How do you solve the equation 3x² + 18x + 15 = 0 by completing the square?

To solve the equation 3x² + 18x + 15 = 0 by completing the square, follow these steps:

1. Divide the entire equation by 3: This makes the calculations easier. Dividing each term gives us:

x² + 6x + 5 = 0

2. Rearrange the equation: Move the constant term to the other side:

x² + 6x = -5

3. Complete the square: Take half of the coefficient of x (which is 6), square it, and add it to both sides. Half of 6 is 3, and 3² is 9. So we add 9 to both sides:

x² + 6x + 9 = -5 + 9

x² + 6x + 9 = 4

4. Factor the left side: The left side is a perfect square trinomial:

(x + 3)² = 4

5. Take the square root of both sides: Remember to consider both the positive and negative roots:

x + 3 = ±2

6. Solve for x: Now, solve both equations:
• x + 3 = 2 ⇒ x = -1
• x + 3 = -2 ⇒ x = -5

Thus, the solutions to the original equation 3x² + 18x + 15 = 0 are:

• x = -1
• x = -5