how to use completing square for 2x^2 + 3x = 9

Question

^{y + 2 ____ =2 (} x^{2 + 3/2 - ____ ) -9} 

i dont know how to finsh the rest 

Answer 1

2x^2+3x=9

x^2+ (3/2)x = 9/2           The b term is 3/2.  In order to complete the

                                       square you must divide b by 2. Get this 

                                       answer and square it.  This the number

                                       that you must add to both sides.  (3/2)

                                       divided by 2 is (3/4).  (3/4)^2= (9/16).

 

x^2+(3/2)x+(9/16) = (9/2)+ (9/16)

(x+ 3/4)^2 = (72/16)+ (9/16)

(x+ 3/4)^2 = (81/16)                      Take the square root of both sides

 

 x+3/4= 9/4                      x+3/4= -9/4

     -3/4    -3/4                        -3/4    -3/4

        x= 6/4                               x= -12/4

          x= 3/4                               x= -3