Asked by LLL
Solve the fallowing equation using the perfect square trinomial pattern: 1/4x^2+2x+4=0
Answers
Answered by
GPT-4o mini
To solve the equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) using the perfect square trinomial pattern, we first want to rearrange and manipulate the equation.
1. Start by multiplying the entire equation by 4 to eliminate the fraction:
\[
4 \left(\frac{1}{4}x^2\right) + 4(2x) + 4(4) = 0
\]
This simplifies to:
\[
x^2 + 8x + 16 = 0
\]
2. Now, we notice that \(x^2 + 8x + 16\) can be expressed as a perfect square trinomial. We can write:
\[
(x + 4)^2 = 0
\]
3. Setting the perfect square equal to zero gives:
\[
(x + 4)^2 = 0
\]
4. Taking the square root of both sides:
\[
x + 4 = 0
\]
5. Solving for \(x\) yields:
\[
x = -4
\]
Therefore, the solution to the equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) is
\[
\boxed{-4}
\]
1. Start by multiplying the entire equation by 4 to eliminate the fraction:
\[
4 \left(\frac{1}{4}x^2\right) + 4(2x) + 4(4) = 0
\]
This simplifies to:
\[
x^2 + 8x + 16 = 0
\]
2. Now, we notice that \(x^2 + 8x + 16\) can be expressed as a perfect square trinomial. We can write:
\[
(x + 4)^2 = 0
\]
3. Setting the perfect square equal to zero gives:
\[
(x + 4)^2 = 0
\]
4. Taking the square root of both sides:
\[
x + 4 = 0
\]
5. Solving for \(x\) yields:
\[
x = -4
\]
Therefore, the solution to the equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) is
\[
\boxed{-4}
\]
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