Answer:
( x + 5)^2 + y^2 = 41
Explanation:
The equation we have is
[tex]x^2+10x+y^2-16=0[/tex]
Let us add 25 to both sides
[tex]x^2+10x+y^2-16+25=25[/tex]
A bit of rewriting gives
[tex](x^2+10x+25)+y^2-16=25[/tex]
Since x^2 + 10x + 25 = ( x+ 5)^2, the above becomes
[tex](x+5)^2+y^2-16=25[/tex]
Adding 16 to both sides gives
[tex](x+5)^2+y^2=25+16[/tex][tex]\boxed{\left(x+5\right)^2+y^2=41.}[/tex]
which is our final answer!
