Answer
The number to add is $\frac{1}{16}$.
The factored form is $\left(x-\frac{1}{4}\right)^2$.
Work Step by Step
The given expression is $x^2-\frac{1}{2}x$.
This is in the form of $x^2-bx$ where $b=\frac{1}{2}$.
To find the number to add to complete the square, use the formula $\left(\frac{1}{2}b\right)^2$.
$\Rightarrow \left(\frac{1}{2}b\right)^2=\left(\frac{1}{2}\cdot \frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2=\frac{1}{16}$
Add $\frac{1}{16}$ to the given expression.
$=x^2-\frac{1}{2}x+\frac{1}{16}$
$=x^2-2\cdot \frac{1}{4} \cdot x+(\frac{1}{4})^2$
Use the special formula $a^2-2ab+b^2=(a-b)^2$ where $a=x$ and $b=\frac{1}{4}$.
$=\left(x-\frac{1}{4}\right)^2$
Hence, the factored form is $\left(x-\frac{1}{4}\right)^2$.
