Due: $$ \frac{3-18-2025}{* *} $$ This Factor the perfect square trinomial 1. $$ x^{2}+18 x+81=1 $$

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**Step 1. Factor the trinomial**

Notice that  
$$
x^{2}+18x+81
$$  
is a perfect square trinomial since  
$$
9^{2}=81 \quad \text{and} \quad 2\cdot x\cdot 9=18x.
$$  
Thus, we can write  
$$
x^{2}+18x+81 = (x+9)^2.
$$

**Step 2. Rewrite the equation**

The given equation is  
$$
x^{2}+18x+81=1.
$$  
Substituting the factorization, we have  
$$
(x+9)^2 = 1.
$$

**Step 3. Take the square root of both sides**

Taking the square root of both sides gives:  
$$
x+9 = \pm 1.
$$

**Step 4. Solve for $$ x $$**

For the case $$ x + 9 = 1 $$:
$$
x = 1 - 9 = -8.
$$

For the case $$ x + 9 = -1 $$:
$$
x = -1 - 9 = -10.
$$

**Final Answer**

The solutions to the equation are  
$$
x = -8 \quad \text{or} \quad x = -10.
$$
The solutions are $$ x = -8 $$ or $$ x = -10 $$.

Due: \( \frac{3-18-2025}{* *} \) This Factor the perfect square trinomial 1. \( x^{2}+18 x+81=1 \)

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