 Let's do a quick review of the quadratic formula as you might see it used in physics courses. Now in your math classes, you commonly see the quadratic formula in this sort of a situation where you've got numbers for a, b, and c, some sort of variable, often x, listed as x squared, x, and then no variable there. In physics, you might see something that looks like this. May not look like it's exactly the same, but if you do some basic algebra on it, rearrange the terms, you end up with an equation of this form. So this may be a situation where, again, I've got numbers for a, b, and c, I've got a variable squared to the first power, this is a quadratic equation. quadratic formula says if I have an equation of that form, then I can find the solution, the value for x, using this. And in general, there's two solutions for every quadratic equation, and one of them is found when you've got the plus sign, and one of them is found when you're using the negative sign. So you actually solve this equation twice. Let's take an example of that with our physics equation that we just had a moment to go. First thing you realize is that we're solving for t, not for x, but if I look at our basic equation, I can pull my numbers out, and I find my a, my b, and my c by looking at the appropriate terms. If I take that, realizing that I've got my values that I'm solving for, my variable, my a, my b, and my c numbers, I can then plug them into my quadratic solution. And for this one, I end up with this sort of a format. And again, you can pause the video at this point and actually plug stuff in and look at it for yourself, but instead of x, I've got t, I'm plugging in for my b, my b squared, my a, my c, my a, plugging in all of those values. Once you've got all those things plugged in, then you want to start simplifying. Putting that same equation up here at the top, we can see that we can start simplifying. If you've got minus signs out here, two minus signs make the positive. My number that I've got squared and my other numbers, I can multiply those out. Do be careful on this squared here, because if your b is negative, it's the negative number that's squared. So it's negative 2.3 times negative 2.3. And so that should always give you a positive number. Putting it just a little bit further in my simplification, I can add up those two numbers, take the square root, and that's going to give me a value. Again as a caution, what you've got underneath the square root must be a positive number. If it's not a positive number, you've either made a mistake in your algebra or you've got bad numbers. Once we've got it down to this form, we can solve it first with the plus and then with the minus. So for these particular numbers, you should get these two solutions. And I encourage you to pause the video, plug it into your own calculator, and find your answers. There's something that goes a little bit beyond math here. In math, these are just the two possible solutions. In physics, these two solutions have meaning. So in this case, if this is time, the fact that I've got one answer positive and one answer negative means this is the answer which happened after the start of the event, and this is a time where I'd have the same physical conditions, but it actually is before the start of the event. So sometimes using a little bit of common sense, you can figure out which of the two solution is correct, but there's always going to be two solutions. We're going to use the quadratic formula as we're solving physics problems throughout this semester, so if you're not really familiar with it, you might want to practice up. Again, go back through the video, pause it where you need to, plug in some different numbers, calculate it out, and make sure you're getting the same answers.