I know that
$$ (-1)^x + 2^x - 2 x - 1 = 0 $$
has a single real root $(x =3)$ and an infinite number of complex roots whose real part appears often negative. Don't the complex roots also have their conjugates as solutions(roots)?
Even I am unable to readily plot its left hand side to be able to see that a wavy graph should appear not cutting negative x-axis. Appreciate an answer about cause of this phenomenon and its remedy.