Help me to find x

Step 1: Identify the given equation. The equation is $x^2 - 18x + 81 = 0$.

Step 2: Recognize the equation as a perfect square trinomial. A perfect square trinomial has the form $a^2 - 2ab + b^2 = (a-b)^2$. In this equation, $a^2 = x^2$ (so $a=x$), and $b^2 = 81$ (so $b=9$). The middle term is $-18x$, which matches $-2ab = -2(x)(9) = -18x$.

Step 3: Factor the trinomial. Using the perfect square trinomial formula, we can rewrite the equation as $(x-9)^2 = 0$.

Step 4: Solve for x. Take the square root of both sides: $\sqrt{(x-9)^2} = \sqrt{0}$. This simplifies to $x-9 = 0$. Add 9 to both sides: $x = 9$.

$x^2 - 18x + 81 = 0$ $(x-9)^2 = 0$ $x-9 = 0$ $x = 9$

The value of x is 9.