Question

Solve the quadratic equation using the perfect square trinomial pattern

1/4x^2 + 2x + 4 = 0

Answer 1

To solve the quadratic equation \( \frac{1}{4}x^2 + 2x + 4 = 0 \) using the perfect square trinomial pattern, we first want to rewrite the equation in a way that makes it easier to work with.

### Step 1: Eliminate the fraction
Multiply the entire equation by 4 to eliminate the fraction:

\[
4 \left( \frac{1}{4}x^2 + 2x + 4 \right) = 0
\]

This simplifies to:

\[
x^2 + 8x + 16 = 0
\]

### Step 2: Identify the perfect square trinomial
Now, observe that \( x^2 + 8x + 16 \) can be factored as a perfect square trinomial:

\[
(x + 4)^2 = 0
\]

### Step 3: Solve for \( x \)
Set the equation equal to zero:

\[
(x + 4)^2 = 0
\]

Take the square root of both sides:

\[
x + 4 = 0
\]

Now, solve for \( x \):

\[
x = -4
\]

### Conclusion
The solution to the equation \( \frac{1}{4}x^2 + 2x + 4 = 0 \) is:

\[
\boxed{-4}
\]