Solving an equation by telling the value of $x^2+y^2$. I have a problem solving an equation. The equation is:
$xy+x+y=44$ and $x^2y+xy^2=448$
and we have to tell the value of $x^2+y^2$
First I tried solving this by doing the following:
$xy+x+y=44~\to~x+y=44-xy~\to~x^2+2xy+y^2=44^2-88xy+x^2y^2~\Rightarrow$
$\Rightarrow~x^2+y^2=44^2-90xy+x^2y^2$
But from here I didn't know what to do. Could you help me in solving this equation?

Here is one suggestion. Let $a=x+y, b=xy$ then $a+b=44,  ab=448$
This gives $a=16, b=28, x^2+y^2=a^2-2b=200$ or $a=28, b=16, x^2+y^2= 752$
The intermediate step is to formulate and solve the quadratic satisfied by $a$ and $b$
