Question

Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

Term to add is (3/8)^2 = 9/64

Explanation:

Here, we want to know the value that must be added to make the equation a perfect square.

x^2 - 3/4x = 5

x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5

x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2

= (x-3/8)^2 = 5 + (3/8)^2

So the term to add is (3/8)^2 = 9/64

Answer 2

`(9)/(64)`

Explanation:

Given the equation:
`x^2-(3)/(4)x=5`

To make the left hand side of the equation a perfect trinomial, we follow these steps.

Step 1: Divide the coefficient of x by 2.

Coefficient of x
`=-(3)/(4)`

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

Step 2: Square your result from step 1

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

Therefore, to make the Left-Hand side a perfect-square trinomial, we add 9/64.