Quadratic Equations by Completing the Square

App

Jan 2014
55
2
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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skeeter

Math Team
Jul 2011
3,355
1,848
Texas
$2x^2+8x+1=0$

$2x^2+8x = -1$

$x^2+4x=-\dfrac{1}{2}$

$x^2+4x+4 = -\dfrac{1}{2} +4$

$(x+2)^2=\dfrac{7}{2}$

$x+2= \pm \sqrt{\dfrac{7}{2}}$

$x = -2 \pm \dfrac{\sqrt{14}}{2} = \dfrac{-4 \pm \sqrt{14}}{2}$
 

Country Boy

Math Team
Jan 2015
3,261
899
Alabama
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.