# How do you solve -x^2 - 3x + 5 = 0 using the quadratic formula?

Feb 27, 2016

$x = \frac{- 3 - \sqrt{29}}{2} \mathmr{and} x = \frac{- 3 + \sqrt{29}}{2}$

#### Explanation:

Given equation= $- {x}^{2} - 3 x + 5 = 0$

Comparing with $a {x}^{2} + b x + c = 0$

We get , $a = - 1 , b = - 3 , c = 5$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{3 \pm \sqrt{- {3}^{2} - 4 \times - 1 \times 5}}{2 \times - 1}$

$x = \frac{3 \pm \sqrt{9 + 20}}{- 2}$

$x = \frac{3 \pm \sqrt{29}}{- 2}$

$x = \frac{3 + \sqrt{29}}{- 2} \mathmr{and} x = \frac{3 - \sqrt{29}}{- 2}$

$x = \frac{- 3 - \sqrt{29}}{2} \mathmr{and} x = \frac{- 3 + \sqrt{29}}{2}$