Given the equation \( \sqrt{3x + 12} = x + 6 \), isolate the radical before solving for x.

To solve the equation \( \sqrt{3x + 12} = x + 6 \), we first isolate the radical, which is already isolated in this case. However, for clarity, we can rewrite it: Start with: \[ \sqrt{3x + 12} = x + 6 \] Now, to eliminate the square root, we can square both sides of the equation: \[ (\sqrt{3x + 12})^2 = (x + 6)^2 \] This gives us: \[ 3x + 12 = (x + 6)(x + 6) \] Expanding the right side: \[ 3x + 12 = x^2 + 12x + 36 \] Next, we can rearrange the equation by moving all terms to one side: \[ x^2 + 12x + 36 - 3x - 12 = 0 \] Simplifying that, we have: \[ x^2 + 9x + 24 = 0 \] Now, we need to solve this quadratic equation for \( x \).