### Home > PC3 > Chapter 9 > Lesson 9.2.3 > Problem9-131

9-131.

Solve each of the following equations for all real $x$.

1. $2\cos(3x) = 1$

$\cos(3x)=\frac{1}{2}$

Let $u = 3x$. Then solve:

$\cos(u)=\frac{1}{2}$

1. $2\cos^2(x) + \cos(x) − 1 = 0$

Let $u = \cos(x)$. Then solve $2u^{2} + u − 1 = 0$ by factoring and using the Zero Product Property.