why solve failed? my error or solve error?

I used command solve but recently I had a new equation:

f1=cos(x)*(2*x)^(1/2) + sin(x)/(2*x)^(1/2);

I used solve, but the ans was wrong, then I used Newton method an check the answers were ok

ans =

      1.8366
  ans =

      4.8158

used solve:

>> syms x
>> f1=cos(x)*(2*x)^(1/2) + sin(x)/(2*x)^(1/2);
>> sf1=solve(f1,x)

sf1 =

-227.76766260117050148062548433664

the ans obvisuly was wrong

why solve failed? was my method or command solve?

Answer 1

[Jan]

The result is obviously correct. Simply try it:

x = -227.76766260117050148062548433664
cos(x)*sqrt(2*x) + sin(x)/sqrt(2*x)

The result is -2.6466e-013i, which is correct inside the expected precision.

Answer 2

[Star Strider]

There are infinitely many real and imaginary roots:

figure(1)
ezplot(real(f1), [-100 100]*pi)
hold on
ezplot(imag(f1), [-100 100]*pi)
hold off