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July 17th, 2018, 02:15 AM  #1 
Senior Member Joined: Nov 2011 Posts: 243 Thanks: 2  completing the square
How I solve execrise 1 in the link below: https://www.maa.org/press/periodical...usingaddition [Execrise 1 in the page] 
July 17th, 2018, 02:25 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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 11:35 AM. 
July 18th, 2018, 07:03 AM  #3 
Member Joined: Oct 2017 From: Japan Posts: 62 Thanks: 3 
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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