The problem is to solve the equation $(7x - 4)^2 = 36$ using the square root property.

1. Problem Description

The problem is to solve the equation $(7x - 4)^2 = 36$ using the square root property.

2. Solution Steps

The given equation is $(7x - 4)^2 = 36$.

Taking the square root of both sides gives

$7x - 4 = \pm \sqrt{36}$.

Since $\sqrt{36} = 6$, we have $7x - 4 = \pm 6$.

This leads to two equations:

$7x - 4 = 6$ and $7x - 4 = -6$.

Solving the first equation, $7x - 4 = 6$, we add 4 to both sides to get $7x = 10$. Then, dividing both sides by 7 gives $x = \frac{10}{7}$.

Solving the second equation, $7x - 4 = -6$, we add 4 to both sides to get $7x = -2$. Then, dividing both sides by 7 gives $x = -\frac{2}{7}$.

Therefore, the solutions are $x = \frac{10}{7}$ and $x = -\frac{2}{7}$.

3. Final Answer

The solutions are $\frac{10}{7}, -\frac{2}{7}$.