Final answer:
To solve x² + 10x + 9 = 0 using the quadratic formula, plug in the values of a, b, and c into the formula (-b ± sqrt(b² - 4ac)) / (2a), and solve for x. The solutions for x are -3 and -7.
Step-by-step explanation:
To solve the equation x² + 10x + 9 = 0 using the quadratic formula, we first identify the values of a, b, and c. In this case, a = 1, b = 10, and c = 9. Substituting these values into the quadratic formula, we get:
x = (-b ± sqrt(b² - 4ac)) / (2a)
Plugging in the values, we have:
x = (-10 ± sqrt(10² - 4(1)(9))) / (2(1))
Calculating the discriminant (b² - 4ac), we find that it is equal to 16. Taking the square root of the discriminant, we get 4. Therefore, the solutions for x are:
x = (-10 + 4) / 2 = -3
x = (-10 - 4) / 2 = -7