## anonymous 4 years ago How do I solve by completing the square for: 1/2 n^2 + n = -1/8?

1. anonymous

I got n = 1 +/- √15/4 but the answer is supposed to be: -0.13, -3.87

2. anonymous

ohhh, never mind I think I got it now!

Step 1. multiply the equation by 2 so that the coefficient of n^2 is 1, getting: n^2 + 2n = -2/8. O.K.

I'll stick around if you want to do the problem, I see you have figured it out.

5. anonymous

okay so I'm getting confused: n + 1 = +/- √3/2 and n = -1 +/- √3/2

I will work it out and you can compare answers. Step 2 take half of the n coefficient (2) and square it and add it to the left side and right side. $n ^{2}+2n + 1 = -2/8 +1$$(n + 1)^{2}=6/8$ We now have a perfect square on the left. Taking the square root of both sides give: n+1 =(6/8)^1/2 $n+1 =\sqrt{6/8}$$n=-1\pm \sqrt{6}/\sqrt{8}$ note that $\sqrt{8}=2\sqrt{2}$and$\sqrt{6}=\sqrt{3}\sqrt{2}$ The fraction now becomes$\sqrt{3}\over 2$ so the answer is:$n =-1\pm \sqrt{3}/2$

Yes, the fraction becomes simpler as it is reduced to sqrt3/2

Looks like we got the same answer. Good luck with these.

9. anonymous

but.. isn't it wrong?

why do you think it is wrong?

Do you the answer as decimal numbers?

$-1\pm.866025403$