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Quadratic equations | Worked example

Sal Khan works through a question on quadratic equations from the Praxis Core Math test.

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  • male robot hal style avatar for user Noah Dixon
    lol, I'm in 6 grade and I did this and got it correct. Quadratic equations are fun. I also watch through the entire video and I did the same thing. Thanks, sal. U dah best.
    (1 vote)
    Default Khan Academy avatar avatar for user

Video transcript

- [Instructor] We are told if four X squared plus nine is equal to 25, and X is greater than zero, what is the value of X? And they've given us five choices here so like always, pause this video and see if you can answer this on your own. Okay now let's do it together. And so we have this equation here, and you might recognize this that if you have a term here that's dealing with an X squared, this is officially a quadratic equation, which is a very fancy word, but it's really just an equation where we have an X being raised to a 2nd power like this. Now lets just rewrite it and think about how we would go about solving it. Now quadratic equations can get quite involved, but in the Praxis, they tend to be pretty straightforward. What we really want to do is isolate the term that has the X in it, and maybe we want to isolate it on the left hand side, and then we can think about how to solve for X. So if we just wanna have the four X squared here on the left we'd want to get rid of this nine. The best way to get rid of that nine is to subtract nine, but of course, in order to maintain the equality, you have to do whatever you do to the left, you have to do to the right. And so we are going to be left with, on the left hand side, the nines cancel out and so you just have four X squared is equal to, and on the right hand side, 25 minus nine is equal to 16. Now if we want just an X squared on this left hand side, the best thing to do would be divide by four. But of course if we want to maintain the equality, we'd have to do the same thing on the right hand side. And so, we get on the left hand side, X squared is equal to, and on the right hand side, 16 divided by four is equal to four. And so, you could say, you could either just try to think through, well what number squared is equal to four, or, and this is where you have to be careful, you could say X is equal to the plus or minus square root of four. Now what is the square root, or some people would call it the principal root of four? Well that's going to be two. So we would say X is going to be plus or minus two, and you might have been able to get that just from this step right over there. Now you might say, I just see a two, where's the negative two, but they tell us that X is greater than zero, so we know that X is going to be positive two, so it's going to be this choice, right over there.