Math 11, solve for x and express in simplest a + bi form

x + (5/x) = 2

Thanks for any help

x+(5/x)=2

Let's work on the left.

x+(5/x)=((x^2)/x)+(5/x)=((x^2)+5)/x

So

((x^2)+5)/x=2

Multiply both sides by x, and you get:

(x^2)+5=2x

Which is the same as the easy quadratic:

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

:)