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In each of the following exercises, solve the given inequality.$$x^{2}-4 x-41>0$$

$$x<2-3 \sqrt{5} \text { or } x>2+3 \sqrt{5}$$

Algebra

Chapter 0

Reviewing the Basics

Section 5

Solving Non-Linear Inequalities

Equations and Inequalities

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:31

In each of the following e…

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02:36

02:40

03:14

02:25

03:13

06:15

02:55

02:45

04:32

05:26

02:11

02:51

Solve each inequality.…

02:24

All right, we've got a question here. X squared minus four X is less than 41. Scuse me. Minus 41 is greater than zero. Okay, What we want to do first is one a factor. This and we can see that it's not a simple factors. We're gonna plug it into a quadratic formula, and we'll get our excess equal to tu minus three, Route five. And you'll get a for your second value to plus three, Route five. Once you get your ex values, after plugging into the quadratic formula, you try out a number line that goes from negative infinity to infinity. And you put two minus three, Route five labeled on there and you put two plus three Route five they put on there. All right. And then what you gonna do is you're gonna solve for the regions within these points between these points and up until infinity and negative infinity to determine what region of X values will satisfy this inequality. So we'll pick a value between two and excuse me two plus three, Route five. And then we will plug it into our main equation here and see whether or not that satisfies the inequality. So two plus three through five is about 8.7. So let's pick nine. And that will be a value between two plus 35 and infinity. We'll do nine squared for our X. We're gonna play a nine for our X. We'll do nine squared minus four times nine minus 41. And we put that in and we'll get 81 minus 36 minus 41. That comes out to before, and we can confirm that four is greater than zero. Therefore, this region does satisfy the inequality. Pick a value in between Tu minus 35 We could pick zero. So with zero minus zero minus 41. And we know negative 41 is not greater than zero. Therefore, this region does not satisfied inequality. We plug in a negative nine here for the value between negative two minus 35 in a negative infinity and we'll get we plug this into our handy dandy calculator will get 81 plus 36 minutes 41. We'll get about 76. We know that 76 is greater than zero. So this region also satisfies inequality. So for our X domain will Right that ex Excuse me. Whenever X is less than two minus three, Blue five. Inequality is satisfied. And then whenever X is greater than two plus three. Route five, we'll say, Well, the inequality is satisfied. All right, well, I hope that clarifies the question. Thank you so much for watching.

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