Solve each equation in Exercises 83–108 by the method of your cho...

Question

Solve each equation in Exercises 83–108 by the method of your choice.

x^2 - 2x = 1

Accepted Answer

Hello today we're going to be solving the following equation using any of our preferred methods. So the equation given to us is x squared minus four X is equal to Now since we want to solve the equation for X we're going to go ahead and set this equation equal to zero. And in order to do that we're going to subtract two to both sides of the equation. Doing so is going to give me X squared minus four. X minus two is equal to zero. And we're gonna go ahead and solve this using the quadratic equation. Now just to quickly recall what the quadratic equation is. It is when X is equal to negative B plus or minus the square root of B squared minus four times A times C. All over two A. And this is when a B and C are equal to the coefficient of a tryin Amiel. Well here is going to be the coefficient in front of our x square term which is going to be one. So A is equal to one. B is going to be the coefficient in front of our X term. So B is equal to negative four and C is just gonna be the constant. So C is equal to negative two. Now we're gonna go ahead and plug this into our quadratic equation and that's gonna give us X is equal to negative B which is negative negative four. So positive four plus or minus the square root of negative four squared minus four times A. Which is one times C which is negative two. All of that over two times a which is one. Now simplifying this four, negative four squared is going to give us 16 and negative four times one times negative two is going to give us eight. So we have X is equal to four plus or minus the square root of 16 plus eight. All over two times one which is two now 16 plus eight is going to give this the value of 24 so X is equal to four plus or minus the square root of 20 for over two. And the square root of 24 can be rewritten as two times the square root of six. So X is going to equal to four plus or minus the square to Times The Square Root of six, All Over two. Now if we pay attention to our numerator, our numerator has coefficients with a common factor of two. So we can factor out a two from our numerator. Doing so is going to give us X is equal to two times two plus or minus the square root of six. All over two. And we can go ahead and cancel out the two from the numerator and denominator that is going to leave us with X is equal to two plus or minus the square root of six and this is going to give us two solutions in total. This is when X is equal to two plus the square root of six. And this is also when X is equal to two minus the square root of six, and this is going to be our solution to the equation given to us. And that also means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to solve this type of equation, and I'll go ahead and see you all in the next video.

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Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 2x = 1