Online Course Discussion Forum

MC I-C Fall 2018 Problem 3.22

 
 
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MC I-C Fall 2018 Problem 3.22
by Kerry Zhang - Monday, October 1, 2018, 8:40 PM
 

What does it mean to "complete the square in" x2+8x32?  Is it like factoring it?

 
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Re: MC I-C Fall 2018 Problem 3.22
by David Reynoso - Tuesday, October 2, 2018, 10:51 AM
 

Compare $x^2 + 8x -32$ and $(x+4)^2 = x^2 + 8x +16$. They are almost the same except for the constant terms. So, we can make $x^2+8x-32$ look similar to $(x+4)^2$. To achieve that we need to have a $+16$ at the end, so we can do $$x^2 + 8x + 16 - 16 -32 = (x+4)^2 - 48.$$ "Completing the square" is the process of adding (and subtracting) $16$ so we can have $(x+4)^2$ in the expression.