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?

$$(x+y)=44-xy..............1$$
$$xy(x+y)=448........................2$$
substitute 1 in 2
$$xy(44-xy)=448$$
$$x^2y^2-44xy+448=0$$
use the quadratic formula
$$xy=22\pm6$$
or
$$x^2y^2=(22\pm6)^2$$
now  square the equ.1
$$x^2+2xy+y^2=44^2-88xy+x^2y^2$$
$$x^2+y^2=44^2-90xy+x^2y^2$$
hence
$$x^2+y^2=44^2-90(22\pm6)+(22\pm6)^2$$
