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.
- 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:
\[ x^2 + 8x + 16 = 0 \]
- Now, we notice that \(x^2 + 8x + 16\) can be expressed as a perfect square trinomial. We can write:
\[ (x + 4)^2 = 0 \]
- Setting the perfect square equal to zero gives:
\[ (x + 4)^2 = 0 \]
- Taking the square root of both sides:
\[ x + 4 = 0 \]
- Solving for \(x\) yields:
\[ x = -4 \]
Therefore, the solution to the equation \(\frac{1}{4}x^2 + 2x + 4 = 0\) is
\[ \boxed{-4} \]