To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, we first want to move all terms to one side of the equation:
\[ x^2 + 54x + 729 = 0 \]
Next, we want to turn the left side into a perfect square trinomial. To do this, we need to complete the square. The coefficient of \( x \) in \( x^2 + 54x \) is 54.
- Take half of 54, which is \( \frac{54}{2} = 27 \).
- Square it: \( 27^2 = 729 \).
Now, we can rewrite the equation as:
\[ (x + 27)^2 = 0 \]
Taking the square root of both sides:
\[ x + 27 = 0 \]
Solving for \( x \):
\[ x = -27 \]
Thus, the solution to the quadratic equation is:
\[ \boxed{-27} \]
1 answer