Complete the square and find x. 9x^2-6x+21=0

Given the equation :

9x^2 -6x
+21 = 0

We need to solve by completing the
square.

==> Let us rewrite 21 = 21
+1

==> 9x^2 -6x + 1 + 20 =
0

==> (3x-1)^2 + 20 =
0

==> Now we will move 20 to the right
side.

==> (3x-1)^2 =
-20

Now we will take the square root of both
sides.

==> 3x-1 = sqrt-20 = 2sqrt-5 =
2sqrt5*i

==> 3x-1
=2sqrt5*i

==> 3x = 1+
2sqrt5*i

==> x1 = (1/3) + (2sqrt5)/3
*i

OR :

-(3x-1) =
2sqrt5*i

==> -3x +1 =
2sqrt5*i

==> -3x = -1 +
2sqrt5*i

==> x2 = (1/3) -(2sqrt5)/3
*i

Then we have two
solutions:

x= { (1/3)+2sqrt5/3 *i ,  (1/3) 8
(2sqrt5/3)*i }