x^2 + y^2 + z^2 - 6 =0.

xyz = -2.

How would you go about finding, say, the maximum value of x as defined by the two equations? There has to be a way, but I can't figure it out (every way I do is either too long or complicated or just doesn't make sense). I have to do it by hand, too, so no cheating with mathematica.

Anyone?