# Solve for x where pi <= x <= 2pi ? Tan^2 x + 2 sqrt(3) tan x + 3 = 0

May 29, 2018

$x = n \pi + \frac{2 \pi}{3}$ where $n \in \mathbb{Z}$

#### Explanation:

$\rightarrow {\tan}^{2} x + 2 \sqrt{3} \tan x + 3 = 0$

$\rightarrow {\left(\tan x\right)}^{2} + 2 \cdot \tan x \cdot \sqrt{3} + {\left(\sqrt{3}\right)}^{2} = 0$

$\rightarrow {\left(\tan x + \sqrt{3}\right)}^{2} = 0$

$\rightarrow \tan x = - \sqrt{3} = \tan \left(\frac{2 \pi}{3}\right)$

$\rightarrow x = n \pi + \frac{2 \pi}{3}$ where $n \in \mathbb{Z}$