Solve the following quadratic equation using the perfect square trinomial pattern: 1/4x^2 + 2x + 4 = 0 .

x = [ ]

1 answer

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.

  1. 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:

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

  1. Next, notice that \( x^2 + 8x + 16 \) can be rearranged into a perfect square trinomial. Specifically, it can be factored as:

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

  1. To solve for \( x \), we can take the square root of both sides:

\[ x + 4 = 0 \]

  1. Now solve for \( x \):

\[ x = -4 \]

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

\[ x = [-4] \]