Question

Which of the following equations is in equation formed when completing the square on y^2 - 12 y= -27

(y-6)^2=-27
(y+6)^2=9
(y-6)^2=9​

Answer 1

`(y-6)^2=9`

Explanation:

Given

`y^2 - 12y = -27`

Required

Get equivalent expression using completing the square

Follow these steps:

• Take the coefficient of y; That is -12

• Divide it by 2; That is (-12/2)

• Square it: (-12/2)^2

Add to both sides of the equation

`y^2 - 12y + ((-12)/(2))^2= -27 + ((-12)/(2))^2`

`y^2 - 12y + (-6)^2= -27 + (-6)^2`

`y^2 - 12y + 36= -27 + 36`

`y^2 - 12y + 36= 9`

Expand the right-hand side

`y^2 - 6y - 6y + 36= 9`

Factorize:

`y(y-6)-6(y-6) =9`

`(y-6)(y-6)=9`

`(y-6)^2=9`