Question

Solve the equation 4x square - 7x + 3.

Answer 1

Solving   4x2-7x+3 = 0 by Completing The Square .

 Divide both sides of the equation by  4  to have 1 as the coefficient of the first term :
   x2-(7/4)x+(3/4) = 0

Subtract  3/4  from both side of the equation :
   x2-(7/4)x = -3/4

Now the clever bit: Take the coefficient of  x , which is  7/4 , divide by two, giving  7/8 , and finally square it giving  49/64 

Add  49/64  to both sides of the equation :
  On the right hand side we have :
   -3/4  +  49/64   The common denominator of the two fractions is  64   Adding  (-48/64)+(49/64)  gives  1/64 
  So adding to both sides we finally get :
   x2-(7/4)x+(49/64) = 1/64

Adding  49/64  has completed the left hand side into a perfect square :
   x2-(7/4)x+(49/64)  =
   (x-(7/8)) • (x-(7/8))  =
  (x-(7/8))2 
Things which are equal to the same thing are also equal to one another. Since
   x2-(7/4)x+(49/64) = 1/64 and
   x2-(7/4)x+(49/64) = (x-(7/8))2 
then, according to the law of transitivity,
   (x-(7/8))2 = 1/64

Answer 2

4x square - 7x + 3 = 4x square - 4x - 3x + 3
= 4x (x - 1) - 3 (x - 1) = (4x - 3) (x - 1).
Hence, your answer is x = 3/4 or x = 1.

Hope it helps you.
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