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Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

6 + 12x + 3x2 = 0
A) (x + 2)2 = 2
B) (x + 2)2 = -2
C) (x + 2)2 = 4
D) (x + 2)2 = -4

Respuesta :

absor201

The correct answer is: A) (x + 2)^2 = 2

Further explanation:

We have to convert the equation into simplest form to complete square

Given equation is:

[tex]6+12x+3x^2=0[/tex]

Rearranging the Equation:

[tex]3x^2+12x+6=0[/tex]

Dividing the equation by 3 gives us:

[tex]x^2+4x+2= 0[/tex]

Subtracting 2 from both sides

[tex]x^2+4x+2-2=0-2[/tex]

[tex]x^2+4x=-2[/tex]

Here

[tex]x=a\\4x=2ab\\Then\\4x=2(x)(b)\\b=\frac{4x}{2x}\\[/tex]

b=2

So,

Adding (2)^2 on both sides

[tex](x)^2+4x+(2)^2=-2+(2)^2\\(x+2)^2=-2+4\\(x+2)^2=2[/tex]

The correct answer is: A) (x + 2)^2 = 2

Keywords: Completing square, factorization

Learn more about factorization at:

  • brainly.com/question/12884373
  • brainly.com/question/12896802

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