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

Aug 18, 2016

$\frac{5 \pm i \sqrt{11}}{2}$

#### 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.
$D = 11 {i}^{2}$ --> $d = \pm i \sqrt{11}$

$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{5}{-} 2 \pm i \frac{\sqrt{11}}{2} = \frac{5 \pm i \sqrt{11}}{2}$