Question

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

Answer 1

a) (x+2)^2=2

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