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Liberty University
Solve Quadratic Equationsby Factoring - Example 3


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equation for X squared plus seven X minus two equals zero. What we're trying to do is we're trying to find what X could be to make this quadratic equation equals zero. I noticed that my A coefficient is greater than one. So what we need to do first is we need to move it over to the sea, tow our constant so that we can fact short factoring. So we're gonna move it over by multiplying. So we're gonna multiply negative two times four, which is negative. Eight. So this is how we'll start factory. So we're gonna look for two factors of negative eight that are going to give may a sum of seven. Well, we know are two factors. We have negative eight and positive one. And when I add them, they give me negative seven. Well, let's switch our negative around and let's do positive eight and negative one. When I add those together, they give me positive seven. So I have those two factors of X plus eight and X minus one. Not these are not a factors yet, because remember how we move this for over. We need to move it back. So we need to go ahead and divide by four. And if we can simplify, simplify. Well, in the case of 8/4, that will change to to. So we'll go ahead and change that to X plus two. Now, in this case, negative 1/4 will not simplify to a whole number. So what I want to do instead is I wanna move my four that denominator in front of my ex, so I'll have four X minus one. And those are my two factors. So we're gonna work out. So we're gonna have X plus two and four X minus one, and they're both going to equal zero. So the work him out, we're gonna make him individually equals zero. So x plus two equals zero and four x minus one equals zero. We're gonna go ahead and start by subtracting, too. So X equals negative to would be your first one. Here. We'll add one. So we have four x equals one and we'll divide by four. X will equal 1/4. So our solutions are negative too. And one fourth