How do you solve #x^2-x=2#?
Since (a - b + c = 0), use shortcut -> One real root is (-1) and the other is (-c/a = 2)
The solutions are
First we note that this is a quadratic equation. We are used to seeing quadratic equations as:
Now we have choices, we could try to factor, we could complete the square, we could use the quadratic formula. I like to try to factor first, because if the quadratic factors easily, I find that fastest. But don't spend a lot of time factoring, because we have 2 other methods that will work even if we can't easily find the factorization.
It is fairly straightforward to factor:
That leads to