<s>[INST] Show that the equation represents a sphere, find center and radius $2x^2 + 2y^2 + 2z^2 = 8x - 24z + 1$
So here's my guess:
$2x^2 - 8x + 2y^2 + 2z^2 + 24z = 1$ 
     Get all variables on one side
$2x^2 - 8x + 16 + 2y^2 + 2z^2 + 24z + 144 = 1 + 16 + 144$ Complete square
$(2x - 8)^2 + 2y^2 + (2z^2 + 24)^2 = 161$ Stopped here
Is it possible to complete the square with the $y$ value too? Would it just be 1?
 [/INST] Note that $(2x)^2 \ne 2x^2$. The answer is:
$$2(x-2)^2 + 2(y-0)^2 + 2(z+6)^2 = 8 + 0 + 72 + 1$$
Thus, center $(2,0,-6)$, and radius $\sqrt{81/2}$.
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