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Liberty University
Solve Quadratic Equations Algebraically - Example 4


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quality Negative X squared minus six. X plus seven is less than or equal to zero. We're gonna solve it Algebraic Lee, and we're gonna do this. We're gonna start off by factoring and finding the factors. So we wanna find two factors of seven that are going to give me a negative six. Well, the best way to do this one is using the quadratic formula. Remember that the quadratic formula says that negative B plus or minus the square root of B squared minus for a C is divided by two A. So for this one, we're gonna have X equals negative negative six plus or minus the square root of negative six squared minus four times negative one, Tom. Seven over. Two times negative one. So that's gonna be a six plus or minus the square root of 36 plus 28 over Negative too. And that's gonna simplify. 36 plus 28 is going to simplify to 64 over negative to now. Square root of negative square root of 64 equals eight. So this is going to be a regular number. Okay, so we're just not gonna be a complex number, so we're gonna start off with six plus eight over negative too. And that's gonna be 14 divided by negative too, Which is going to be negative. Seven. The other one we're gonna have is X is gonna be six minus eight over negative too. So that's negative to over negative two, which is one. So I'm gonna have X equals negative seven and X equals positive one. So in my number line, that's how I'll draw it. So have one. We'll have negative seven. And in between, we'll have zero. It's not gonna be exactly in between, but it's enough to kind of show our demonstration. All right, so we're gonna divide this into three parts. The first part is where X is less than negative seven, where X is greater than one and negative seven is less than X, which is less than one. So let's start off with X is less than negative seven. So we're gonna pick a number less than negative seven. Let's just do negative eight, and we're gonna plug that in, so we're gonna have negative negative eight squared minus six times negative, eight plus seven. So when I work that out, I'm gonna get negative nine. And we're saying negative nine is less than or equal to zero. And that statement is true. So that means we're going to come over here and we're gonna check X is greater than one. So let's pick a number greater than one. Let's pick two. So we're gonna use negative two squared minus six times two plus seven. And when I use that, I'm going to get negative. Non is less than or equal to zero, which is true. So that means that both these are true. So my final answer is X is less than negative. Seven or X is greater than or equal to one.