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May 4th, 2016, 11:54 AM  #1 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2  Completing the square? I think?
Hi, I'm really stuck on this question could someone please help me out? Imgur: The most awesome images on the Internet 
May 4th, 2016, 12:28 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,875 Thanks: 766 
Use either "completing the square" or the "quadratic formula" to solve the equation. Either is fairly simple.

May 4th, 2016, 12:42 PM  #3 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2  
May 4th, 2016, 12:47 PM  #4 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2 
So I have to work out that x=20 and x=3.3 for a and this is the answer for it, just to work it out?

May 4th, 2016, 01:29 PM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339  adding 10 meters to the width = x+10 adding 20 meters to the length = 3x+20 area of the extended playground is double the original ... original area = $3x^2$, doubled = $6x^2$ $(x+10)(3x+20) = 6x^2$ expand the left side, combine like terms & set = 0 ... $3x^2 + 50x + 200 = 6x^2$ $0 = 3x^2  50x  200$ kapish? 
May 4th, 2016, 02:06 PM  #6 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2 
But for b it says calculate the area of the original playground; which x value do I use?
Last edited by skipjack; May 5th, 2016 at 12:56 PM. 
May 4th, 2016, 03:10 PM  #7  
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339  Quote:
Solve for $x$ from the doubling equation $3x^250x200 = 0$ ... (fyi, $3x^250x200$ will factor) ... now determine the original area by evaluating the value of $3x^2$ using what you got for the one and only $x$. Last edited by skipjack; May 5th, 2016 at 12:57 PM.  
May 5th, 2016, 09:13 AM  #8 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2 
How am I supposed to work out x? I thought you had to do the completing the square method.
Last edited by skipjack; May 5th, 2016 at 12:58 PM. 
May 5th, 2016, 09:30 AM  #9  
Math Team Joined: Jul 2011 From: Texas Posts: 2,678 Thanks: 1339  Quote:
$3x^2  50x  200 = 0$ $3x^2  50x = 200$ $x^2  \dfrac{50}{3}x = \dfrac{200}{3}$ $x^2  \dfrac{50}{3}x + \left(\dfrac{25}{3}\right)^2 = \dfrac{200}{3}+ \left(\dfrac{25}{3}\right)^2$ finish it ... Last edited by skipjack; May 5th, 2016 at 12:58 PM.  
May 5th, 2016, 10:00 AM  #10 
Senior Member Joined: Jan 2015 From: London Posts: 106 Thanks: 2 
I get x=20 or x=10/3, so would I use 20 and then do 3*20=60 60*20=1200 so the area is 1200m^2? Is this right? Last edited by skipjack; May 5th, 2016 at 12:59 PM. 

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