#### Answer

The given equation has one rational solution (with multiplicity 2).

#### Work Step by Step

The given equation has $a=25$, $b=110$, and $c=121$.
RECALL:
(1) The discriminant is equal to $b^2-4ac$.
(2) A quadratic equation has the following types of solutions based on the value of the discriminant:
(a) when $b^2-4ac\gt0$, the equation has two unequal rational solutions;
(b) when $b^2-4ac=0$, the equation has one, repeated rational solution; and
(c) when $b^2-4ac\lt0$, the equation has two complex number solutions;
The discriminant of the equation above is:
$$b^2-4ac =110^2 - 4(25)(121) = 12,100-12,100=0$$
The discriminant is zero.
Thus, the given equation has one rational solution (with multiplicity 2).