How to Complete the Square

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In math, completing the square is an important tool in solving quadratic equations, and it is used frequently in college algebra classes. Try to work with one "x" squared when completing the square with help from a math teacher in this free video series on math help and lessons.

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Video Transcript

So how does one complete the square? Hi, my name is Jimmy Chang, I've been teaching college math for nine years now, and completing the square is actually one of the most and very important tools in solving quadratic equations. Now, it us used a lot in the college algebra type courses, as well as those of pre-calculus algebra. So here's an introduction as to how this method works. Now, you have an equation, for example, of X squared minus four X minus twelve is equal to zero. Now, the first thing that you want to be sure of when completing the square is make sure that the number in front of the X squared is just one. If it's not one, then it's a good idea to divide through, divide by the number in front. And so, for example, if it had been a two, you want to divide everything by two. It's always easier to work with the one X squared than anything else. The other thing you want to be sure of is that you want to be sure that the constant term, this last number, negative twelve, is moved over to the other side. So, to move it over you add twelve. So what you have here is X squared minus four X is equal to twelve. Now, notice here we're leaving a gap in between, because there's going to be something else that's put in there. Now, to complete the square, here's the key step. Take the number next to the X, which in this case is negative four, and take half of it. Now, one half of negative four is negative two. Now, pay attention to that number, too, because it's always going to come back later. Now, what you do with that number, is you're going to square it. Negative two squared is four. Now what do you do with that four? You're going to add that to both sides. Now why both sides? Well, because since this is an equation, you want to keep the balance on both sides. What you do to one side, you have to do to the other. So as a result you have now X squared minus four X plus four equal to sixteen. Now, from here, you can factor the left hand side. X squared breaks up to X and X. But folks, one half of negative four equals negative two. That number is going to take the place of both parenthesis. Negative two and negative two, it will always work out that way. Okay? Now, because the two of them have the same parenthesis, you can rewrite it as X minus two squared equals to sixteen, and then, to solve, take the square root of both sides. Now what's going to happen after that is the left side's going to be X minus two, but the squared of sixteen is four, but you definitely want to put a plus or minus sign, because the square root method says you need to do that. After that, break it up as two separate equations, X minus two equals to four. X minus two is equal to a negative four, and solve for X. So, I'm Jimmy Chang, and that's a demonstration as to how to complete the square.


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