Question: Issue with solve reporting incorrect solutions

I seem to be getting false solutions with Maple 2019.2 from solve and cannot figure out why.

Example :

f := x -> x*sqrt(4*x^2 + 1) + arcsinh(2*x);
sol := solve(f(x) = 5., x);
sol := 1.247747277, -1.839602523, 0.2519279800 - 1.361107684 I,
  0.2519279800 + 1.361107684 I
f(sol[1]); =    4.999999999
f(sol[2]); =   -9.027641618
 

Thus the second reported solution is not a solution after all.

Any ideas are most welcome.

 

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