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#
