# Math Help - stuck

1. ## stuck

Hi, I'm almost at the end of a question but i seem to be stuck. I have the answer though.. so im up to here so can someone please help me arrange this

$(\frac{n + \frac{1}{c}}{\frac{s}{n} }) [\mu^2 - 2\mu(\frac{n \overline{y}}{n+\frac{1}{c}})]$

and make it equal to

$\frac{n + \frac{1}{c}}{\frac{s}{n} + \frac{\overline{y}(\frac{1}{c})}{(n + \frac{1}{c})}}[\mu - (\frac{n\overline{y}}{n + \frac{1}{c}})]^2$

or if you don't want to give me the full thing, the next line would really help guide me coz i just have no idea what to do
thank you, coz ive tried everything i could think of and nothing seems to work.. Please?

2. $(\frac{n + \frac{1}{c}}{\frac{s}{n} })$ $[\mu^2 - 2\mu(\frac{n \overline{y}}{n+\frac{1}{c}})]$

Notice that what's in the square brackets is almost a perfect square.

So, add and subtract the ((last term inside the square brackets)/2)^2 all squared), a form of 0, inside the square brackets. The first three terms in the square brackets make up the perfect square equal to ... can you finish?

3. double post

$(\frac{n + \frac{1}{c}}{\frac{s}{n} })$ $[\mu^2 - 2\mu(\frac{n \overline{y}}{n+\frac{1}{c}})]$

Notice that what's in the square brackets is almost a perfect square.

So, add and subtract the ((last term inside the square brackets)/2)^2 all squared), a form of 0, inside the square brackets. The first three terms in the square brackets make up the perfect square equal to ... can you finish?
ahhh thank you!!

but okies, so here's what i have:
$(\frac{n + \frac{1}{c}}{\frac{s}{n} }) [(\mu - \frac{n\overline{y}}{n + \frac{1}{c}})^2 - (\frac{n\overline{y}}{n + \frac{1}{c}})^2]$

but i don't know what to do with the leftover $(\frac{n\overline{y}}{n + \frac{1}{c}})^2$.. did i do the perfect square thing wrong?

5. Oh right, sorry, should have said (coefficient/2)^2 for completing the square, my bad. I would say expand and see where that takes you.

6. hmm..? sorry im really dumb, what do you mean by coefficient? which coefficient?

7. $[\mu^2 - 2\mu(\frac{n \overline{y}}{n+\frac{1}{c}})]$

The coefficient of your second term is $2(\frac{n \overline{y}}{n+\frac{1}{c}})$, which is the one you need to divide by two and then square to get what you need to add and subtract to complete the square.

You completed the square correctly.