Answer
The third step is wrong, and the correct answer is $x^2-x+\frac{1}{4}=2+\frac{1}{4}$.
Work Step by Step
The given equation is
$\Rightarrow 2x^2-2x-4=0$
Add $4$ to each side.
$\Rightarrow 2x^2-2x-4+4=0+4$
Simplify.
$\Rightarrow 2x^2-2x=4$
Divide each side by $2$.
$\Rightarrow x^2-x=2$
Find the value of $(\frac{b}{2})^2$.
Substitute $-1$ for $b$.
$=(\frac{-1}{2})^2$
Simplify.
$=\frac{1}{4}$
Add $\frac{1}{4}$ to each side of the equation.
$\Rightarrow x^2-x+\frac{1}{4}=2+\frac{1}{4}$
Hence, the third step is wrong, and the correct answer is $x^2-x+\frac{1}{4}=2+\frac{1}{4}$.