To find the value of x in the quadratic equation x² + 6x + 9, we can factor or use the quadratic formula. First, let’s look for factors.
The equation can be rewritten as:
x² + 6x + 9 = 0
We need two numbers that multiply to 9 (the constant term) and add to 6 (the coefficient of x). The numbers 3 and 3 fit this requirement, so we can factor the equation like this:
(x + 3)(x + 3) = 0
This means:
(x + 3)² = 0
To find the value of x, we can take the square root of both sides:
x + 3 = 0
Therefore, x = -3.
This means that the quadratic equation has one solution, x = -3, which is known as a double root. In conclusion, the only value of x that satisfies the equation x² + 6x + 9 = 0 is:
x = -3