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.

4x^2 - 16 = 0

Accepted Answer

Hello today we're going to be solving this equation using any preferred method. So the equation given to us is five, X squared minus 245 is equal to zero. Now on the left hand side, both of our terms have a common factor of five. So we can go ahead and factor out five from the left hand side of the equation. Doing so is going to give me five times X squared minus 49 is equal to zero. And I can go ahead and divide both sides of the equation by five. So this way I can isolate the values of x squared minus 49 divided by five is going to give me X squared minus 49 is equal to zero. Now X squared minus 49 is a difference of squares as it can factor to the values X plus seven times X minus seven. And that is going to be equal to zero. So we can solve this algebraic lee by using our zero property and applying the zero property to both of these quantities is going to give us X plus seven is equal to zero and x minus seven is equal to zero. Now, in order to solve these quantities, I'm gonna go ahead and subtract seven to both sides of this equation and add seven to both sides of this equation. And this is going to give me X is equal to negative seven and X is equal to positive seven. And these are gonna be the solutions to our given equation. And since these are the solutions to our equation, 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.

Watch next