To solve the quadratic equation \( \frac{1}{4}x^2 + 2x + 4 = 0 \) using the perfect square trinomial pattern, we first want to manipulate the equation into a simpler form.
- Start by multiplying the entire equation by 4 to eliminate the fraction:
\[ 4 \left( \frac{1}{4}x^2 + 2x + 4 \right) = 0 \]
This simplifies to:
\[ x^2 + 8x + 16 = 0 \]
- Next, notice that \( x^2 + 8x + 16 \) can be rearranged into a perfect square trinomial. Specifically, it can be factored as:
\[ (x + 4)^2 = 0 \]
- To solve for \( x \), we can take the square root of both sides:
\[ x + 4 = 0 \]
- Now solve for \( x \):
\[ x = -4 \]
Thus, the solution to the equation \( \frac{1}{4}x^2 + 2x + 4 = 0 \) is:
\[ x = [-4] \]
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