To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, we first aim to put the equation in standard form:
\[ x^2 + 54x + 729 = 0 \]
Next, we want to express the left side as a perfect square trinomial. To do this, we need to find the term that will complete the square. The coefficient of \( x \) is 54. We take half of this coefficient and square it:
\[ \left(\frac{54}{2}\right)^2 = 27^2 = 729 \]
Now, we can rewrite the quadratic as follows:
\[ (x + 27)^2 = 0 \]
To solve for \( x \), we take the square root of both sides:
\[ x + 27 = 0 \]
Subtracting 27 from both sides gives us:
\[ x = -27 \]
Thus, the solution to the quadratic equation \( x^2 + 54x = -729 \) is
\[ \boxed{-27} \]
1 answer