10.1. Solve the equation $\left|x^{2}-100\right|=10 x+90$.
Answer. $x_{1}=5+\sqrt{215}, x_{2}=-5+\sqrt{35}$. Solution. If $x^{2}-100 \geq 0$, i.e., under the condition $|x| \geq 10$, we have the equation $x^{2}-10 x-190=0, x=5 \pm \sqrt{215}$. The root $5+\sqrt{215}$ satisfies the condition $|x| \geq 10$, while the root $5-\sqrt{215}$ does not. If $|x|<10$, then we have the equation $x^{2}+10 x-10=0, x=-5 \pm \sqrt{35}$, and the condition $|x|<10$ is only satisfied by the root $x=-5+\sqrt{35}$.