Question

Brian is solving the equation x2-3/4x=5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

divide 3/4 by 2 and then square it. 3/4/2=3/8 squared which is 9/64.

Answer 2

we have

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

Divide the term
`(3)/(4)` by
`2` and then square it

`(((3/4))/(2))^(2)= (9)/(64)`

Add to both sides

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

Rewrite as perfect square

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

therefore

the answer is

`(9)/(64)`