Question

What number must be added to the expression below to complete the
square?
x² - 18x

Answer 1

`\boxed {\boxed {\sf 81}}`

Explanation:

The standard form of a quadratic is:

`ax^2+bx+c`

To complete the square, the a (leading coefficient) must be 1 and there can only be terms with variables on one side.

The expression given:

`x^2-18x`

follows these rules. Next, we divide the b (linear coefficient) by 2, then square it. Basically:

`((b)/(2))^2`

The b in the expression is -18.

`((-18)/(2))^2`

`(-9)^2= -9*-9= 81`

This is the number that is added.