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AoPS Wiki talk:Problem of the Day/June 7, 2011

Problem

AoPSWiki:Problem of the Day/June 7, 2011

Solution

$\sqrt{x+2}=x-18 \implies$ $x+2=(x-18)^2=x^2-36x+324 \implies$ $x^2-37x+322=0 \implies$ $(x-23)(x-14)=0$.

Clearly $x=14$ is extraneous, so our answer is $x=\boxed{23}$.

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