The the method of completing the square to transform the quadratic equation into the equation form (c+p) ^2=q.

6+12x+3x^2=0

a) (x+2) ^2=2

b) (x+2) ^2=-2

c) (x+2) ^2=4

d) (x+2) ^2=-4

a) (x+2) ^2=2

Step-by-step explanation:

To complete the square, take the middle term bx and divide it in two. Then take the square.

6+12x+3x^2=0 should be rewritten as 3 (x^2 + 4x) = - 6 has bx = 4x. Take 4/2 = 2. Square 2^2 = 4.

Now to finish completing the square by adding 4 to each side.

3 (x^2 + 4x + 4) = - 6 + 3 (4)

3 (x^2 + 4x + 4) = - 6 + 12

3 (x+2) ^2 = 6

(x+2) ^2 = 2