Answer
$x = 0, \pi, \frac{3\pi}{4}, \frac{7\pi}{4}$
Work Step by Step
$tan^{2}(x) + tan(x) = 0$
Factor the expression:
$tan(x) (tan(x) + 1) = 0$
Since it is equal to 0, it can be divided into:
tan(x) = 0 and tan(x) + 1 = 0
For tan(x) = 0:
x = 0, $\pi$
For tan(x) + 1 = 0:
We manipulate the equation as follows:
tan(x) = -1
x = $\frac{3\pi}{4}, \frac{7\pi}{4}$
The solutions are:
$x = 0, \pi, \frac{3\pi}{4}, \frac{7\pi}{4}$
