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

Feb 16, 2016

Solution is $\frac{- 1 + i \sqrt{15}}{2}$ and $\frac{- 1 - i \sqrt{15}}{2}$

#### Explanation:

For an equation $a {x}^{2} + b x + c = 0$, quadratic formula gives the solution as $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

As in the given equation ${x}^{2} + x + 4 = 0$, $a = 1 , b = 1$ and $c = 4$

Solution is given by $\frac{- 1 \pm \sqrt{{1}^{2} - 4 \cdot 1.4}}{2 \cdot 1}$ or

$\frac{- 1 \pm \sqrt{- 15}}{2}$ or $\frac{- 1 \pm i \sqrt{15}}{2}$

Hence solution is $\frac{- 1 + i \sqrt{15}}{2}$ and $\frac{- 1 - i \sqrt{15}}{2}$