In this video, we're looking at how we can use the completing the square method to solve quadratic equations like these two. The first step in questions like this is to rearrange the equations into the form of x plus p squared plus q, which is the form that we'll end up with when we complete the square. We've actually already covered how to do this in our last video though. So in this one we'll assume that we've already rearranged them, which would make our two equations look like this. Once we've got them in this form, we have to rearrange them a bit more to get the x by itself.
So for this one on the left, x minus 5 squared minus 7 equals 0, the first thing we want to do is add 7 to both sides to get x minus 5 squared equals 7. Then we can square root both sides to get x minus 5 equals plus or minus root 7. Because remember, whenever we square root a number, there are two possible solutions, a positive one and a negative one. And lastly, we need to add 5 to both sides to get x equals plus or minus root 7 plus 5. So really, we have two solutions for x. Either x equals positive root 7 plus 5, or x equals negative root 7 plus 5. And if they ask for the answer to a certain number of decimal places or significant figures, then you can just plug each of these into your calculator. For this next question, x plus 3 squared minus 1 equals 0, we do basically the same thing.
So first, we add 1 to both sides to get x plus 3 squared equals 1. Then we square root both sides to get x plus 3 equals plus or minus root 1, which is really just plus or minus 1 because the square root of 1 is just 1. And then we can subtract 3 from both sides to get x equals plus or minus 1 minus 3. So again we have two possible solutions, either x equals positive 1 minus 3, which means x equals negative 2, or x equals negative 1 minus 3, in which case x equals negative 4. So to sum all of this video up, whenever you want to solve a quadratic equation using the completing the square technique, you need to first of all rearrange it, into the form of x plus p squared plus q, which we do by completing the square, and then you need to rearrange it again to get the x by itself. And whatever x is equal to is your solution, but you'll normally end up with two solutions. That's everything for this video though, so hope you found it useful, and thanks for watching!