Question

What number must you add to complete the square? x2-20x=17

A. 100
B. -10
C.-100
D. 10

Answer 1

The number is 100

A is correct

Explanation:

Given:
`x^2-20x=17`

We need to make completing square at left side.

Rule: We add a number " take half of the coefficient of x and then square it"

Coefficient of x = 20

Half of 20 = 10

Square of 10 = 100

So, we will add 100 both sides make completing square.

Now we make completing square to add 100

`x^2-20x=17`

Add 100 both sides

`x^2-20x+100=17+100`

Now we will factor left side perfect square

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

`(x-10)^2=117`

`(x-10)^2` is completing square or perfect square.

Hence, The number is 100