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

1 Answer
Jul 20, 2018

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