In Exercises 127–130, solve each equation by the method of your c...

Question

In Exercises 127–130, solve each equation by the method of your choice.

√2 x^2 + 3x - 2√2 = 0

Accepted Answer

Welcome back. I'm so glad you're here. We are Given an equation. We've got the square root of five X squared minus two. X minus three squared to five equal zero. And we get to solve for X. Using any method that we want. Which I mean that's very exciting. Except this is just one of the most unb you Biffle formulas ever. I mean look at this. If this is R A x squared plus bx plus C equals zero. Are a value is the squared of five, R B is negative two. That's not too bad. And r C is negative three squared to five. I mean yuck. Ok when you have something looking like this, just go straight to the quadratic formula. Um So instead of trying to factor that our U substitution or something, I don't even know. Let's just go for the quadratic formula. Our good friend, the reliable quadratic formula which is as you recall from previous lessons negative B plus or minus the square root of B squared minus four times a times C. All over two. A. Okay, we've identified our A's and B's and c's. So now let's go ahead and start filling that in. So negative B. That's a negative negative two plus or minus the square root of B squared. So that's negative two squared minus four times A. Which is the square to five times C which is negative three squared five. Bring over that radical and all over two times the square root of five. Okay, we can do this negative negative two is two plus or minus. The square root of negative, two squared is four minus. Okay, let's do this a chunk at a time. So four times square to five is going to be four square to five. Still times negative, three squared to five. All over two times square to five is two square to five. And continuing to simplify inside that radical, that'll be two plus or minus the square root of four. So a negative four square to five times a negative three squared to five gives us a plus 12 square root of five times five is 25 all over two square five. Okay, so continuing to simplify two plus or minus inside the radical we've now got four plus 12 times the square of 25 is five Over two sq - five. And continuing to simplify to plus or minus the square root of four plus 12 times five is 60. This is looking good over two square to five. So inside that radical, two plus or minus the square root of Over two square to five and that is two plus or minus eight. The squared of 64 is eight All over two square to five, exciting. Okay, so now we've got two problems because one is going to be the plus and one is going to be the minus. So we've got two plus 8/2 square to five and we've got two minus 8/ square +252 plus eight is 10/2 square to five and two minus eight is negative 6/2 square to five. And then doing just one more step of simplification. 10 divided by two is five over the square to five and negative six divided by two is negative three over the square to five. Okay, I'm going to rewrite that higher up so that when I scroll up we'll still see it five over the square 25 and negative three over the square root of five. Normally we don't want to leave a square root of five in the denominator, but if you look at our answer choices, they do have some with the square to five in the denominator. So we could be looking at A or D. Here but none of our answer choices are five square to five. So let's do the work to get that squared of five out of the denominator and see if it matches either negative square root of five or positive square root of five. So we're going to multiply both the numerator and the denominator by the square to five because the square to five over the square to five, that's just one. And so in the top, multiplying straight across, that's five square to five. And on the bottom that is the square root of 25. So we've got five squared to five over squared of is five. Fives cancel out. And that gives us the square root of five for this first one. So which answer choice matches those two solutions that is going to be answer choice. D. Well done. We'll catch you on the next one.

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