# What is the solution set for (3x - 1)2 = 5?

Aug 6, 2015

I think you mean ${\left(3 x - 1\right)}^{2} = 5$

#### Explanation:

In that case there are two solutions:
(1)
$3 x - 1 = + \sqrt{5} \to x = \frac{1 + \sqrt{5}}{3}$
(2)
$3 x - 1 = - \sqrt{5} \to x = \frac{1 - \sqrt{5}}{3}$

Sometimes this is summarised as:
$3 x - 1 = \pm \sqrt{5} \to {x}_{1 , 2} = \frac{1 \pm \sqrt{5}}{3}$