Question

What number must be added to the expression below to complete the square x2-20x?

Answer 1

100

Explanation:

I believe you meant x^2 - 20x; " ^ " denotes exponentiation.

Take half the coefficient of the x term (which in this problem is -20). We get -10. Now square this, obtaining 100.

Adding 100 to x^2 - 20x "completes the square."

Answer 2

100.

Explanation:

We have been given an expression
`x^2-20x`. We are asked to find the number that must be added to the expression to complete the square.

We know that a perfect square is in form
`a^2+2ab+b^2`.

To complete a square we need to add the half the square of b that is
`((b)/(2))^2`.

Upon looking at our given expression we can see that b is equal to 20, so
`((b)/(2))^2` would be:

`((b)/(2))^2=((20)/(2))^2=(10)^2=100`

`x^2-20x+100=(x-10)^2`

Therefore, we must add 100 to our given expression to complete the square.