#### Answer

The center is $(-4,3,-1)$ and the radius is $3$.

#### 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.
$x^2+y^2+z^2+8x-6y+2z+17=0$
$(x^2+8x)+(y^2-6y)+(z^2+2z)=-17$ (rearrange terms)
$(x^2+8x+16)+(y^2-6y+9)+(z^2+2z+1)=-17+16+9+1$ (complete the square)
$(x^2+4)^2+(y^2-3)^2+(z^2+1)^2=9$
Now that the equation is in the form:
$(x−h)^2+(y−k)^2+(z−l)^2=r^2$
The center is $(-4,3,-1)$ and the radius is $3$.