Solve for $x$ in the equation $123 + (3x - 9)^2 = 323$.

1. Problem Description

Solve for $x$ in the equation $123 + (3x - 9)^2 = 323$.

2. Solution Steps

First, isolate the squared term by subtracting 123 from both sides of the equation:

$123 + (3x - 9)^2 - 123 = 323 - 123$

$(3x - 9)^2 = 200$

Next, take the square root of both sides of the equation:

$\sqrt{(3x - 9)^2} = \pm\sqrt{200}$

$3x - 9 = \pm\sqrt{200}$

Simplify the square root of 200:

$\sqrt{200} = \sqrt{100 \cdot 2} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2}$

So, $3x - 9 = \pm 10\sqrt{2}$

Add 9 to both sides of the equation:

$3x = 9 \pm 10\sqrt{2}$

Divide both sides by 3:

$x = \frac{9 \pm 10\sqrt{2}}{3}$

$x = 3 \pm \frac{10\sqrt{2}}{3}$

3. Final Answer

$x = 3 \pm \frac{10\sqrt{2}}{3}$