2(x-3/2)^2+1/2
Step-by-step explanation:
1. Move the coefficient of x to the front and write the rest normally divided by the coefficient.
2(x^2-3x+5/2)
2. Divide the coefficient of x by 2 squared.
2[x^2-3x+(-3/2)^2-(-3/2)^2+5/2]
3. Put the first terms into ( )^2
2[(x-3/2)^2-9/4+5/2]
4. Add the last 2 terms
2(x-3/2)^2+1/2