Question

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

Answer 1

`x = 1/2(-3+-sqrt(89))`

Explanation:

`-20 = (x-5)(x+8)=x^2+3x-40`

Add `20` to both ends to get:

`0 = x^2+3x-20`

Multiply by `4` and complete the square:

`0 = 4x^2+12x-80`

`=(2x)^2+2(3)(2x)+3^2-89`

`=(2x+3)^2-(sqrt(89))^2`

`=(2x+3-sqrt(89))(2x+3+sqrt(89))`

Hence `x = 1/2(-3+-sqrt(89))`