Question

What number must be added to the expression below to complete the square x^+5x

Answer 1

`(25)/(4)`

Explanation:

We are given the following expression and we are to complete its square:

`x^2+5x`

To complete the square of the above expression, we will divide the coefficient of x by 2 and add its square to the expression.

Since the coefficient of x here is 5, so we will divide it by 2 and add its square to get:

`x^2+5x+((5)/(2) )^2`

`x^2+5x+(25)/(4)`

Therefore, the missing term to complete the square of the given expression is
`(25)/(4)`.

Answer 2

`(25)/(4)`

Explanation:

The given expression is

`x^2+5x`

Since the coefficient of the quadratic term is 1, you must add the square of
`(5)/(2)`

which is

`=((5)/(2))^2`

We square both the numerator and the denominator to obtain,

`=(5^2)/(2^2)`

This will give us

`=(25)/(4)`