The problem is to solve the equation $(3x + 1)^2 = 6$ for $x$ using the square root property. The solution must be in exact form, using radicals if necessary.

1. Problem Description

The problem is to solve the equation $(3x + 1)^2 = 6$ for $x$ using the square root property. The solution must be in exact form, using radicals if necessary.

2. Solution Steps

The equation is $(3x + 1)^2 = 6$. To solve for $x$, first take the square root of both sides:

$\sqrt{(3x+1)^2} = \sqrt{6}$

$3x+1 = \pm\sqrt{6}$

Next, subtract 1 from both sides:

$3x = -1 \pm \sqrt{6}$

Finally, divide by 3:

$x = \frac{-1 \pm \sqrt{6}}{3}$

Thus, the two solutions are $x = \frac{-1 + \sqrt{6}}{3}$ and $x = \frac{-1 - \sqrt{6}}{3}$.

3. Final Answer

$\frac{-1+\sqrt{6}}{3}, \frac{-1-\sqrt{6}}{3}$