The problem is to solve the quadratic equation $x^2 + 8x + 4 = 0$.

1. Problem Description

The problem is to solve the quadratic equation $x^2 + 8x + 4 = 0$.

2. Solution Steps

We can solve this quadratic equation using the quadratic formula.

The quadratic formula is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation $ax^2 + bx + c = 0$.

In this case, we have $a = 1$, $b = 8$, and $c = 4$.

Plugging these values into the quadratic formula, we get:

$x = \frac{-8 \pm \sqrt{8^2 - 4(1)(4)}}{2(1)}$

$x = \frac{-8 \pm \sqrt{64 - 16}}{2}$

$x = \frac{-8 \pm \sqrt{48}}{2}$

We can simplify $\sqrt{48}$ as $\sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}$.

$x = \frac{-8 \pm 4\sqrt{3}}{2}$

Now we can divide both terms in the numerator by 2:

$x = -4 \pm 2\sqrt{3}$

Therefore, the two solutions are:

$x_1 = -4 + 2\sqrt{3}$

$x_2 = -4 - 2\sqrt{3}$

3. Final Answer

$x = -4 + 2\sqrt{3}$ and $x = -4 - 2\sqrt{3}$