### Home > APCALC > Chapter 7 > Lesson 7.2.2 > Problem7-65

7-65.

Once again, Greta is in a pickle! She is trying to solve the following equation and knows she can use $u$-substitution.

$3 \tan^2(x) - \tan(x) - 10 = 0$

1. Greta thinks if she lets $u = \tan(x)$ she can write the equation as a quadratic equation. Show Greta she is correct.

$3u^2 − u − 10 = 0$
Solve for $u$.
Then solve for $x$.

2. Use your answer to part (a) to solve for $x$.

$x=\tan^{−1}(2)\approx1.107+\pi n$