Question

How do you solve the quadratic `2x^2-6x+5=0` with complex numbers?

Answer 1

`x = 3/2+-1/2i`

Explanation:

`0 = 2(2x^2-6x+5)`

`color(white)(0) = 4x^2-12x+10`

`color(white)(0) = (2x)^2-2(2x)(3)+3^2+1`

`color(white)(0) = (2x-3)^2+1^2`

`color(white)(0) = (2x-3)^2-i^2`

`color(white)(0) = ((2x-3)-i)((2x-3)+i)`

`color(white)(0) = (2x-3-i)(2x-3+i)`

So:

`2x = 3+-i`

and:

`x = 3/2+-1/2i`