Question

Solve the following quadratic equation using the perfect square trinomial pattern: x2+54x=−729
.(1 point)
x=
Remaining Attempts : 3

Answer 1

To solve the quadratic equation \( x^2 + 54x = -729 \) using the perfect square trinomial pattern, we first need to rearrange the equation so that one side is zero:

\[
x^2 + 54x + 729 = 0
\]

Next, we'll complete the square. We take the coefficient of \( x \) (which is 54), divide it by 2, and square it:

\[
\left( \frac{54}{2} \right)^2 = 27^2 = 729
\]

Since we already have \( +729 \) on the left side, we recognize that the left side can be expressed as a perfect square:

\[
(x + 27)^2 = 0
\]

Taking the square root of both sides gives us:

\[
x + 27 = 0
\]

Now, solving for \( x \):

\[
x = -27
\]

Thus, the solution to the equation \( x^2 + 54x = -729 \) is:

\[
\boxed{-27}
\]