Hi Ariana,

To complete the square of $y^2 + 9y$ you divide the coefficient of $y$ by 2 to get $\frac92$ and then add the square this quantity. Thus you need to add

\[\left( \frac92 \right)^2 = \frac{81}{4}.\]

This gives you

\[y^2 + 9y + \frac{81}{4} = \left(y + \frac92 \right)^2 .\]

Hence if you add $\frac{81}{4}$ to both sides of $x^2 + 2x + y^2 + 9y = 5$ you can rewrite it as

\[x^2 + 2x + \left(y + \frac92 \right)^2 = 5+ \frac{81}{4}.\]

Can you complete the problem now?

Write back if you need more assistance,
Penny