Question

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

Answer 1

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

Answer 2

ohhh, never mind I think I got it now!

Answer 3

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

Answer 4

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

Answer 5

okay so I'm getting confused:

n + 1 = +/- √3/2 and n = -1 +/- √3/2

Answer 6

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:\[n =-1\pm \sqrt{3}/2\]

Answer 7

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

Answer 8

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

Answer 9

but.. isn't it wrong?

Answer 10

why do you think it is wrong?

Answer 11

Do you the answer as decimal numbers?

Answer 12

\[-1\pm.866025403\]