Solve 3x² + 12x - 5 = 0 by completing the square. Give the roots to 2 decimal places.

Step 1. Divide by 3. $x^2 + 4x - \tfrac{5}{3} = 0$, so $x^2 + 4x = \tfrac{5}{3}$.

Step 2. Complete the square. $x^2 + 4x + 4 = \tfrac{5}{3} + 4 = \tfrac{17}{3}$, so $(x + 2)^2 = \tfrac{17}{3}$.

Step 3. Square root. $\sqrt{\tfrac{17}{3}} \approx 2.380$, so $x + 2 = \pm 2.380$.

Step 4. Solve. $x \approx -2 + 2.380 = 0.38$, or $x \approx -2 - 2.380 = -4.38$.