 This video will talk about the quadratic formula. If we have a quadratic formula, it's going to be in the form of AX squared plus BX plus C equal to zero, and notice I have two separate squares here because it has to be equal to zero. It must be equal to zero. And then when we talk about A and the formula is going to have ABs in season and so A is the coefficient on X squared, not the first term necessarily, it has to be the coefficient on X squared. And B is the coefficient on X, and C is always the constant. And then the quadratic formula is, and I learned from one of my students several years ago that you could see pop goes a weasel. So we would say X is equal to negative B plus or minus a square root of B squared minus four AC all over two A. So let's simplify, and then we'll talk about the quadratic formula. This is like half of a quadratic formula. So we have negative four minus a square root of, and then this gives us sixteen, and then I like to have you solve them like this. Minus and then four times one would be four times negative three, and four times negative three would be negative twelve. And then all over two, two times one, and we're almost there. Negative four minus the square root of sixteen, but minus a negative is the same thing as plus twelve all over two. So we have negative four minus the square root of twenty-eight all over two. That would be as simple as we need to get it. So it's underneath the radical, this four X squared minus four times one times negative three in our case, or just B squared minus four AC, that's called the discriminant. And then discriminant is kind of nice, because it tells us what kinds of answers we're going to have. If it's a positive number like what we have here, you'll have two real solutions. Now, and the one we just did, we don't, because we did half of a quadratic formula. But if you remember, it says plus or minus the square root. So we can add the square root and subtract the square root, and that gives us two answers. If it's zero, well, the square root of zero is just zero. So we know we're going to have one real solution. And if it's a negative number, again, we can't take the square root of a negative number, so we know that we have no real solution. So let's try. And if we look at this, A is the coefficient on X squared, so that would be one. B is the coefficient on X, so that's five. C is the constant, which is six, and negative B, just because that's part of our formula. If this is B, then negative B is going to be negative five. So X is equal to, and then we have negative B, so negative five, plus or minus the square root of B squared, so five is our B squared, minus, and then in Barakas we have four times A, which is one, times C, which is six, and then all over two times A, which is two times one. So that's negative five, plus or minus the square root of, now we'll simplify, five square root is 25, minus, and in the Barakas here we have four times one is four times six is 24, all over two times one are just two. So we have negative five, plus or minus the square root of, 25 minus four would be one over two, and I'm running out of space, so I'm going to go across. That's negative five, but the square root of one we happen to know is one. And when you get rid of the radical you've got extra work to do. This means we have negative five plus one over two, and we have negative five minus one over two. So negative five plus one is going to be negative four over two, which is negative two. And negative five minus one will give us negative six over two, which will be negative three. Try again. A is one, B is negative six, oh wait a minute, it said it had to be equal to zero. So we can't tell what our constant is yet because it has to go to the other side. We really need to rewrite it as y squared minus six y, and then add the nine to both sides equal to zero. So the A is still one, and my B is still negative six, but now I know my C is positive nine, and just because the formula has negative B in it, I might be helpful to just list it. This is negative six, so negative B, or the opposite of B would be a positive six. So x is equal to, and then we have our B, negative B, which is going to be six, plus or minus the square root of six, which is our B squared, actually negative six squared, sorry about that, minus, and then in brackets four times A, which is one, times C, which is positive nine, and that's all over two times that one. So six plus or minus the square root of, and then negative six squared is positive thirty-six, and then four times one is four times nine is thirty-six, all over two. So six plus or minus the square root of, that's thirty-six minus six is zero, all over two. So it's really just six over two. I'm just going to add and subtract zero, which always will give me six, so I have three. Remember when the discriminant was zero, we had one answer, and that's what we got. So we come in here now and look at this one. Again, we have to get everything to one side. It doesn't matter what side we take it to, especially when we're doing the quadratic formula. When we're factoring, we like to keep the x squared term positive, but if I just move this one term, I'm only moving one thing, less chance of error. So I'm going to subtract two x squared from both sides. That gives me zero over here, equal to negative four x, that's a four, plus seven, that's a seven, minus two x squared. Now I did that on purpose because what is a? A is the coefficient on x squared, so it's negative two. What is b? b is the coefficient on x, which is that negative four. It's not the first term, second term, third term, it's coefficients. And then c is going to be our constant, which is going to be seven. And negative b is going to be, or the opposite of b, would be a positive four. So here we go again. This is equal to negative b, so that's the four, plus or minus the square root of b squared, negative four squared, minus, and then in brackets, four times a, which is negative two, times c, which is seven, got a little more work to do this time, all over two times a, which is negative two. So four, plus or minus the square root of negative four squared is sixteen, four times negative two is negative eight times seven, and negative eight times seven is going to give us a minus a negative 56, all over two times negative two, which would be negative four. So four, plus or minus the square root of, and minus a negative becomes plus a positive. So I'm adding 16 and 56. So that gives me 12, carry the one, six, seven, 72, all over negative four. And for me, I'm okay to leave it here. You can't simplify radicals, but we are not going to talk about simplifying radicals so we can just leave it like this. It's not a perfect square, so I can't take the square root, so I'll just leave it like that.