Find \(A^2_{}\), where \(A^{}_{}\) is the sum of the absolute values of all roots of the following equation: $$x = \sqrt{19} + \frac{91}{{\sqrt{19}+\frac{91}{{\sqrt{19}+\frac{91}{{\sqrt{19}+\frac{91}{{\sqrt{19}+\frac{91}{x}}}}}}}}}$$

(第九届AIME1991 第7题)