Question

What number must you add to the polynomial below to complete the square?

x2 + 15x

Answer 1

The number
`(225)/(4)` is added to the polynomial below to complete the square.

Explanation:

Perfect square binomial:

A perfect square binomial is given by:

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

In this question:

We have that:

`a^2 + 2ab + b^2 = x^2 + 15x + ?`

Since
`a = x`, we have that:

`2ab = 15x`

`2b = 15`

`b = (15)/(2)`

Completing the square:

The term that completes the square is
`b^2`. So

`b^2 = ((15)/(2))^2 = (225)/(4)`

The number
`(225)/(4)` is added to the polynomial below to complete the square.