# prove this equation has at least two real solutions

I want to prove that $2^x=2-x^2$ has at least two real solutions. I am trying to use Bolzano theorem to prove this, that is if $f(x)=2^x-2+x^2$=$0$ then $f(x)$ is continuous on R will be negative somewhere and positive somewhere and so satisfy Bolzano theorem and there will be some real value that $f(c)=0$, but I don't know how to show or prove this equation has at least two real solutions.

I appreciate anyone who show that for me.

Thank you.

Try $x=0$, $x=1$, and $x=-2$ as inputs for $f$.