Completing the square is very easy once you get the pattern down for it. You always want the x quanity and the x^2 quantity on the same side of the equation and you want the plain number quanity on the other side. You also want the x^2 quantity to have a coefficient of 1.
In this case we have to divide by 5 first. And then we move the move the 4/5x over to the other side of the equation in order to set up properly:
x^2 - 4/5x = -2/5
Now that we have set up, we go about solving by completing the square. First you want to take half the coefficient of the term with the x on it and square it. In this case, take the -4/5 from (-4/5x), and divide it in half to get -2/5 and then square it to get 4/25. You then add this number to both sides of the equation:
x^2 - 4/5x + 4/25 = -2/5 + 4/25.
x^2 - 4/5x + 4/25 = -6/25
You then examine the left side of the equation. It can now be factored in the form x + half the coeffeicent of the x term, squared, like so:
(x + -2/5) ^ 2.
Finally, you take the square root of both sides and you get:
x - 2/5 = +- $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}$$
x = 2/5 +- $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{5}}}}{\mathtt{\,\times\,}}{i}$$
