\(\Rightarrow100x^2+\left(1+2+...+100\right)=15050\\ \Rightarrow100x^2+\dfrac{\left(100+1\right)\cdot100}{2}=15050\\ \Rightarrow100x^2+5050=15050\\ \Rightarrow100x^2=10000\\ \Rightarrow x^2=100\\ \Rightarrow\left[{}\begin{matrix}x=10\\x=-10\end{matrix}\right.\)