
\vspace*{-2em}
\begin{align*}
x^2\equiv-11\mod100
& \iff x^2\equiv300-11\mod100\\
& \iff x^2\equiv289\mod100\\
& \iff x^2\equiv17^2\mod100\\
& \iff x^2-17^2\equiv0\mod100\\
& \iff (x-17)(x+17)\equiv0\mod100\\
& \iff x\equiv17\mod100\qquad\text{ou}\qquad x\equiv-17\mod100\\
& \iff \boxed{x\equiv17\mod100 \qquad\text{ou}\qquad x\equiv83\mod100}
\end{align*}
