Asked by T-Swizzle
Solve the following quadratic equation using the perfect square trinomial pattern: x^2 + 54x = -729
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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
\[
\boxed{-27}
\]
\[
x^2 + 54x + 729 = 0
\]
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
\[
\boxed{-27}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.