Question

What is x^2+8x-5 in vertex form? Please explain.

Answer 1

$x^2+8x-5=\\ x^2+2\cdot4\cdot x-5=\\ x^2+2\cdot4\cdot x+4^2-4^2-5=\\ (x+4)^2-16-5=\\ (x+4)^2-21$

Answer 2

$x^2+8x-5=\\ x^2-8x+16-21=\\ (x-4)^2-21$