Exercise 48 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. 36w^2=121 ⇔ 36w^2-121=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

36w^2-121=0

WritePow

Write as a power

6^2w^2-11^2=0

ProdPowII

a^m b^m = (a b)^m

(6w)^2-11^2=0

FacDiffSquares

a^2-b^2=(a+b)(a-b)

(6w+11)(6w-11)=0

Now we are ready to use the Zero Product Property.

(6w+11)(6w-11)=0

▼

Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc6w+11=0 & (I) 6w-11=0 & (II)

SubEqn

(I): LHS-11=RHS-11

l6w=- 11 6w-11=0

DivEqn

(I): .LHS /6.=.RHS /6.

lw=- 116 6w-11=0

AddEqn

(II): LHS+11=RHS+11

lw=- 116 6w=11

DivEqn

(II): .LHS /6.=.RHS /6.

lw=- 116 w= 116

We found that the solutions to the given equation are w=- 116 and w= 116. To check our answer, we will graph the related function y=36w^2-121 using a calculator. Note that the calculator will use variable x instead of w.

We can see that the x-intercepts are - 116, or - 1.83, and 116 or 1.83. Therefore, our solutions are correct.