To solve the quadratic equation \( x^2 + 10x + 25 = 0 \) using the perfect square trinomial pattern, we first recognize that the left side can be factored as a square.
The equation can be rewritten as:
\[ (x + 5)^2 = 0 \]
We achieve this by observing that \( 10x \) is \( 2 \times 5 \times x \) and \( 25 \) is \( 5^2 \). Hence, we can factor this into \( (x + 5)(x + 5) = 0 \) or simply \( (x + 5)^2 = 0 \).
Next, we set the factor equal to zero:
\[ x + 5 = 0 \]
Solving for \( x \):
\[ x = -5 \]
Thus, the solution to the equation \( x^2 + 10x + 25 = 0 \) is:
\[ \boxed{-5} \]