Can you calculate Pi using a Solver?

[EdS2]

I found a couple of not-great examples of the sort of thing I might hope exists...

There's a good approximation for pi as a root of an 8th order polynomial:

0=1−1635840576x−343853312x^2 +60576043008x^3 +1865242664960x^4 −16779556159488x^5 +37529045696512x^6 −29726424956928x^7 +6181548457984x^8

And there's a bad approximation as a solution to
x=(1+1/x)^(x+1)

Here's a quartic:
0=16-160x+168600x^2-841000x^3+250625x^4