I saw that I would have to use -1 and -2 to get the +2 (since the middle term was negative). And then I realized that -2*1 and -1*3 would give me the -5 that I needed.
We don't necessarily have to use the quadratic formula - particulaly if we can factor a quadratic equation. In fact, I always see if I can factor first, before resorting to it.
This is an example of a quadratic equation.
Since you can't factor easily, you should use the quadratic formula.
Your two solutions should be:
x=1 & x=0.6666666667
This factors as
(3x-2) (x-1)
If you're tryig to find the "zeroes," just set each factor to 0. You will obtain x = 2/3 and x = 1.
How did you know to use those numbers inside of the parenthesis? I understand the 3, but I don't know how you knew to use -2 and 1. The way I was taught was to find two numbers that added to equal b, (-5) and multiplied to equal c, (2). And if you couldn't do that, refer to the formula.
I saw that I would have to use -1 and -2 to get the +2 (since the middle term was negative). And then I realized that -2*1 and -1*3 would give me the -5 that I needed.
We don't necessarily have to use the quadratic formula - particulaly if we can factor a quadratic equation. In fact, I always see if I can factor first, before resorting to it.