Exercise 55 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. 4a^2=9/64 ⇔ 4a^2-9/64=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

4a^2-9/64=0

WritePow

Write as a power

2^2a^2-(3/8)^2=0

ProdPowII

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

(2a)^2-(3/8)^2=0

FacDiffSquares

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

(2a+3/8)(2a-3/8)=0

Now we are ready to use the Zero Product Property.

(2a+3/8)(2a-3/8)=0

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Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc2a+ 38=0 & (I) 2a- 38=0 & (II)

SubEqn

(I): LHS-3/8=RHS-3/8

l2a=- 38 2a- 38=0

DivEqn

(I): .LHS /2.=.RHS /2.

la=- 316 2a- 38=0

AddEqn

(II): LHS+3/8=RHS+3/8

la=- 316 2a= 38

DivEqn

(II): .LHS /2.=.RHS /2.

la=- 316 a= 316

We found that the solutions to the given equation are a=- 316 and a= 316. To check our answer, we will graph the related function, y=4a^2- 964, using a calculator. Since 964=0.140625, we will use decimal instead of the fraction. Note that the calculator will use the variable x instead of a.

We can see that the x-intercepts are - 316, or - 0.1875 and 316, or 0.1875. Therefore, our solutions are correct.