# How do you solve the quadratic with complex numbers given 5x^2+8x+5=0?

Sep 4, 2016

#### Answer:

$x = - \frac{4}{5} - i \frac{3}{5}$ and $x = - \frac{4}{5} + i \frac{3}{5}$

#### Explanation:

Quadratic formula gives the solution of quadratic equation $a {x}^{2} + b x + c = 0$ as

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

Hence solution of $5 {x}^{2} + 8 x + 5 = 0$ is given by

x=(-8+-sqrt(8^2-4×5×5))/(2×5)

= $\frac{- 8 \pm \sqrt{64 - 100}}{10}$

= $\frac{- 8 \pm \sqrt{- 36}}{10}$

= $\frac{- 8 \pm i 6}{10} = - \frac{4}{5} \pm i \frac{3}{5}$

i.e. $x = - \frac{4}{5} - i \frac{3}{5}$ and $x = - \frac{4}{5} + i \frac{3}{5}$