Question

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

Answer 1

Answer:

100.

Step-by-step 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 $(\frac{b}{2})^2$.

Upon looking at our given expression we can see that b is equal to 20, so $(\frac{b}{2})^2$ would be:

$(\frac{b}{2})^2=(\frac{20}{2})^2=(10)^2=100$

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

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

Answer 2

Answer:

100

Step-by-step 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."