Solve the equation by the square root property. \[ (3 x-4)^{2}=33 \] Choose the correct answer below. A. The solution set is $\left\{ \pm \frac{29}{3}\right\}$. B. The solution set is $\left\{\frac{4-\sqrt{33}}{3}\right\}$. C. The solution set is $\left\{\frac{4 \pm \sqrt{33}}{3}\right\}$ D. The solution set is $\left\{\frac{4+\sqrt{33}}{3}\right\}$.

Step 1 ：The given equation is a quadratic equation in the form of \((ax+b)^2 = c\). To solve this equation, we can use the square root property, which states that if \((ax+b)^2 = c\), then \(ax+b = \sqrt{c}\) or \(ax+b = -\sqrt{c}\). So, we can solve for \(x\) by subtracting \(b\) from both sides and then dividing by \(a\).

Step 2 ：Substitute \(a = 3\), \(b = -4\), and \(c = 33\) into the equation, we get two solutions: \(x = \frac{4}{3} - \frac{\sqrt{33}}{3}\) and \(x = \frac{4}{3} + \frac{\sqrt{33}}{3}\).

Step 3 ：Final Answer: The solution set is \(\boxed{\left\{\frac{4 \pm \sqrt{33}}{3}\right\}}\). So, the correct answer is C.