The given expression is
[tex]x^2+2x+y^2+10y=15[/tex]First, we divide the coefficients 2 and 10 by 2, then we find their square power
[tex]\begin{gathered} (\frac{2}{2})^2=1^2=1 \\ (\frac{10}{2})^2=5^2=25 \end{gathered}[/tex]We add 25 and 1 to each side of the equation
[tex]\begin{gathered} x^2+2x+1+y^2+10y+25=15+1+25 \\ \end{gathered}[/tex]Now, we factor both trinomials
[tex](x+1)^2+(y+5)^2=41[/tex]Where h = -1 and k = -5. So, the center is C(-1, -5).
The radius would be
[tex]\begin{gathered} r^2=41 \\ r=\sqrt[]{41}\approx6.4 \end{gathered}[/tex]The radius is 6.4 units long.