What is the largest root of the equation $(x-37)^{2}-169=0$?
(a) 39
(b) 43
(c) 47
(d) 50
(e) 53
The correct option is (d).

Solution 1: Using the factorization $a^{2}-b^{2}=(a-b)(a+b)$, we have $0=(x-37)^{2}-169=(x-37)^{2}-13^{2}=(x-37-13)(x-37+13)=(x-50)(x-24)$.

Therefore, the roots are 24 and 50.

Solution 2: Taking the square root on both sides of $(x-37)^{2}=13^{2}$, we get $x-37=13$, or $x-37=-13$. Thus, $x=50$ or $x=24$.