How do you find the solution set for x^2 + 6x + 9 = 0?

Factor.

(x+3)(x+3) = 0

x = -3

twice :)

To find the solution set for the equation x^2 + 6x + 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Let's apply this formula to the given equation x^2 + 6x + 9 = 0:

a = 1 (coefficient of x^2)
b = 6 (coefficient of x)
c = 9

Substituting these values into the quadratic formula:

x = (-6 ± √(6^2 - 4(1)(9))) / 2(1)
x = (-6 ± √(36 - 36)) / 2
x = (-6 ± √(0)) / 2
x = (-6 ± 0) / 2

Since the discriminant (the expression inside the square root) is zero, the solutions are equal.

x = -6 / 2
x = -3

Therefore, the solution set for the equation x^2 + 6x + 9 = 0 is {x = -3}.