This problem is pretty much similar to the previous one except one difference, the coefficient of x² is not 1 but 2.
In such case the first thing you do is taking common or dividing the whole expression by the coefficient of x².
First dividing the whole expression by 3
2(x²-5x+1/2)
Now we have to apply the completing square method on the expression inside the brackets.
x²-2(5/2)x+1/2 (breaking the coefficient of x into two parts)
=>x²-2(5/2)+1/2+25/4-25/4 (adding and subtracting 25/4 which is the square of 5/2 )
=>(x-5/2)²-23/4 (.: x²-2(5/2)+25/4=(x-5/2)² & 1/2-25/4= -23/4)
but in our final answer we have to include the 2 we took common in the start of the solution
=>2[(x-5/2)²-23/4] this is our final answer
