As we have to solve the quadratic equation by completing square method and 2x^2 is not a square, let us first divide 2x^2+7x-4=0 by 2, which gives us
x^2+7/2x-2=0. ....(A)
Now recall the identity (x+a)^2=x^2+2ax+a^2 which shows that to complete square we must add square of half of x's coefficient. As coefficient of x is 7/2, we add and subtract (7/4)^2=49/16 and equation (A) becomes
x^2+7/2x+49/16-49/16-2=0 or
(x+7/4)^2-(49+32)/16=0 or
(x+7/4)^2-81/16=0 or
(x+7/4)^2-(9/4)^2=0 and using identity (x^2-a^2)=(x+a)(x-a), we get
(x+7/4+9/4)(x+7/4-9/4)=0 or
(x+16/4)(x-2/4)=0
(x+4)(x-1/2)=0
i.e. x=-4 or x=1/2
