Answer
The center is $(1,2,-4)$ and the radius is $6$.
Work Step by Step
The equation for a sphere is represented by:
$(x−h)^2+(y−k)^2+(z−l)^2=r^2$
in which the point $(h,k,l)$ is the center of the sphere and $r$ is the radius.
To get the given equation into this form, we must complete the square for all three variables.
In order to do this add $(\frac{b}{2})^2$ to both sides of the equation ($b$ is the coefficient before the $x$, $y$, or $z$ term). Since there are three different variables, we must complete the square three times.
$x^2+y^2+z^2-2x-4y+8z=15$
$(x^2-2x)+(y^2-4y)+(z^2+8z)=15$ (rearrange terms)
$(x^2-2x+1)+(y^2-4y+4)+(z^2+8z+16)=15+1+4+16$
$(x-1)^2+(y-2)^2+(z+4)^2=36$
Now that the equation is in the form:
$(x−h)^2+(y−k)^2+(z−l)^2=r^2$
The center is $(1,2,-4)$ and the radius is $6$.