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Liberty University
Solve Quadratic Equations Algebraically - Example 3


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the X squared minus four X is less than or equal to five outta Brickley. So in order to do that, let's rewrite this as a quadratic equation. So X squared minus four X minus five would equal zero so we can factor the South. So we're looking for two factors of negative five that add together and give me negative four. Well, that's gonna be negative five and positive one. So my factors air X minus five, an X plus one, and they'll equal zero. So now that we have that, let's work those out. So X minus five equals zero X plus one equals zero. We're gonna add five. So X is going to equal five. We're going to subtract one. So X is going to equal negative one. So let's create our number line. So we have X equals five and we have X equals negative one. All right, so we'll have negative one, and we'll have positive five, and we'll have zero. I know that's not exactly even, but we just kind of wanna demonstration to show, so we're going to buy this into three sections. The first section is where X would be less than negative one. We have a section where X is greater than five and we have the section where negative one is less than X, which is less than five. So we're gonna test our number. So negative one. Let's do negative too. So we're gonna put in negative two squared minus four times negative two, and we're gonna see if that's less than or equal to five as four plus eight and four plus aid is 12. 12 is not less than or equal to five. So I'm gonna go ahead and check this middle section instead of the last section. Because usually if the if this section is false, typically this one is gonna be too. So let's go ahead and check this middle section a number between negative one and five. We can just do zero we that works. So we will do zero squared minus four times zero, which is going to give me zero. And we want to know if zero is less than or equal to five. And the truth is it ISS. So this means that my solution is negative. One less than X, which is less than five. So negative one is less than X, which is less than five