How to factorize $2x^2 + 2x + 1$?

Question

How to factorize $2x^2 + 2x + 1 = 0$ into $2(x + 0.5)^2 + 0.5$ ?

What is the process behind this factorization?

Edit: Thanks guys, have updated this post. Updated the tag to complete the square.

Answer 1

it's $$2\left(x^2+x+\frac{1}{2}\right)=2\left(\left(x+\frac{1}{2}\right)^2+\frac{1}{4}\right)=2\left(x+\frac{1}{2}\right)^2+\frac{1}{2}.$$

Answer 2

I believe you mean $2x^2+2x+1 = 2((x+0.5)^2+0.5^2)$.

This is not a factorization, this is completing the square.

A factorization would be in the form $$ax^2+bx+c=k(px+q)(rx+s)$$

Notice that there are no leftover terms, including constants.

Answer 3

In $ \mathbb C$:

The zeros of $2z^2+2z+1$ are $z_1= \frac{1}{2}(-1+i)$ and $z_2 = \overline{z_1}.$

Hence we have the factorization

$$2z^2+2z+1=2(z-z_1)(z-z_2).$$