Solve the following equation exactly for the variable $x.$

$1-2x+\frac{6}{2!}{x}^2-\frac{24}{3!}{x}^3+$cdots$=81$

$x=-\frac{8}{9}$

$x=-1\frac{1}{9}$

$x=-1\frac{1}{9}$ and $x=-\frac{8}{9}$

$x=-10$