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How do I solve a quadratic function with absolut values?

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Hello!

It's my first post here and I don't have English as my 1st language, so please excuse any mistakes.

I was there, solving some quadratics, when a wild function appeared. It was:

|x|² -3|x| -10 = 0

And I have absolutely no idea what to do with the absolut values here. I found it interesting that |5|² has only one value (as -5.-5=25 and 5.5=25), so I think that |x|² = x².
But I don't know how to solve it for x. What are the a, b and c values here?!

Thanks!

PS.: I know there are lots of threads here saying 'help!', and that many here are only people trying to get some help for homework. I, too, need help for an important test, but I'm also intrigued by this matter, and I studied so much that this has become interesting. Thank you!
 May 3, 2012

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 #1
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|x|² -3|x| -10 = 0

[input]plot( abs(x)^2 - 3*abs(x) - 10 , x=-10..10 )[/input]

[input]x^2 -3*x -10 = 0[/input]
this would be the results if there where no |x| in the equation: {x=-2, x=5}
these are candidates for solutions for |x|² -3|x| -10 = 0.

[input]|-2|² -3|-2| -10[/input]
this is not equal to 0, so not a solution



[input]|5|² -3|5| -10[/input]
this is equal to 0, so x=5 is the only solution.
 May 5, 2012

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