Some really basic maths help

[divine`]

My mind has gone totally blank and all my GCSE/ALevels notes are a mess and I can't find what im looking for online as i'm not sure what the process is called.

Anyway

Say I have √15

I want to simplify it a bit. I remember from A Level there is a way of moving 'some' of it outside the root and creating a number like 3√13 etc.

How do I actually do this though? I would like to get a 2 outside as it would simplify the rest of the work a fair amount if I could.

I thought 2√11 might be it but I don't think it is :/

Any help?

 

[divine`]

ah i see, so i'm not really going to be simplify it to anything useful then

 

[divine`]

Basically I need to solve the quadratic m+m+4=0

Which unless I am mistaken leaves me with the roots as


(-1+√-15)/2 and (-1-√-15)/2

which i've then made

(-1+√15i)/2 and (-1-√15i)/2

However I then need to use those for the rest of my problem (solving a differential equation) so having them like that is a slight pain :/

 

[divine`]

What is the next part of the question?

a) Find the Complementary Function
b) Determine a Particular Integral
c) Find the complete solution
d) Plot the curve of the solution x(t)

This quadratic stuff was part of a)

It's an inhomogeneous second order differential equation problem.

I'm not going to put the full problem up because it's coursework and I don't want to get kicked out of uni because they think I got you lot to do all my coursework for me