COMPLETING THE SQUARE

Rewriting the expression  in the equivalent form as  for some  is usually named completing the square.

Since   we have that .

1)      Insert a zero in the expression written as

2)      Rewrite the first three terms as the square of a binomial

 

Ex 1: Complete the square for .

Ex: 2. Complete the square for

Ex: 3. Complete the square for

 

Ex: 4. Complete the square for

 

Ex: 5. Solve , by completing the square.

Ex: 6. Solve , by completing the square.

 

Ex: 7. Find the center and the radius of the circle