Algebra: Completing the square

You first step implies that 2x^(2) + 8x = 2(x + 4)^(2). This is not the case (to see, try expanding 2(x+4)^(2)). You are correct to factor out the 2 from the first two terms, but you have gotten a bit ahead of yourself with "taking the square out" (which is not a thing).

So, try starting with 2x^(2) + 8x + 2 = 2(x^(2) + 4x) + 2 and see what you can accomplish from there.
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.
>A) 2x² + 8x + 2

2(x^2 +4x+(4/2)^2 )-2(4/2)^2 +2

2(x+2)^2 -8+2

2(x+2)^2 -6
Once you've factored out the 2, and you have 2(x\^2 + 4x + 1) = 2(x\^2 + 4x) + 2, how did you get to 2(x + 4)\^2 + 2? In particular, that seems to be implying x\^2 + 4x = (x\^2 + 4)\^2 . Is that accurate?