



 
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,  


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