Help complete the square f(x)=-x^2-4x-8

Question

anonymous · Answer

again start with 
$$f(x)=-(x+4)-8$$ then 
$$f(x)=-(x+2)^2+k$$ and find $k$ via $k=f(-2)$

anonymous · Answer

sorry i meant start with 
$$f(x)=-(x^2+4x)-8$$

amoodarya · Answer

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anonymous · Answer

I believe you take $$-x^2-4x-8$$ and set it equal to zero. You then proceed to isolate the -x^2 - 4x. 
So then you have $$-x^2-4x=8$$
The next thing I did was to multiply through by -1 on both sides.
$$x^2+4x=-8$$
Now to complete the square you have to get the x^2+4x into the form (x+c)(x+c)=(x+c)^2
To do this you divide the coefficient of the 4x by 2 and then square it. So you should get positive 4. The next step is to add this 4 to both sides of $$x^2+4x=-8$$
So you should get $$x^2+4x+4=-4$$
Simplifying the equation gives 
$$(x+2)^2=-4 $$
or
$$(x+2)^2+4=0$$