Let me write out where I got stuck.

(x + b/2a)

^{2}= -c/a + b

^{2}/4a

^{2}

What I can't figure out is how the common denominator of 4a is gotten. Let me give an example. Lets say we want to add together 1/4 and 5/8. We would look of course at the multiples of 4 and find one that's equal to other denominator. So we find that 8 is the least common denominator for both fractions. We multiply 1/4 by 2/2 to get 2/8, and now we can solve.

Now lets look at -c/a. Any variable without a coefficient has an implied coefficient of 1 yes? So really we can look at -c/a as -1c/1a. How can we get a common denominator of 4 from 1, when 1 only has itself as multiple? This doesn't make sense to me. The only way I could figure it out was if both bases were the same, we could just say the fraction was equal to 1 and turn that into 1/2, therefore giving us the ability to get 4. Someone please explain this to me.