Question on completing the square

[geramul]

Something about the lesson given here confuses me. I understand how to complete the square, but this is bothering me and I need to know why this happens.

So we have sample question 4x² - 2x - 5 = 0

I understand everything up until I have to convert the left side to squared form, let me show you why.

-2x becomes -1/2x, which becomes - 1/4 which becomes 1/16. Now we add 1/16 to both sides.

x² - 1/2x + 1/16 = 5/4 + 1/16.

Now we have (x - 1/4)² = 21/16

My question is, what happened to the 1/16 on the left side? It can't be added to 1/2x right? So for a while I was wondering how 1/2 became 1/4, but I figured it becomes 1/4 when I convert the left side to squared form. So where does that 1/16 go? Do we just assume it vanished? Something has to happen to the 1/16 on the left side, it can't just "go away" can it?

[stapel_eliz]

x² - 1/2x + 1/16 = 5/4 + 1/16.

Now we have (x - 1/4)² = 21/16

My question is, what happened to the 1/16 on the left side?

What is (x - 1/4)² equal to, after expansion?

[geramul]

x² - 1/2x + 1/16 = 5/4 + 1/16.

Now we have (x - 1/4)² = 21/16

My question is, what happened to the 1/16 on the left side?

What is (x - 1/4)² equal to, after expansion?

Ahhhhhh I see. I hate and love math because of tricky dicky shit like this lol. Thanks.