Question

9x2+9x+2 use completion of square method​

Answer 1

Step-by-step explanation:

Solving   9x2-9x+2 = 0 by Completing The Square .

 Divide both sides of the equation by  9  to have 1 as the coefficient of the first term :

   x2-x+(2/9) = 0

Subtract  2/9  from both side of the equation :

   x2-x = -2/9

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4 

Add  1/4  to both sides of the equation :

  On the right hand side we have :

   -2/9  +  1/4   The common denominator of the two fractions is  36   Adding  (-8/36)+(9/36)  gives  1/36 

  So adding to both sides we finally get :

   x2-x+(1/4) = 1/36

Adding  1/4  has completed the left hand side into a perfect square :

   x2-x+(1/4)  =

   (x-(1/2)) • (x-(1/2))  =

  (x-(1/2))2 

Things which are equal to the same thing are also equal to one another. Since

   x2-x+(1/4) = 1/36 and

   x2-x+(1/4) = (x-(1/2))2 

then, according to the law of transitivity,

   (x-(1/2))2 = 1/36

We'll refer to this Equation as  Eq. #4.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

( answer is continued in the attachment )