Completing the Square examples: Sometimes, the quadratic polynomials are not easily factorable.
For Example, consider 
It is difficult to make factors of 
In such a case the factorization and hence the solution of a quadratic equation can be found by the method of completing the square and extracting square roots.
Completing the Square Examples
Say we have a simple expression like 
. Having 
twice in the same expression can make life hard. What can we do?
Well, with a little inspiration from Geometry we can convert it, like this:
Example#1 (Completing the Square)
Solve the equation 
by completing the square.
Solution:
we have
Now, for completing the square, adding both side 
Hence by completing the square
Solution set={19,-23}
Example#2 (Completing the Square)
Solve the equation 
by completing the square.
Solution:
we have
Now, for completing the square, adding both side 
Hence by completing the square
Solution set={31.-29}
you can also see quadratic formula