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

Answer:

$(y-6)^2=9$

Step-by-step 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

$y^2 - 12y + (\frac{-12}{2})^2= -27 + (\frac{-12}{2})^2$

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

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

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

Expand the right-hand side

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

Factorize:

$y(y-6)-6(y-6) =9$

$(y-6)(y-6)=9$

$(y-6)^2=9$