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by exoticanb4u » Sun Oct 11, 2009 6:28 pm
Can someone please solve this question?

I am getting -16 as answer, but the OA says -8 :?

What is the sum of all roots of the equation
|x + 4|^2 - 10|x + 4| = 24?

BTW the source is magoosh
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by cooline » Mon Oct 12, 2009 5:32 am
I am getting 4 for an answer, can you please give the explanation.
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by mp2437 » Mon Oct 12, 2009 6:54 am
I get an answer of 8.

Distribute:
|x + 4|^2 - 10|x + 4| = (x^2 + 8x + 16) - 10x - 40 = 24
x^2 - 2x - 48 = 0. Factors are (x - 8)(x+6) = 0, so you get roots x = +8, x = -6.

To check: plug in each root and see if it works. x = -6 doesn't, so the only root that fits the bill is x = 8.

I did the same thing taking the negative part of the absolute value, but the check did not work when I plugged in the values.

Not sure where -8 comes into play. Can someone clarify.
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