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.

5x^2 + 2 = 11x

Accepted Answer

Hello. Today we're going to be solving the equation using any of our preferred methods. So the equation given to us is eight X squared minus three is equal to 10 X. Now since we want to sulfur X we want to go ahead and set this equation equal to zero. So I'm gonna go ahead and subtract 10 X to both sides of the equation. Doing so is going to give me eight X squared minus 10 X minus three is equal to zero. Now this is a fact arable trin Amiel because this try no meal is going to factor into the quantities four X plus one times two X minus three. And both of these quantities are going to be equal to zero. So we're gonna go ahead and solve this algebraic lee by using the zero property and that allows us to take both of these quantities and set them equal to zero. So doing so is going to give me four X plus one is equal to zero and two X minus three is equal to zero. So on the left hand side in order to solve for X we're going to subtract one to both sides of the equation. Doing so is going to give me four X is equal to negative one. And finally we're going to divide by four and that's going to give me X is equal to negative 1/4. Which is going to be our first solution. Now we need to solve the right hand side in order to do that. I'm gonna go ahead and add three to both sides of the equation. Doing so is going to give me two. X is equal to three, and all I have to do is divide the equation by two, And I'm gonna get our second solution for X, which is going to be 3/2. So we have two solutions for X. In total we have X is equal to negative 1/4, and X is equal to 3/2. With that being said, the solution to this problem is going to be C. 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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