Solve each equation in Exercises 73–81 by the method of your choi...

Question

Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0

Accepted Answer

Hello today we're going to solve an equation using any method of our choice. So the equation given to us is two, X squared minus five, X plus one is equal to zero. And I'm gonna go ahead and choose the method of the quadratic equation to solve this. So let's go ahead and recall what the quadratic equation is. Quadratic equation. The quadratic equation states that if we have a trine Amiel in the form of a X squared plus bx plus C equal to zero then we have X. Is equal to negative B plus or minus the square root of B squared minus four times a times C. All of that over to a. So we're gonna use this equation to go ahead and solve the values for X. Well what is our A B and C in this case? Well A is just the number in front of the X squared term. So in this case here A is going to be two. B is the number in front of our x term and in this case our B is going to be negative five and c is just the constant at the end of the tri no meal and c is gonna be one. So now all we need to do is take these three values and plug it in to our quadratic equation. Doing so is going to give me X is equal to negative negative five plus or minus the square root of negative five squared -4 times two times 1. All of that over two times 2. Okay now we just need to go ahead and simplify this a little bit negative. Negative five is just gonna give me positive five, -5 Squared is going to give me and negative four times two is negative eight times one is still going to be negative eight and all that is going to be over two times two, which will be four. Now let's just go ahead and simplify a little further, 25 minus eight is going to give me 17 so we have five plus or minus the square root of 17/4. Now there's really nothing much that we can do to simplify the study further. So this is gonna be our solution right here. That also means that the solution to this problem is going to be a so I hope this video helps you in understanding how to use the quadratic equation and I'll see you all in the next video.

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