An interesting introduction to completing the square

My older son started a new section in Art of Problem Solving’s Introduction to Algebra book today. The chapter begins to look at quadratics in a bit more depth. Given the question my son picked for today’s movie I assume that one of the topics will be completing the square. It is always interesting to see how a kid approaches an advanced topic before really knowing much about that topic.

The question asks you to find the minimum value of x^2 + 10x - 7. Here’s his work:

 

After he finished his work I gave a really basic introduction to completing the square using this problem as an example:

 

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