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 expressed as a square of a binomial.
The equation can be factored as:
\[ (x + 5)^2 = 0 \]
Now, we can set the squared term equal to zero:
\[ (x + 5)^2 = 0 \]
Next, we take the square root of both sides:
\[ x + 5 = 0 \]
Now, solve for \( x \):
\[ x = -5 \]
So the solution to the equation is:
\[ \boxed{-5} \]