Find the coordinates of the center and radius of the circle.

$\displaystyle x^2+y^2-8x+10y=-5$

So I like to rewrite it

$\displaystyle x^2-8x+y^2+10y=-5$

then I write it as the standard circle equation

$\displaystyle (x-h)^2+(y-K)^2=r^2$

So If I did this right I should have $\displaystyle (x-4)^2+(y+5)^2=-46$

and then my $\displaystyle (h,k) is (4,-5) and r=\sqrt46$

Please I need someone to confirm to me I did this properly?

Side note $\displaystyle x^2-8x$ is expanded to $\displaystyle (x-4)^2+16$ and I move the 16 over to the other side of the = sign in the equations.