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July 17th, 2018, 01:15 AM   #1
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completing the square

How I solve execrise 1 in the link below:
https://www.maa.org/press/periodical...using-addition
[Execrise 1 in the page]
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July 17th, 2018, 01:25 AM   #2
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The point is that a "perfect square" is of the form $\displaystyle (x+ a)^2= x^2+ 2ax+ a^2$. Notice that "2a" coefficient of $\displaystyle x$. Exercise 1 has $\displaystyle x^2+ 12x$. So the "2a" coefficient of $\displaystyle x$ is 12. If 2a = 12, what is a? And then what is the "$\displaystyle a^2$" you need to add to make that a "perfect square"? Of course, you have to add that number to both sides of the equation.

Last edited by skipjack; July 17th, 2018 at 10:35 AM.
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July 18th, 2018, 06:03 AM   #3
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From my experience most students who have problems understanding the method do not realise that when a quadratic is solved by completing the square you are in fact completing a square. I made a couple of videos to visually show that.



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