The Quadratic Formula

So here we're dealing with the quadratic formula. We're gonna say the quadratic formula is used for algebraic equations that contain a variable X rays to the second power. Now, a customary expression is a X to the to plus B times X plus c. Okay, so here a and B are just numerical values. Okay, so the actual numbers they're saying here on the same thing would CIA's well, exes are just missing variables. We're going to see the quadratic formula, which is shown here. It's X equals negative B plus or minus square root of B squared minus four a c over to a here. It says the quadratic formula is most commonly used for questions dealing with chemical equilibrium. So when we get to the sections dealing with chemical equilibrium, we're gonna use things that are called ice charts. And these ice charts helping me toe find equilibrium concentrations. So equilibrium amounts or concentrations. That's when we typically use thes. Now you may use the quadratic formula before then within your lab, so it's still important to remember. So we're gonna say although the presence of the positive negative sign gives two possible values for X on Lee. One of them will be significant and used as the answer. So again, because there's a plus or minus here. That means we have a possibility of two answers for our X when we do different types of questions usually means that we have only one possibility when it comes to our final answer. Now, knowing this, let's see if we can solve this question here it says using the quadratic formula solve for X when given the following algebraic expression. So let me take myself out of the image guys, because we're need room to do this. So we're gonna say, here we have four X equals two point negative, 2.13 times 10 to the negative, four plus 1.75 times 10 to the negative five over X. Again, we want our expression toe look, something like this, and we want at least have an X that is squared to be able to do the quadratic formula here. We don't have that and we have this number over X. So we're gonna do here is we're gonna multiply both sides by X, and when we do that, we're gonna get four x squared equals negative. 2.13 times 10 to the negative four x This x will cancel out with this X, so we're gonna get 1.7 plus 1.75 times 10 to the negative five. All right, now we're gonna say that this X variable has the larger power. So it's our lead term. That means that everything has to meet, be moved over to its side. So we're gonna add to 13 times 10 to the negative four x to both sides and then we're gonna subtract 1.75 times 10 to the negative five from both sides. So here's what we're gonna get At the end for expression is four x squared plus 2.13 times 10 to the negative four x minus 1.75 times 10 to the negative five. So this represents my a might be and my seat. So my quadratic formula is remember negative B plus or minus go up up so you can see it. Plus or minus B squared minus four a. C squared B squared minus four c over to a. Alright, so here the sign of B is positive So when I throw it in, it's gonna become negative now, plus or minus B squared, minus four for a the value in front of a is a four. And then see the value is this. Do not forget the negative sign. Okay? So if there was a negative sign here for be, let's say that this was negative, then this would have been positive, have been the opposite. And then we would have had to put the negative. There is. Well, okay, so don't forget the signs get introduced. A swell divided by two times four fight. So Oops. So now we're gonna say that I'm gonna take the square root of everything in here. Okay? So what I'm gonna do first, I'm gonna figure out what everything is in there. Now, if you do it correctly, your calculator You should get square root of 2.0 times 10 to the negative four, divided by eight, then realize they're gonna get two x variables. Because, remember, it's plus or minus. So X equals negative. 2.13 times 10 to the negative. Four plus. So when I take the scroll to that number, it's gonna give me 40. which gets divided by eight. So that gives me 002065 for X. Then remember, we could also have X equals negative 213 times 10 to the negative four minus because, remember, it's plus or minus divided by eight. And in this case, X equals negative. 0. So these are my two answers that X could be again. When we finally use this within our lectures, we're gonna be using it for usually equilibrium questions. So chemical equilibrium questions and only one of these answers will be the vital answer. And usually it's. The positive answer is the one that we use. We discard the negative one, but we'll talk about that later on when we're dealing with chemical equilibrium, ice charts and all that stuff. But for now, just remember what the quadratic formula is, what makes it up and how the expression needs to be. It needs to take on the form of X squared, plus BX plus C to give us the variables that we need in order to solve. For X will get two answers and usually only one of them is a viable answer. The other one will be discarded. We'll talk about the conditions and reasons for discarding which one later on.