Exercise 53 Page 62

We want to solve the given equation by factoring. Let's consider our equation. 81-1/25x^2=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

81-1/25x^2=0

WritePow

Write as a power

9^2-(1/5)^2x^2=0

ProdPowII

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

9^2-(1/5x)^2=0

FacDiffSquares

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

(9+1/5x)(9-1/5x)=0

Now we are ready to use the Zero Product Property.

(9+1/5x)(9-1/5x)=0

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Solve using the Zero Product Property

ZeroProdProp

Use the Zero Product Property

lc9+ 15x=0 & (I) 9- 15x=0 & (II)

SubEqn

(I): LHS-9=RHS-9

l 15x=- 9 9- 15x=0

MultEqn

(I): LHS * 5=RHS* 5

lx=- 45 9- 15x=0

SubEqn

(II): LHS-9=RHS-9

lx=- 45 - 15x=-9

MultEqn

(II): LHS * (- 5)=RHS* (- 5)

lx=- 45 x=45

We found that the solutions to the given equation are x=- 45 and x=45. To check our answer, we will graph the related function, y=81- 15x^2, using a calculator. Since 125=0.04, we will use decimal instead of the fraction.

We can see that the x-intercepts are - 45 and 45. Therefore, our solutions are correct.