The sum of two numbers is 6 and their product is 4. How do you find the larger of the two numbers?
Write the conditions as two equations and solve to obtain:
the larger of the two numbers is
Let the two numbers be
We are told that
Rearranging  we have
Substituting  into 
Which simplifies as
Using the quadratic formula
Since in  and 
The larger of these possibilities is
Write an equation and solve it.
The larger number is 5.236..
It is possible to do this using one variable.
If two numbers add up to 6, they can be written as
Their product is 4
This does not factorise, but it is a good example for using completing the square because
5.236 is the larger.