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.

2x^2 - x = 1

Accepted Answer

Hello today we're going to solve this equation using any of our preferred methods. So the equation given to us is four X squared minus two, X is equal to six. Now since we want to go ahead and solve this equation we're gonna go ahead and set it equal to zero in order to do that. We're just gonna go ahead and subtract six to both sides of the equation and doing so is going to give me four, X squared minus two, X minus six is equal to zero. Now if you notice to the coefficients of every term here we have 42 and six. Each of these terms has a common factor of two. So what we can go ahead and do is divide the entire equation by two and doing so is going to give us two, X squared minus x minus three is equal to zero. Now this is a fact arable trin Amiel as this try no meal is gonna factor to the quantities X plus one times two x minus three equal to zero. And what we can go ahead and do is solve this algebraic lee by using our zero property by using the zero property. We get two instances where X plus one is equal to zero and two X minus three is equal to zero. So let's go ahead and solve the right hand side first. Since we want to solve for x we're 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 finally what I want to do is divide both sides of this equation by two. And that's going to give me X is equal to 3/2, which is our first solution for X. Now we're gonna go ahead and solve the left hand side and we only have to do one step which is subtract one to both sides of the equation. And what we are left with is X is equal to negative one, which is going to be our second solution. So in total, we have two solutions for X. X is equal to negative one and X is equal to 3/2. With that being said, the solution to this problem is going to be a 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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