Use completion of squares method to solve : 6x^2 + 36x + 18 = 0

We'll divide by 6 entire
equation:

x^2 + 6x + 3 =
0

Now, we'll shift 3 to the right to become much more easy
to see what has to be added to complete the square:

x^2 +
6x = -3

We'll consider the
formula:

(a+b)^2 = a^2 + 2ab +
b^2

We'll identify the first 2
terms:

a^2 = x^2 and 2*a*b =
2*x*3

The missing term is b and we'll identify it as being
3.

We'll raise to square 3 and we'll add it both
sides:

x^2 + 6x + 9 = -3 +
9

(x+3)^2 = 6

We'll take the
square root both sides:

x + 3 = sqrt
6

x = -3 + sqrt 6

x + 3 = -
sqrt 6

x = -3 - sqrt
6

The roots of quadratic have been determined
and they are:{-3 - sqrt 6 ; -3 + sqrt 6}.