Why does `solve` miss the solutions without warnings?

The output  means that there is no real solution, but clearly, both and  satisfy the original equation: 

So, why does `solve` lose the real solutions without any warning messages? 
Code: 

restart;eq := 9*(x^2 + 2*cos(x)) = Pi^2 + 9;RealDomain:-solve(eq, [x]);[]:-solve({eq, x >= 0}, [x]); # as (lhs - rhs)(eq) is an even function []