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?

 Dec 8, 2019

Split it.


So just go like:




Solve that AND




I think.


Can somebody verify me?

 Dec 8, 2019

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

 Dec 8, 2019

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


       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 ?

 Dec 8, 2019

OH ok thank you!! so when i have something like that, i have to make it +- on the other side of the equation?

atlas9  Dec 11, 2019

Yes that sounds right.

Melody  Dec 11, 2019

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