I have question asking to find an equation for a sphere with points $P$ such that the distance from $P$ to $A$ is twice the distance from $P$ to $B$ with $A(-2,5,2)$ and $B(5,2,-1)$.
I have:
$$4[(x-5)^2+(y-2)^2+(z+1)^2] = [(x+2)^2+(y-5)^2+(z-2)^2]$$ $$=> 4[(x^2-10x+25)+(y^2-4y+4)+(z^2+2z+1)] - (x^2+4x+4) - (y^2-10y+25)-(z^2-4z+4)=0$$
$$=>3x^2-44x+96+3y^2+6y-9+3z^2+12z=0$$
$$=>3x^2-44x+3y^2+6y+3z^2+12z=(-87)$$ $$=>x^2-22x+y^2+2y+z^2+4z=(-29)$$ $$=>(x^2-11x+121)+(y^2+y+1)+(z^2+2z+4)=(97)$$ $$=>(x+11)^2+(y-1)^2+(z-2)^2=(97)$$
I looked it over a few times and found one error I had originally made but it's still not coming out right and I can't find where else I messed up.
The first error is in the coefficient of $y$ : $$3x^2-44x+3y^2\color{red}{-}6y+3z^2+12z=-87$$ The second error is in the coefficient of $x$ : $$x^2-\color{red}{\frac{44}{3}}x+y^2-2y+z^2+4z=-29$$ Now, add $(-22/3)^2+(-1)^2+2^2$ to the both sides.