To solve the quadratic equation \( x^2 + 10x + 25 = 0 \) using the perfect square trinomial pattern, we can recognize that it can be factored as follows:
\[ (x + 5)^2 = 0 \]
To find the value of \( x \), we solve the equation:
\[ x + 5 = 0 \]
Subtracting 5 from both sides, we get:
\[ x = -5 \]
Thus, the solution to the equation \( x^2 + 10x + 25 = 0 \) is:
\[ x = -5 \]