In Exercises 115–122, find all values of x satisfying the given c...

Question

In Exercises 115–122, find all values of x satisfying the given conditions.

y = 2x^2 - 3x and y = 2

Accepted Answer

Welcome back. I'm so glad you're here. We have this equation. We have Y equals four X squared minus four X. And we're also told that Y equals negative ones so we can go ahead and substitute that in for why now? It's negative one equals four X squared minus four X. And we are to solve for X. Let's start off by scooting that negative one over to the right hand side of the equation so that this is equal to zero and perhaps we can do some factoring or some quadratic formula. Fun. Okay, we've got zero equals four X squared minus four X plus one. Well, let's see if we can factor that. What times what will give us a four X squared? Well we've got options but let's go ahead and work with two X times two X. Because what times what will give us a positive one? Well that's either positive one times positive one or negative one times negative one. But we know that the middle has to add up to be a negative four. So let's do a negative one in a negative one. And when we foil this out you'll see that this will add up to that negative four. So two x times two X. Our first give us four X squared our Outsides to X times negative one will be a negative two X. Our insides negative one times two X will be a negative two X. And our last negative one times negative one is plus one combining like terms in the middle four X squared minus four X plus one. There we go That matches. So we factored correctly and they're the same factor. They're both two x minus one. So we can just set one of those equal to zero to solve for X. Two X minus one equals zero. We will add one to both sides. So we've got two X equals one. We'll divide both sides by two and we'll get X equals one half. We look at our answer choices and that matches with answer choice B. Well done will catch on the next one.

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