Notez [tex]a= x^{2} -2x.[/tex]
[tex]( x^{2} -2x)( x^{2} -2x+5)+4=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ a(a+5)+4=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ a^{2} +5a+4=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ a^{2} +a+4a+4=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ a(a+1)+4(a+1)=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ (a+1)(a+4)=0=\ \textgreater \ a=-1~sau~a=-4. \\ \\ a=-1=\ \textgreater \ x^{2} -2x=-1\ \textless \ =\ \textgreater \ x^{2} -2x+1=0\ \textless \ =\ \textgreater \ (x-1) ^{2} =0=\ \textgreater \ \\ =\ \textgreater \ x-1=0=\ \textgreater \ \boxed{x=1}. \\ \\ a=-4=\ \textgreater \ x^{2} -2x=-4\ \textless \ =\ \textgreater \ x^{2} -2x+1=-3\ \textless \ =\ \textgreater \ (x-1) ^{2} =-3,~imposibil }.[/tex]
Solutia ecuatie este x=1.
