How do you solve the quadratic #3x^2-4x+5-0# by completing the square?
To start completing the square, you must factor your first coefficient out of your equation (in this case the 3). So pull the 3 out of the first two terms (leave the 3rd one out for now), and this is what you'll get:
Then, you need to add something to this equation that makes it a perfect square (which is, after all, what completing the square is).
But what do we need to add? Well, we know that the equation of a perfect square binomial
Now, we need to add this to our equation. However, keep in mind that because we're adding, we need to add it to the other side as well.
Now you may have noticed that I added
Now, you can bring it together as an
Now. it's just a matter of simplifying and solving for
Those are your solutions.
Also, here's a video I made that you can watch on completing the square in general.
Hope that helped :)