Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2+54x=−729 .(1 point) x=Asked by monday
Solve the following quadratic equation using the perfect square trinomial pattern: 1/4 x^2+2x+4=0 .(1 point) x=?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the quadratic equation \( \frac{1}{4} x^2 + 2x + 4 = 0 \) using the perfect square trinomial pattern, we will first rewrite the equation in a form that makes it easier to identify a perfect square.
1. Multiply the entire equation by 4 to eliminate the fraction:
\[
x^2 + 8x + 16 = 0
\]
2. Notice that \( x^2 + 8x + 16 \) can be rewritten as a perfect square:
\[
(x + 4)^2 = 0
\]
3. Set the perfect square equal to zero:
\[
(x + 4)^2 = 0
\]
4. Solve for \( x \) by taking the square root of both sides:
\[
x + 4 = 0
\]
5. Finally, isolate \( x \):
\[
x = -4
\]
Thus, the solution to the equation \( \frac{1}{4} x^2 + 2x + 4 = 0 \) is
\[
\boxed{-4}
\]
1. Multiply the entire equation by 4 to eliminate the fraction:
\[
x^2 + 8x + 16 = 0
\]
2. Notice that \( x^2 + 8x + 16 \) can be rewritten as a perfect square:
\[
(x + 4)^2 = 0
\]
3. Set the perfect square equal to zero:
\[
(x + 4)^2 = 0
\]
4. Solve for \( x \) by taking the square root of both sides:
\[
x + 4 = 0
\]
5. Finally, isolate \( x \):
\[
x = -4
\]
Thus, the solution to the equation \( \frac{1}{4} x^2 + 2x + 4 = 0 \) is
\[
\boxed{-4}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.