# How do you solve x^2 + 4x + 1 = 0 using the quadratic formula?

Mar 11, 2018

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

#### Explanation:

$\text{Given the quadratic equation in standard form}$

•color(white)(x)ax^2+bx+c=0 color(white)(x);a!=0

$\text{We can solve for x using the "color(blue)"quadratic formula}$

•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)

${x}^{2} + 4 x + 1 = 0 \text{ is in standard form}$

$\text{with "a=1,b=4" and } c = 1$

$\Rightarrow x = \frac{- 4 \pm \sqrt{16 - 4}}{2} = \frac{- 4 \pm \sqrt{12}}{2}$

$\textcolor{w h i t e}{x} = \frac{- 4 \pm 2 \sqrt{3}}{2} = - 2 \pm \sqrt{3} \leftarrow \textcolor{red}{\text{exact values}}$