To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, we first rewrite the equation in standard form by moving \(-729\) to the left side:
\[ x^2 + 54x + 729 = 0 \]
Next, we will complete the square. The general formula for completing the square is to add and subtract \(\left(\frac{b}{2}\right)^2\), where \(b\) is the coefficient of \(x\).
Here, \(b = 54\), so we calculate:
\[ \left(\frac{54}{2}\right)^2 = 27^2 = 729 \]
Adding and subtracting \(729\) gives us:
\[ x^2 + 54x + 729 = 729 \]
Now we can rewrite the equation as:
\[ (x + 27)^2 = 0 \]
Now, we take the square root of both sides:
\[ x + 27 = 0 \]
Solving for \(x\):
\[ x = -27 \]
Thus, the solution to the equation \( x^2 + 54x = -729 \) is:
\[ \boxed{-27} \]