Alright so,
Rearragnge the equation to better see what to do!
![](https://latex.codecogs.com/png.latex?\bg_white x^2 + 4x + y^2 - 2y = -1)
Now, complete the square for
![](https://latex.codecogs.com/png.latex?\bg_white x^2 + 4x)
to:
![](https://latex.codecogs.com/png.latex?\bg_white x^2 + 4x + 4 - 4)
Remember, this is done by using
![](https://latex.codecogs.com/png.latex?\bg_white \left (\frac{b}{2} \right )^2 )
Do the same with
![](https://latex.codecogs.com/png.latex?\bg_white y^2 -2y)
You'll get
![](https://latex.codecogs.com/png.latex?\bg_white (x +2)^2 + (y -1)^2 - 5 = -1)
Which is
Do this for the rest.
Yo Latex is a blast. Never put so much effort into the steps of a simple question