To solve the quadratic equation \(x^2 + 10x + 25 = 0\) using the perfect square trinomial pattern, we can recognize that the left-hand side can be factored as follows:
The expression \(x^2 + 10x + 25\) can be rewritten as:
\[ (x + 5)^2 = 0 \]
Now, to solve for \(x\), we will take the square root of both sides:
\[ x + 5 = 0 \]
Subtracting 5 from both sides gives:
\[ x = -5 \]
Thus, the solution to the equation \(x^2 + 10x + 25 = 0\) is:
\[ \boxed{-5} \]
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