Exercise 55 Page 70

A perfect square trinomial equation in which the middle term is negative and the last term is a fraction looks as follows. ( ax)^2 - 2( ax)(b/c) + (b/c)^2 = 0 In the equation above a, b, and c are any real numbers and b and c have no common factors. Let's pick, for example, a= 2, b= 3, and c = 4. ( 2x)^2 - 2( 2x)(3/4) + (3/4)^2 = 0 ⇓ 4x^2 - 3x + 9/16 = 0 The final equation is the one we were requested to find. Next, let's solve this equation for x.

4x^2 - 3x + 9/16 = 0

WritePow

Write as a power

2^2x^2 - 3x + 3^2/4^2 = 0

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Simplify left-hand side

ProdPow

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

(2x)^2 - 3x + 3^2/4^2 = 0

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

(2x)^2 - 3x + (3/4)^2 = 0

Rewrite

Rewrite 3x as 2(2x)(3/4)

(2x)^2 - 2(2x)(3/4) + (3/4)^2 = 0

FacNegPerfectSquare

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

(2x - 3/4)^2 = 0

To continue solving the equation, we can take the square root of each side.

(2x - 3/4)^2 = 0

SqrtEqn

sqrt(LHS)=sqrt(RHS)

2x - 3/4 = ± 0

AddEqn

LHS+3/4=RHS+3/4

2x = 3/4

DivEqn

.LHS /2.=.RHS /2.

x = 3/8

In conclusion, the solution to the equation we wrote is x= 38. Keep in mind that the equation presented above is just an example and your answer may vary.