Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

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Accepted Answer

Welcome back. I'm so glad you're here. We get to solve for X. And we've only got two terms. Three X to the fourth equals one oh eight X squared. And I want to get them both on the same side so that they're equal to zero. So let's subtract one oa X squared from both sides. So we'll have three X to the fourth minus one away X squared and that will equal zero. Cool. Now do those two terms have anything in common that we could factor out? Well yeah three can come out of both of those and x squared can come out of both of those. So for the first term that will leave us with just an X squared three X to the fourth divided by three X squared is just X squared and that second term um negative 108 divided by three is negative 36 x squares cancel out. So cool we've got two things being factor but we can go one step further with our factoring and we can look at this X squared minus 36 say hey that's a difference of squares. So you recall from previous lessons that when we've got a difference of squares, we've got our first term X times X will give us our X squared, our first square and then our second square is 36. Well that's going to be six times six and one will be added and one will be subtracted and that's our difference of squares. So now we've got three factors and we can set each one of them equal to zero. So we can say three X squared equals zero. We'll solve for that X. We've got X plus six equals zero. We'll solve for that X. We've got x minus six equals zero. And we'll solve for that X. For this. First this three X squared divide both sides by three. Three's cancel out while zero divided by three, that's still zero. So X squared equals zero. Take the square root. Herbal signs. Well squared of zero is just going to be zero. So this X equals zero. Hey cool. That's our choice B. Let's look at the next one. X plus six equals zero. Subtract six from both sides. So that's going to be X equals negative six. Hey that's our answer choice A. And X plus six equals zero. Or x minus six equals zero will add six to both sides. And that's going to give us X equals six. And that is our answer choice C. So we get to go with D. All of the above. Well done. We'll catch you on the next one.

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