1. **State the problem:** Solve the equation $$3x^2 = 27$$ for $$x$$. 2. **Formula and rules:** To solve for $$x$$, we first isolate $$x^2$$ by dividing both sides by 3. 3. **Isolate $$x^2$$:** $$3x^2 = 27$$ Divide both sides by 3: $$\frac{\cancel{3}x^2}{\cancel{3}} = \frac{27}{3}$$ which simplifies to $$x^2 = 9$$ 4. **Solve for $$x$$:** Take the square root of both sides: $$x = \pm \sqrt{9}$$ 5. **Evaluate the square root:** $$x = \pm 3$$ 6. **Final answer:** The solutions are $$x = 3$$ and $$x = -3$$.