Find all solutions of the equation |x^2-20x-1|=20.

i don't want the answer, but what am i supposed to do with the absolute value?

atlas9 Dec 8, 2019

#1**+1 **

Split it.

So just go like:

\(x^2-20-1=20\)

Solve that AND

\(-x^2+20+1=-20\)

I think.

Can somebody verify me?

tommarvoloriddle Dec 8, 2019

#2**+1 **

lol i'm actually trying to answer your question too :D

i thought what you said too, i just don't know if absolute value is the same as plus or minus

atlas9 Dec 8, 2019

#3**+3 **

This is what you should be doing :

\(|x^2-20x-1|=20\\~\\ \color{blue}x^2-20x-1=20 \qquad or \qquad x^2-20x-1=-20 \\\)

Think about this simple example

|x|=5

What this says it that the **distance x is from 0** is 5. So x could be 5 or maybe -5.

If you let \(y=x^2-20x-1\)

then your question is asking, **for what values of x is y 20 units away from 0**.

So y can equal 20 or y can equal -20.

You will get 4 answers. They will not necessarily all be real.

I expect you are only interested in real answers so if some are not real you can discard them.

Now you must substitute the real ones into the original equation to check that they work properly.

Discard any that do not work.

Is that enough help ?

Melody Dec 8, 2019