Complete the square for the binomial.

Question

Complete the square for the binomial. Then factor the resulting perfect square trinomial. 

 

x² +12x

 

 

Answer 1

When you square a binomial, you get:

 

(x + a)² = x² + 2ax + a²

 

The coefficient of the x term is 2a.  The constant term is a², which is 1/2 of 2a squared, (2a/2)² - and that is the secret to "completing the square".  For your problem, the coefficient of the x term is 12.  The constant term we need then is one-half of 12 squared, that is (12/2)² = 6² = 36.

 

x² + 12x + (12/2)² = x² + 12x + 36 = (x+6)²

 

Remember that 12 = 2a, so a = 6.