Why do we "complete the square"?

Video Description

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): http://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: http://www.math.cornell.edu/~dwh/papers/geomsolu/geomsolu.html While researching this post, I came across a website that offers a visual interpretation of the quadratic formula that helped me design the graphics: https://sites.google.com/site/butwhymath/algebra/the-quadratic-formula Special thanks to Patrons! Kyle Alberto Nishikawa Henry Segerman If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews) http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews) http://amzn.to/1o3FaAg "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) http://amzn.to/XRm7M4