To find the values of x in the quadratic equation x² + 6x + 9 = 0, we can apply the factoring method as this equation is a perfect square trinomial.
First, we rewrite the equation:
x² + 6x + 9 = 0
Next, we recognize that the quadratic can be expressed as:
(x + 3)² = 0
This means that:
x + 3 = 0
Now, solving for x, we subtract 3 from both sides:
x = -3
Since the quadratic is a perfect square, this means there is only one value for x:
x = -3
In conclusion, the solution to the quadratic equation x² + 6x + 9 = 0 is:
- x = -3
This indicates that -3 is a repeated root of the equation, and the parabola represented by the equation only touches the x-axis at this point.