The problem asks us to solve the equation $(7x - 3)^2 = 49$ using the square root property.

1. Problem Description

The problem asks us to solve the equation $(7x - 3)^2 = 49$ using the square root property.

2. Solution Steps

We are given the equation $(7x - 3)^2 = 49$.

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

$\sqrt{(7x - 3)^2} = \pm\sqrt{49}$

$7x - 3 = \pm 7$

Now we have two cases:

Case 1: $7x - 3 = 7$

$7x = 7 + 3$

$7x = 10$

$x = \frac{10}{7}$

Case 2: $7x - 3 = -7$

$7x = -7 + 3$

$7x = -4$

$x = -\frac{4}{7}$

Therefore, the two solutions are $x = \frac{10}{7}$ and $x = -\frac{4}{7}$.

3. Final Answer

$\frac{10}{7}, -\frac{4}{7}$