So, or at least that you did it, did it to a full understanding. So the main important thing, guys, if you just follow the process, the first thing you want to do is always make sure our quadratic is set equal to zero, right? Good.
Next thing, we need to label our a, our b, and our c. Please note a and b are coefficients and c is your constant. They do not include the variables. So our a, in this case, is going to be 1. Our b in this case is going to be negative 5, and our c in this case is negative 9. Everybody understand that point? Okay, so now the next thing I would say is determine the discriminant.
b squared minus 4 times a times c. So we just plug in what b is, which is negative 5 squared minus 4 times a times c. Right?
And when we get that value, we have 25. Negative 4 times negative 9 is going to be a positive 36. Yes? So therefore, that equals 61. However, the question is saying not find the discriminant. The question is saying what is the solutions. However, by knowing what the discriminant is, I determine that that is not a square number. So therefore, I am going to have two real irrational solutions.
You should just know that in your head by studying, you know, from those notes. If they ask you, that's what you would answer, but they're asking for the solutions. So to find the solutions, remember x equals is going to be our solutions.
Opposite of b, plus or minus, square root. A b squared minus 4 times a times c all over 2 times a. That's the quadratic formula.
We need to know it. We're not going to sing a song to remember it. You just need to make sure you memorize it.
Write it down in the mirror in your bathroom and keep on saying it over and over, and you guys will be good. The nice thing about this, at least the quadratic formula, is if you guys remember b squared minus 4 times a times c, you understand that that's what goes under the radical. All you need to do then is do the opposite of b.
So since b is negative 5, B is, or opposite of B is going to be positive 5. So X equals, basically it looks like this, opposite of negative 5, plus or minus the square root. Well, we already know B squared minus 4 times A times C is 61. Let me make this green so you guys can see the color code. Divided by 2 times A, which is 1. Does everybody see how I plugged in all that information?
Yes? No? Questions?
Good. So now we just simplify. Well, opposite of negative 5 is going to be 5, plus or minus. I cannot take the square root of 61, so I'm going to leave it like that, and then that's over 2. Okay?
Yes? When you're finding the solutions of a quadratic, you are using the quadratic formula. This problem was the first seven problems that I asked you to do, where it says just find the discriminants.
For the last six, it says find the solutions. What does x equal? So you have to plug it into the quadratic formula. So for the last six problems, you're using this formula for all of them.
So now that is a correctable, that is a correct way to write the problem. You could also break up the plus or minus and you could say x equals, you can also write it as in a solution set like this, 5 plus the square root of 61 over 2, comma 5 minus the square root of 61 over 2. Those are both acceptable solutions. One last thing also to understand, you can also divide the 2 into both of those terms. So it could also look like this. And I'm just telling you guys this because, you know, I don't really know how the answer is going to look.
But these are all acceptable ways. You can also divide the 2 into both of those. And if it can be simplified, usually that's what we do. In this case, that can't be simplified.
You can't divide the 2 into the 5 or the 2 into square root of 61. So leaving it like that is perfectly fine. However, if it is something you can divide into, that's another way to write those numbers or the solutions. Okay? All right.
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