# How do you solve the quadratic using the quadratic formula given x^2+4x+2=0?

Nov 16, 2016

The solutions are $S = \left\{- 3.414 , - 0.586\right\}$

#### Explanation:

The quadratic equation is ${x}^{2} + 4 x + 2 = 0$

Let's calculate the discriminant

$\Delta = {b}^{2} - 4 a \cdot c = {4}^{2} - 4 \cdot 2 = 16 - 8 = 8$

As $\Delta > 0$

Therefore, we expect 2 real roots.

The solutions are $x = \frac{- b \pm \sqrt{\Delta}}{2 a}$

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

${x}_{1} = - 2 - \sqrt{2}$ and ${x}_{2} = - 2 + \sqrt{2}$

${x}_{1} = - 3.414$

and ${x}_{2} = - 0.586$