# What do you need to add to complete the square for x^2+8x?

Apr 1, 2018

16

#### Explanation:

Since the $8 x$ is positive, the equation ${\left(x + y\right)}^{2}$ must have $y$ as a positive number. Let's see this!

An easy way to complete the square if you have the constants for ${x}^{2}$ and $x$ but not the non-variable number is to divide the $x$ constant, and then square it. Just like this:

$8 x$/$2$$= 4$.
${4}^{2} = 16$.

The last number must be 16. Let's check it.

${\left(x + 4\right)}^{2} = {x}^{2} + 8 x + \textcolor{red}{16}$

The answer is $16$.

Yay!