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 perfect square:
\[ x^2 + 10x + 25 = (x + 5)^2 \]
Now, we can rewrite the equation:
\[ (x + 5)^2 = 0 \]
Next, we take the square root of both sides:
\[ x + 5 = 0 \]
Now, we solve for \( x \):
\[ x = -5 \]
Thus, the solution to the equation \( x^2 + 10x + 25 = 0 \) is:
\[ \boxed{-5} \]
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