You could use the general formula, then it is just a matter of plugging in a,b, and c.
In this case, a=2, b=-3, c=7
2x^2 = 3x - 7
I understand up to a certain point ;
1. 2x^2 = 3x - 7 ( subtracting 3x )
2. 1/2(2x^2 - 3x ) = 1/2(-7) ( multiplying by 1/2 to make the x^2 - coefficent 1)
3. x^2 - 3/2x = -7/2 ( miltiplying and simplifying )
according to the text it says
x^2 - 3/2x + 9/16 = -7/2 + 9/16 i don't understand how they
got that result
Look at your step 3, to complete the square you need b^2 as missing third item in general formula: (a+b)^2= a^2+2ab+b^2. Your a^2 is x^2, 2ab is 3/2x, which gives you b: 2ab= 3/2x=2* x* 3/4, 3/4 is b, then b^2 is 9/16. If it's missing, add it to both sides and your left side is completed!