When I was a high school student in Korea, I learned two types of quadratic formula.
If the quadratic equation is in the form of .
As you know, the first quadratic formula is the famous .
We learned one more thing. The other one is used only if b is a even number.
If we let b be 2d in the quadratic equation, it will be , right?
Then, the new quadratic formula becomes .
You already figured out how I got the second one!!
If we substitute 2d into b in the original quadratic formula,
which is and we can just reduce them.
And finally got the new quadratic formula ,
when the quadratic equation is .
Do you know why we used two types of quadratic formula in Korea? We had to solve all the math problems mentally without any calculator in a short time. Believe or not, the second quadratic formula sometimes helped me a lot to save time!
You can try it now.
Solve using the second type of quadratic formula
(Hint: in this case, d becomes 12/2, which is 6)