = 8.185352772 + 10

Combine like terms: -10 + 10 = 0
0 + m = 8.185352772 + 10
m = 8.185352772 + 10

Combine like terms: 8.185352772 + 10 = 18.185352772
m = 18.185352772

Simplifying
m = 18.185352772


Subproblem 2
m + -10 = -8.185352772

Simplifying
m + -10 = -8.185352772

Reorder the terms:
-10 + m = -8.185352772

Solving
-10 + m = -8.185352772

Solving for variable 'm'.

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

Add '10' to each side of the equation.
-10 + 10 + m = -8.185352772 + 10

Combine like terms: -10 + 10 = 0
0 + m = -8.185352772 + 10
m = -8.185352772 + 10

Combine like terms: -8.185352772 + 10 = 1.814647228
m = 1.814647228

Simplifying
m = 1.814647228


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {18.185352772, 1.814647228}

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