Question:
What are some real world applications of completing the square?

Replies:
Real world applications" of completing the square kind of misses the
point of carrying out that process. "Completing the square" is one of a
large number of algebraic manipulations that one uses to convert an
algebraic expression into a simpler form. And the whole subject of
algebra has to do with solving algebraic equations. So like the
"quadratic" formula, and various other techniques for factoring and
simplifying algebraic expressions, the motive is to obtain an
expression that is easy to solve an algebraic equation with the
minimum amount of pain and discomfort.

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