We are given a quadratic equation to solve: $x^2 - 6x + 9 = 0$. We need to find the value(s) of $x$ that satisfy this equation.

1. Problem Description

We are given a quadratic equation to solve: $x^2 - 6x + 9 = 0$. We need to find the value(s) of $x$ that satisfy this equation.

2. Solution Steps

We can solve this quadratic equation by factoring. We look for two numbers that multiply to 9 and add up to -

6. These numbers are -3 and -

3. Therefore, the quadratic equation can be factored as:

$(x - 3)(x - 3) = 0$

This can also be written as:

$(x - 3)^2 = 0$

Taking the square root of both sides, we have:

$x - 3 = 0$

Adding 3 to both sides gives us:

$x = 3$

Since both factors are the same, there is only one solution.

3. Final Answer

$x = 3$