Question

Brian is solving the equation x^2 - 3/4x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

The value that must be added to both sides of the equation is 9/64

Explanation:

we have

`x^(2) -(3)/(4)x=5`

Divide the term -3/4 by 2

`((-3/4))/(2)=-(3)/(8)`

squared the term (-3/8)

`(-(3)/(8))^(2)=(9)/(64)`

Adds the term 9/64 both sides of the equation

`x^(2) -(3)/(4)x+(9)/(64)=5+(9)/(64)`

Rewrite as perfect square

`(x-(3)/(8))^(2)=(329)/(64)`

therefore

The value that must be added to both sides of the equation is 9/64