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.

(3x - 4)^2 = 16

Accepted Answer

Hello today we're going to be solving the equation using any preferred method. So the equation given to us is the quantity two x minus one squared is equal to nine. Now I want to go ahead and solve for X. So I need to get this quantity outside of the square in order to do that, I'm going to go ahead and take the square root of both sides of the equation and doing so is going to give me two. X minus one is equal to the square root of nine which is three. Now you need to be careful though because every time you take the square root of a number it's going to produce a positive and negative value. So two x minus one is actually equal to positive and negative three. So you have two instances of this equation, one where two x minus one is equal to positive three and the other where two x minus one is equal to negative three. And we're going to need to solve for X in both cases on the left hand side and can go ahead and add one to both sides of the equation. And doing so is going to give me two, X is equal to four. Now finally I can divide both sides of the equation by two and that's going to give me X is equal to positive two. And that's going to be the first solution to our equation. Now on the right hand side I'm gonna go ahead and add one again to both sides of the equation. Doing so is going to give me two X is equal to negative three plus one, which is negative two. And if I divide both sides of the equation by two, X is going to equal to negative one and this is going to be the other solution to our equation. So in total, there are two solutions to this equation. X is equal to two, and X is equal to negative one. With that being said, the answer to the problem is going to be deep. 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.

Watch next