Question: Almost a rational solution to a transcendental equation

While solving an exercise in class, I ran into the following interesting solution of a transcendental equation.  It was not intentionally designed to be like this.

restart;
eq := 2*exp(-2*t) + 4*t = 127:
fsolve(eq, t=0..infinity);
                         31.75000000

The solution looks like a rational number while it was expected to be transcendental.  Let's increase the number of digits:

Digits := 20:
fsolve(eq, t=0..infinity);
Digits := 10:
                     31.750000000000000000

Let's make it even more accurate:

Digits := 29:
fsolve(eq, t=0..infinity);
Digits := 10:
                 31.750000000000000000000000000

And even more:

Digits := 40:
fsolve(eq, t=0..infinity);
Digits := 10:
           31.74999999999999999999999999986778814353

Is there a deep reason why the solution is so close to being a rational or is it just a coincidence?