The first step to complete the square is to make the coefficient of x2 1. This is done by factorising the 2 out of the equation.
2x2−16x+24
2(x2−8x+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[x2−8+(−4)2−(−4)2+12]
This is the completed square before being factored:
x2−8x+(−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
