Expert: Richard J. Raridon - 5/29/2009

Question
Why are perfect squares useful in solving quadratic equations?

Answer
It's generally called "completing the square."
Suppose you had x^2+6x+3 = 12
You could re-write it x^2+6x-9 = 0 and use the binomial theorem to solve it.  
Or you could add 6 to each side to get x^2+6x+9 = 18
Now, (x+3)^2 = 18 and x+3 = +/-(18)^1/2 or x = -3 +/-(18)^1/2,
in this case, quicker.