# How do you solve 2x^2 + 4x +10 = 0 using the quadratic formula?

May 11, 2016

The solutions for the equation are:
color(blue)( x = -1 + 2i

 color(blue)(x = -1 - 2i

#### Explanation:

$2 {x}^{2} + 4 x + 10 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 2 , b = 4 , c = 10$

The Discriminant is given by:

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

$= {\left(4\right)}^{2} - \left(4 \cdot 2 \cdot 10\right)$

$= 16 - 80 = - 64$

The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 4\right) \pm \sqrt{- 64}}{2 \cdot 2} = \frac{- 4 \pm 8 i}{4}$

$= \frac{- 4 \pm 8 i}{4} = \frac{4 \left(- 1 \pm 2 i\right)}{4}$

$= \frac{\cancel{4} \left(- 1 \pm 2 i\right)}{\cancel{4}}$

$= - 1 \pm 2 i$

$x = - 1 + 2 i$

$x = - 1 - 2 i$