Question 28491
X^2/4-X/1=5/4   ----(*)
Multiplying by 4 through out 
x^2-4x=5  ----(2)
(observe that the first term is square of x,the mid term is negative and (-4x) is therefore the product -2X(2)X(x) which is of the form -2ab.We have on the LHS an expression of the form (a^2-2ab) and so we need the quantity b^2 = 2^2 to complete the square)
Adding 2^2 on both the sides,
[(x)^2-2X(2)X(x) +(2)^2] = 5 +(2)^2  
[(x-2)^2]=9
(x-2)= (+ or minus)3
x= +2 (+ or minus)3
That is x= 2+3 or x = 2-3
x=5 and x = -1
Answer: x=5 and x = -1
Verification: x = 5 in (*) implies
LHS = 25/4-5 = 5/4 =RHS
x= -1 in (*)
LHS = 1/4+1 = 5/4 = RHS
Note: Always verify things by substituting the values in the given raw form of data instead of in your  simlified later forms.