\(2x^2+100x-10000=0\)
\(\Leftrightarrow2x^2+200x-100x-10000=0\)
\(\Leftrightarrow2x\left(x+100\right)-100\left(x+100\right)=0\)
\(\Leftrightarrow\left(2x-100\right)\left(x+100\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x-100=0\\x+100=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=50\\x=-100\end{cases}}\)