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August 25th, 2017, 02:50 AM   #1
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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
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Last edited by skipjack; August 25th, 2017 at 06:55 AM.

 August 25th, 2017, 03:04 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,628 Thanks: 1308 $2x^2+8x+1=0$ $2x^2+8x = -1$ $x^2+4x=-\dfrac{1}{2}$ $x^2+4x+4 = -\dfrac{1}{2} +4$ $(x+2)^2=\dfrac{7}{2}$ $x+2= \pm \sqrt{\dfrac{7}{2}}$ $x = -2 \pm \dfrac{\sqrt{14}}{2} = \dfrac{-4 \pm \sqrt{14}}{2}$
 August 25th, 2017, 08:33 PM #3 Member   Joined: Jan 2014 Posts: 55 Thanks: 2 Thank you!
 August 26th, 2017, 01:14 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,656 Thanks: 681 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.

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