 Okay, we are going to discuss one other method of solving quadratics. This video will discuss how to solve quadratics using square roots. So you can use the square root method in a couple of different cases. The most common case to use the square root method will be whenever your b value is zero, or in other words, you don't have an just x term, you only have x squared terms. So this is a very basic example, x squared equals nine. Once the x squared is by itself, you can simply take the square root of each side. And in this case, we would get x is equal to, and here is what most students forget, positive or negative three. Because it's a square root, an even root, it has to include both the positive and the negative value of the number. So in this case, x could equal positive or negative three. Now, here we also have a very basic example because we just have x squared is equal to a number again, but notice in this case that x squared is equal to a negative value. Now we know that whenever we square a number, it will give you a positive value, but that only is the case if we're dealing with real numbers. So here, whenever we take the square root of a negative, we will end up with a complex number solution. So when we take the square root of each side, we still have to include the positive and the negative, and so here we would get x equals positive or negative square root of negative one. And as we learned earlier, whenever you have the square root of a negative, that introduces the number i, and the square root of negative one is just simply one i. So the solution to this problem would be x equals positive or negative i. Let's look at a few that are a little bit trickier. Not much, but just a bit. So in order to solve this problem like the previous two problems, what we'll want to do is we want to first isolate the x squared. In order to isolate the x squared, we first can move the 5 to the other side of the equation by adding it to each side. Now you could take the square root at this point, but it will be a little bit trickier with this coefficient, so i would first divide each side by that coefficient so that the x squared is completely by itself. And to solve this, then, is just like the previous two examples. We get the square root of each side, and the square root of one is a positive or a negative one. So x, in this case, is equal to a positive or a negative one. Now these next examples that we're going to look at still will use the square root method, but they just look a little bit different than before. Whenever we have an expression that is written as a perfect square, so x plus one squared, and then it has no just single x's on the other side of the equation, that's a good case where we can again use the square root method. So what you want to do in this case to use the square root method is take the square root of each side, just like we have in the past. When you do that here, you end up with x plus one on the left side of the equation, and then on the right, it will equal a positive or a negative three. So when you isolate the x, you'll subtract one from each side, and you would end up with negative one plus or minus three. Now, I don't think you should leave your answer like that because you can easily evaluate each expression there. You can add the two together, negative one plus three will give you two, and then you could subtract as well. Negative one minus three will equal a negative four. And so the two solutions again that we get are that x is equal to either two or negative four. So just like before, make sure you're getting two solutions for each problem, but this one just requires an extra step at the end. All right, let's look at just one more example of using the square root method. Here, we have x plus two quantity squared equals negative 16. So hopefully what you notice here is because we have this quantity squared equal to a negative, we're going to end up with some imaginary numbers in our answer. First, I'm going to take the square root of each side of the equation, and in doing so that cancels out the squared on the left, I get x plus two. On the right, I have positive or negative square root of negative 16. Now, when we take the square root of a negative, it introduces an imaginary number. So the square root of 16 is four, but because it was a negative, it will be four i. So we end up with x plus two equals positive or negative four i. Then to solve for x, we'll subtract two from each side. We get x equals negative two plus or minus four i. And unlike the previous problem, we can't combine terms here because this has an i with it, the four does, whereas the negative two doesn't have an i. So we just have both a real and imaginary part to our answer. Our answer will be x equals negative two plus four i and x equals negative two minus four i. So that's a quick rundown of how to solve quadratics using square roots. I hope that helps as you go through the rest of your practice problems.