we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]-x^{2} +2x+1=0[/tex]
so
[tex]a=-1\\b=2\\c=1[/tex]
substitute in the formula
[tex]x=\frac{-2(+/-)\sqrt{2^{2}-4(-1)(1)}} {2(-1)}[/tex]
[tex]x=\frac{-2(+/-)\sqrt{8}} {-2}[/tex]
[tex]x1=\frac{2-\sqrt{8}} {2}=1-\sqrt{2}[/tex]
[tex]x2=\frac{2+\sqrt{8}} {2}=1+\sqrt{2}[/tex]
therefore
the answer is
the positive solution is [tex]1+\sqrt{2}[/tex]
