# How do you solve x^2 - 4x + 13=0 using the quadratic formula?

Apr 14, 2017

Solution: $x = 2 + 3 i , x = 2 - 3 i$

#### Explanation:

Comparing with standard equation $a {x}^{2} + b x + c = 0$, we get here a=1, b=-4,c=13 ; D=b^2-4ac= 16-52= -36.

Discriminant (D) is negative , so roots are complex in nature.

Roots are $x = - \frac{b}{2 a} \pm \frac{\sqrt{{b}^{2} - 4 a c}}{2 a} \mathmr{and} x = \frac{4}{2 \cdot 1} \pm \frac{\sqrt{16 - 52}}{2 \cdot 1} = 2 \pm \frac{6 \cdot i}{2} = 2 \pm 3 i$

Solution: $x = 2 + 3 i , x = 2 - 3 i$ [Ans]