Question

How do you solve `-x^2 + 5x - 9 = 0`?

Answer 1

`(5 +- isqrt11)/2`

Explanation:

y = - x^2 + 5x - 9 = 0
Use the improved quadratic formula (Socratic Search):
D = d^2 = b^2 - 4ac = 25 - 36 = - 11.
There are no real roots because D < 0. There are 2 imaginary roots.
`D = 11i^2` --> `d = +- isqrt11`

`x = - b/(2a) +- d/(2a) = -5/-2 +- isqrt11/2 = (5 +- isqrt11)/2`