To solve the quadratic equation \( x^2 + 10x + 25 = 0 \) using the perfect square trinomial pattern, we can first recognize that the left side of the equation can be expressed as a perfect square.
The expression \( x^2 + 10x + 25 \) can be rewritten as:
\[ (x + 5)^2 \]
Now, we can rewrite the equation as:
\[ (x + 5)^2 = 0 \]
Next, we take the square root of both sides:
\[ x + 5 = 0 \]
Solving for \( x \), we subtract 5 from both sides:
\[ x = -5 \]
Thus, the solution to the quadratic equation \( x^2 + 10x + 25 = 0 \) is:
\[ \boxed{-5} \]