Rewriting a constraint as a standard SOC constraint.

FOIWATER
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I am trying to rewrite this constraint as a second order cone constraint of the form $$||Ax+b|| \leq C^Tx+d$$

$$x^2-(x-5)y-yz+3(z-5)^2 \leq 1+x$$

I am having a hard time of knowing where to start.. any information appreciated.
 
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I usually graph it, look at the surface from several angles, think about the projection in the coordinate planes, and scratch my head.
 

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