Finding the Equation of the Ellipse By Completing the Square I have the following equation of an ellipse:
$$5x^2+9y^2+40x=100$$
I need to put it in the form: 
$$\frac{(x-h)^2}{m^2} + \frac{(y-k)^2}{n^2} =1 $$ 
I was trying to complete the square with the coefficients that have an $x$ variable. 
$$5x^2 + 40x + 9y^2 = 100$$
$$5(x^2 + 8x) + 9y^2 = 100$$
$$5(x^2 + 8x + 16) + 9y^2 = 100 + 16$$
$$5(x+4)^2 + 9y^2 = 116$$
I then divided both sides of the equation by $116$. 
$$\frac{5(x + 4)^2}{116} + \frac{9y^2}{116} = 1$$
However, when I graph the equation I do not get the same ellipse that was represented with the original equation of $5x^2 + 9y^2 + 40x = 100$. From the graph, it seems like they are two similar ellipses. Where am I making the mistake? Any help will be appreciated. 

You did a good job just you made a mistake here
$$5(x^2 + 8x + 16) + 9y^2 = 100 + 16$$
Should be
$$5(x^2 + 8x + 16) + 9y^2 = 100 + 80$$
$$5(x^2 +4)^2 + 9y^2 = 180$$
$$\frac {(x^2 +4)^2}{36} + \frac {y^2}{20} = 1$$
$$.....$$
