Exercise 50 Page 62

We want to solve the given equation by factoring. Let's consider our equation. 64x^2-1=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

64x^2-1=0

WritePow

Write as a power

8^2x^2-1^2=0

ProdPowII

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

(8x)^2-1^2=0

FacDiffSquares

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

(8x+1)(8x-1)=0

Now we are ready to use the Zero Product Property.

(8x+1)(8x-1)=0

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Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc8x+1=0 & (I) 8x-1=0 & (II)

SubEqn

(I): LHS-1=RHS-1

l8x=- 1 8x-1=0

DivEqn

(I): .LHS /8.=.RHS /8.

lx=- 18 8x-1=0

AddEqn

(II): LHS+1=RHS+1

lx=- 18 8x=1

DivEqn

(II): .LHS /8.=.RHS /8.

lx=- 18 x= 18

We found that the solutions to the given equation are x=- 18 and x= 18. To check our answer, we will graph the related function, y=64x^2-1, using a calculator.

We can see that the x-intercepts are - 18, or - 0.125, and 18 or 0.125. Therefore, our solutions are correct.