completing sqaure

Question 1

what to do when completing the square with coefficient off more than 1 eg 2x^2

Answer 1

factorise the equation except the last c value with the coefficient so you are left with x^2 in a bracket with the second term also in the bracket with a factor of the co-efficient taken out of it then complete the square like normal but remember to multiply your result from the do the squared and put it negative step by the factor outside the bracket (the original co-efficient so it can leave the bracket and the two terms can be tidied up
. so you will need two sets off brackets to keep the original last value from being multiplied by the factor outside bracket

make sure to leave the last term alone and don’t place it in the bracket.
ignore it until the end and treat the rest of it as the real equation until the end point where you need to tidy it up

eg 3x^2+2x-5
3(x^2+2/3x) -5
[3(x+1/3)^2 -1/9] -5
3(x+1/3)^2 -1/3-5
3(x+1/3)^2 -1/3-15/3
3(x+1/3)^2 -16/3

Question 2

point to remember when dealing with completing the square with co-efficients o

Answer 2

just leave the third term out of the beginning steps- it should always be outside the bracket
only bring it in at the end when it needs to be tidied up