Exercise 52 Page 62

To solve the given equation by factoring, we will start by rewriting it, so that all terms are on the left side of the equality sign. 1/4b^2=16 ⇔ 1/4b^2-16=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

Now we are ready to use the Zero Product Property.

We found that the solutions to the given equation are b=- 8 and b=8. To check our answer, we will graph the related function, f(b)= 14b^2-16, using a calculator. Note that the calculator will use the variable x instead of b. Also, as 14=0.25, we will use the decimal instead of the fraction.

File:Solution5736 1.svg

File:Solution5736 2.svg

We can see that the x-intercepts are - 8 and 8. Therefore, our solutions are correct.