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.
The expression \( x^2 + 10x + 25 \) can be rewritten as:
\[ (x + 5)^2 \]
This is because:
\[ (x + 5)(x + 5) = x^2 + 5x + 5x + 25 = x^2 + 10x + 25 \]
So, we can rewrite the equation as:
\[ (x + 5)^2 = 0 \]
Next, we take the square root of both sides:
\[ x + 5 = 0 \]
Now, we solve for \( x \):
\[ x = -5 \]
Thus, the solution is:
\[ x = -5 \]
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