X²−6x+9=0 express

The given quadratic equation $x^2 - 6x + 9 = 0$ is in the form of a perfect square trinomial, $a^2 - 2ab + b^2 = (a-b)^2$.

Comparing $x^2 - 6x + 9$ with $a^2 - 2ab + b^2$:
$a^2 = x^2 \implies a = x$
$b^2 = 9 \implies b = 3$

Check if $-2ab$ matches the middle term $-6x$:
$-2ab = -2(x)(3) = -6x$. This matches.

Since it fits the pattern, we can factor it as $(a-b)^2$:
$x^2 - 6x + 9 = (x-3)^2$

Set the factored expression equal to zero:
$(x-3)^2 = 0$
Take the square root of both sides:
$x-3 = 0$
Add 3 to both sides:
$x = 3$