Complete the square and write in standard form. Show all work.

Given:
[tex]x^2+8x+4y-8=0[/tex][tex]\begin{gathered} x^2+8x+16-16+4y-8=0 \\ (x+4)^2+4y-24=0 \\ (x+4)^2=-4y+24 \\ (x+4)^2=-4(y-6) \end{gathered}[/tex]Therefore, the standard form is
[tex](x+4)^2=-4(y-6)[/tex]