# How do you use the quadratic formula to solve x^2+6x+10=0?

Mar 4, 2018

Solution: $x = - 3 + 1 i \mathmr{and} x = - 3 - 1 i$

#### Explanation:

${x}^{2} + 6 x + 10 = 0$

Comparing with standard quadratic equation $a {x}^{2} + b x + c = 0$

$a = 1 , b = 6 , c = 10$ Discriminant $D = {b}^{2} - 4 a c$ or

$D = 36 - 40 = - 4$ If discriminant positive, we get two real

solutions, if it is zero we get just one solution, and if it is negative

we get complex solutions. Discriminant is negative , so it has

complex roots. .Quadratic formula: $x = \frac{- b \pm \sqrt{D}}{2 a}$or

$x = \frac{- 6 \pm \sqrt{- 4}}{- 2} = - 3 \pm i \left[{i}^{2} = - 1\right]$

So roots are $x = - 3 + 1 i \mathmr{and} x = - 3 - 1 i$ [Ans]