Question

Which of the following equations is the result of completing the square on x2 - 6x - 9 = 0? (x - 3)2 = 0 (x - 3)2 = 9 (x - 3)2 = 18

Answer 1

(x-3)² = 18

Explanation:

We have given an equation.

x²-6x-9 = 0

We have to find the equation after completing square.

Adding 9 to both sides of above equation, we have

x²-6x-9+9 = 0+9

x²-6x = 9

Adding half of the term -6 to both sides of above equation, we have

x²-6x+(-3)² = 9+(-3)²

(x-3)² = 9+9

(x-3)² = 18 which is the answer.

Answer 2

`(x-3)^2=18`

Explanation:

The given equation is;

`x^2-6x-9=0`

Group the constant on the Right Hand Side.

`x^2-6x=9`

Add half the square of the coefficient of
`x` to both sides.

`x^2-6x+(-3)^2=9+(-3)^2`

The left hand side is now a perfect square.

`(x-3)^2=9+9`

`(x-3)^2=18`