# How do you solve the quadratic (x-5)(x+8)=-20 using any method?

Aug 16, 2016

$x = \frac{1}{2} \left(- 3 \pm \sqrt{89}\right)$

#### Explanation:

$- 20 = \left(x - 5\right) \left(x + 8\right) = {x}^{2} + 3 x - 40$

Add $20$ to both ends to get:

$0 = {x}^{2} + 3 x - 20$

Multiply by $4$ and complete the square:

$0 = 4 {x}^{2} + 12 x - 80$

$= {\left(2 x\right)}^{2} + 2 \left(3\right) \left(2 x\right) + {3}^{2} - 89$

$= {\left(2 x + 3\right)}^{2} - {\left(\sqrt{89}\right)}^{2}$

$= \left(2 x + 3 - \sqrt{89}\right) \left(2 x + 3 + \sqrt{89}\right)$

Hence $x = \frac{1}{2} \left(- 3 \pm \sqrt{89}\right)$