The Quadratic Formula - Problem 1

We’re asked to solve this equation by using the quadratic formula. Some of you guys you're going to be angry because you can look at this you can tell it could be easily factored and you want top solve it that way. But I just want to how you that sometimes the quadratic formula works, actually it always works and sometimes you get whole number answers.

So here we go. I’m going to sing the formula. Do you guys know it? X equals -b plus or minus square root of b² minus 4ac all over 2a. If you don’t know that yet, start memorizing. Okay I’m going to write that out and then we’re going to go through and talk about what that means.

In order to plug things into this formula first I need to find out what a, b and c are. They are the coefficients, a is what’s the coefficient for my x² term, b is the coefficient for my x term and c is the coefficient of my constant. I guess it’s not really a coefficient. It’s just a constant. Okay a, b and c. Let’s plug in into that formula. X is going to be -(-2) which is like +2, plus or minus square root, b² is -2 times itself which is positive 4 minus 4 times 1 times 8, 4ac. Please be really careful with negative signs. The place where students make errors in these problems is because they lose those negatives. They are really important. Also make sure you remember it’s all over 2a.

Okay let’s go through and start simplifying. That means I’m going to have 2 plus or minus the square root of 4 minus 4 times 1 times -8. Well 4 times 1 times -8 is -32 and it’s been subtracted. So what I really have is 4 plus 32 under the square root. I’m going to move over here because I’m running out of space.

Okay so now I have x equals 2 plus or minus square root of 4 plus 32 is 36 all over 2. Square root of 36, you guys already know what that is, square root of 36 is 6. So I’ll have two different answers. X is going to be 2 plus 6 divided by 2 and I also have to do 2 minus 6 divided by 2. This plus/minus thing means I’m going to have two different answers. 2 plus 6 is 8 divided by 2 is 4, that’s one of my solutions for x. The other solution will come from 2 take away 6 divided by 2, -2. I think my answers for x are 4 and -2. The way I could check would be to go back to the original problem substitute them in one at a time and make sure they are equal to zero.

So let’s do that with 4. We want to make sure that 4², 16, take away 2 times 4 which is 8 take away 8 more equals 0. Good. That guy works. Now let’s go back and try it with negative 2. Is it true that if I do -2 times itself take away 2 times -2 take away 8, I get 0? Let’s see, 4 plus 4 equals 8, good yeah. That’s how I can check my work and make sure I got these correct. These are my solutions for x. If I had to graph this, these would be my x intercepts.

So it’s kind of a long mess but you guys will get better at it especially once you memorize the formula but again please be really, really careful with those minus signs. Don’t mess those up. Write everything out and don’t try to do it in your head because that’s where most of the errors happen.