to change 2x²+8x+2 into a(x+b)²+c, what I did is this.

factor 2, we get. x²+4x+1.

isolate 1, x²+4x=-1.

now, we wanted to make the left side be a square. So we should add a number that is a square that adds up to 4, which is (-b/2a)² = (-4/2•1)² = (2)² = 4.

add 4 to both sides, x²+4x+4= 3, factor the left.

(x+2)²=3

(x+2)²-3=0. This is equal to the original equation, but 2 is factored so we need it back. *multiply it by 2*

2(x+2)²-6.