Exercise 37 Page 69

To solve the given equation by factoring, we will start by identifying the values of a, b, and c. x^2- 3/2x+ 9/16=0 ⇔ 1x^2 - 3/2x + 9/16=0 Notice that this equation follows a special pattern. It can be factored as a perfect square trinomial.

x^2-3/2x+9/16=0

FacNegPerfectSquare

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

(x-3/4)^2=0

Now we are ready to use the Zero Product Property.

(x-3/4)^2=0

ZeroProdProp

Use the Zero Product Property

x-3/4=0

AddEqn

LHS+3/4=RHS+3/4

x=3/4

We found that the solution to the given equation is x= 34. To check our answer, we will graph the related functions y=x^2- 32x+ 916 and y=(x- 34)^2 in the same coordinate plane using a graphing calculator.

We see that only one graph appears. This means that both graphs coincide. Therefore, 34 is the correct solution. ✓