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August 25th, 2017, 03:50 AM  #1 
Member Joined: Jan 2014 Posts: 55 Thanks: 2  Quadratic Equations by Completing the Square
Hi, I'm working on this equation where (b/2)^2 = 8/2=4^2=16. However, I'm stuck where I think I need to square both sides, as you can see a purple star there. I also scratchy on how to factor x^2+4x+8? which the answer becomes in the end is in red. 2 plus or minus sq of 14 Last edited by skipjack; August 25th, 2017 at 07:55 AM. 
August 25th, 2017, 04:04 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,663 Thanks: 1328 
$2x^2+8x+1=0$ $2x^2+8x = 1$ $x^2+4x=\dfrac{1}{2}$ $x^2+4x+4 = \dfrac{1}{2} +4$ $(x+2)^2=\dfrac{7}{2}$ $x+2= \pm \sqrt{\dfrac{7}{2}}$ $x = 2 \pm \dfrac{\sqrt{14}}{2} = \dfrac{4 \pm \sqrt{14}}{2}$ 
August 25th, 2017, 09:33 PM  #3 
Member Joined: Jan 2014 Posts: 55 Thanks: 2 
Thank you! 
August 26th, 2017, 02:14 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753 
Your basic error was that you did not have $\displaystyle x^2+ 8x+ 1$ that you are trying to make a "complete square", you have $\displaystyle 2x^2+ 8x+ 1$ and that "2" multiplying $\displaystyle x^2$ makes all the difference. skeeter took care of that by first dividing the equation by 2.


Tags 
completing, equations, quadratic, square 
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