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Question 28491: X^2/4-X/1=5/4
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! 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.
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