Question

Solve for x by completing the square:

-4x^2-8x-2=0

I got: x=-1+/-the square root of 1
Is this answer correct?

Answer 1

`-4x^2-8x-2=0\\\\-4\big(x^2+2x+(1)/(2)\big)=0\quad|:(-4)\\\\x^2+2x+(1)/(2)=0\\\\x^2+2x+1-(1)/(2)=0\\\\ \big(x^2+2x+1\big)-(1)/(2)=0\\\\ \big(x+1\big)^2-(1)/(2)=0\\\\\big(x+1\big)^2=(1)/(2)\quad|√((\ldots))\\\\\\x+1=\sqrt{(1)/(2)}\qquad\vee\qquad x+1=-\sqrt{(1)/(2)}\\\\\\ \boxed{x=\sqrt{(1)/(2)}-1\qquad\vee\qquad x=-\sqrt{(1)/(2)}-1}`

or in different forms:


`\boxed{x=(1)/(√(2))-1\qquad\vee\qquad x=-(1)/(√(2))-1}\\\\\\ \boxed{x=(√(2))/(2)-1\qquad\vee\qquad x=-(√(2))/(2)-1}`