The first step to complete the square is to make the coefficient of #x^2# 1. This is done by factorising the 2 out of the equation.

#2x^2 -16x + 24#

#2(x^2 -8x +12)#

Now we complete the square by halving the coefficient of #x# and adding and subtracting this number squared (this effectively does not change the equation as in total zero is being added).

#2[x^2 -8 +(-4)^2 - (-4)^2 +12]#

This is the completed square before being factored:

#x^2 -8x + (-4)^2#

Simply take the #(-4)# and place inside the brackets which are being squared (As you would to factorise a normal equation). This is your completed square. You also need to collect the other values in the equation.

#2[(x - 4)^2 -(-4)^2 +12]#

Evaluate the constants

#2[(x - 4)^2 -16 +12]#

#2[(x - 4)^2 -4]#

This is your answer, you can take the constant out of the [] brackets if you like.

#2(x -4)^2 -8#