Question

Solve for x in `pi^x=-2x^2+6x-9`?

Answer 1

No real solution
`x approx 0.990542 +- 1.50693 i`

Explanation:

This equation has no real solution for `x`.

We can see this by plotting `f(x)=pi^x` and `g(x)= -2x^2+6x-9` below.

graph{(y-pi^x)(y-(-2x^2+6x-9))=0 [-22.78, 22.83, -11.4, 11.38]}

It is clear that `f(x) != g(x) forall x in RR`

However, we can apply numerical methods to compute the complex roots below:

`x approx 0.990542 +- 1.50693 i`