The problem is to solve the equation $(5x - 2)^2 = 16$ using the square root property.

1. Problem Description

The problem is to solve the equation $(5x - 2)^2 = 16$ using the square root property.

2. Solution Steps

We are given the equation $(5x - 2)^2 = 16$.

To solve for $x$, we take the square root of both sides of the equation:

$\sqrt{(5x - 2)^2} = \sqrt{16}$

$5x - 2 = \pm 4$

Now we have two cases to consider:

Case 1: $5x - 2 = 4$

$5x = 4 + 2$

$5x = 6$

$x = \frac{6}{5}$

Case 2: $5x - 2 = -4$

$5x = -4 + 2$

$5x = -2$

$x = -\frac{2}{5}$

3. Final Answer

The solutions are $x = \frac{6}{5}, -\frac{2}{5}$.