9y^2-12y+13=0 solve by factoring or by completing the square

Question

hero · Answer

This quadratic has no real solutions

hero · Answer

It's factorable, it just won't look pretty

anonymous · Answer

it has to

anonymous · Answer

i need help don't understand it

hero · Answer

Are all of your signs correct? Double check

anonymous · Answer

yes

anonymous · Answer

or solve by completing the square

hero · Answer

I'm sorry to hear that. It has no real solutions

anonymous · Answer

i typed that and i got it wrong. can you solve by completing the square

hero · Answer

You could, but it wouldn't yield a real solution

hero · Answer

Yeah, satellite, help me out here

anonymous · Answer

complete the square as follows
$$9y^2-12y+13=0$$
subtract 13
$$9y^2-12y=-13$$
divide by 9
$$y^2-\frac{4}{3}y=-\frac{13}{9}$$
take half the coefficient of the middle term square and add to both sides to make a perfect square 
$$(y-\frac{2}{3})^2=-\frac{13}{9}+\frac{4}{9}=-\frac{9}{9}=-1$$
take the square root
$$y-\frac{2}{3}=\pm \sqrt{-1}=\pm i$$
solve for y
$$y=\frac{2}{3}\pm i$$

anonymous · Answer

you can also use the quadratic formula, but you will not be able to factor unless you know the zeros to begin with

hero · Answer

What about myininaya's method?

anonymous · Answer

thanks that helped alot