### Home > PC > Chapter 7 > Lesson 7.3.3 > Problem7-120

7-120.

Kiara was trying to solve the problem $\sin^{2}\left(3x − 5\right) − \sin\left(3x − 5\right) + 0.24 = 0$. She originally made the substitution $u = 3x − 5$.

1. What new equation did she get?

$\sin^{2}u − \sin u + 0.24 = 0$

2. She decided that she needed to make another substitution using the variable $v$. What would be a good substitution to make?

Let $v = \sin u$

3. What is Kiara’s equation now?

$v^{2} − v + 0.24 = 0$

4. If she had done the substitution in one step, what would $v$ equal?

$v = \sin\left(3x − 5\right)$