Answer:

Step-by-step explanation:

The solutions to these quadratic equations are:

3. x2 + 15x + 9 = 0

We can solve this equation by completing the square. Begin by subtracting 9 from both sides, giving us x² + 15x = -9. From there, we can factor out x and complete the square as follows:

x² + 15x + 9 - 9 = -9

x² + 15x + 0 = -9

(x + 5)² - 9 = -9

(x + 5)² = 0

x + 5 = ±sqrt(0)

x + 5 = 0

x = -5

Therefore, the solutions to the equation are x = -5.

4. x2 - 15x - 9 = 0

Again, we can solve this equation by completing the square. Begin by subtracting 9 from both sides, giving us x² - 15x - 9 = 0. From there, we can factor out x and complete the square as follows:

x² - 15x - 9 - 9 = 0

x² - 15x - 0 = -9

(x - 3)² - 9 = -9

(x - 3)² = 0

x - 3 = ±sqrt(0)

x - 3 = 0

x = 3

Therefore, the solutions to the equation are x = 3.

5. x2 + 21x + 15 = 0

We can use the quadratic formula to solve this equation:

x = [-21 ± sqrt(21² - 4(1)(15)]/(2×1)

x = [-21 ± sqrt(264)]/(2)

x = -10.5 ± sqrt(264)/2

However, we can't take the square root of a negative number, so this equation doesn't have any real solutions.

Therefore, the equation has no real solutions.