Question

Find the roots of x 2 - 5x + 4 =0 by completing the squares method

Answer 1

     
  Given,

     $x^{2}$ - 5x + 4                                = 0
or, $x^{2}$ - 5x + 4 + $(-5/2)^2$ = $(-5/2)^2$ 
     
     The above technique is most used in completing the square problems.        You take the coefficient of the  $x^{2}$ term and divide the whole      equation by it (it happens to be 1 in this case). Then take the coefficient        of the x term along with it's sign, and halve it. Then square this half, and      add that on both sides of the equation. Then you can go ahead and              complete the square.                                                        

or, $(x-5/2)^2$                                        = 25/4 - 4
or, $(x-5/2)^2$                                        = 9/4
or, x - 5/2                                                           =+3/2 or -3/2.

Therefore, x = 4 or x = 1

Answer 2

x^2-2*5/2x+4=0
x^2-2*5/2+25/4=25/4-4
(x-5/2)^2 =9/4
x=-9/4 +5/2 or x=9/4 +5/2
x = 1/4 or x=19/4