Why do we "complete the square"?

The quadratic formula is really useful, but its derivation is confusing to many. Like what is the point of "completing the square" anyway? In this video, I show how "completing the square" has a geometric interpretation--you are actually making the areas of two squares equal to each other!
Blog post (text/image summary): wp.me/p6aMk-4kG
You can read more about the history of the quadratic formula and its geometric roots from Cornell Mathematics professor David W. Henderson: www.math.cornel...
While researching this post, I came across a website that offers a visual interpretation of the quadratic formula that helped me design the graphics: sites.google.c...
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