Exercise 38 Page 48

We know that $M$ is the midpoint of $\overline{XY}.$

Since $M$ is the midpoint, we know that the lengths of $\overline{XM}$ and $\overline{MY}$ are equal. Thus, we can write the following equation. Now, we will solve this equation for $x.$ We will start by subtracting $x$ from both sides. Then we can factor the equation. To factor this equation, we need to think of two numbers that add to be $\text{-}1$ and multiply to be $\text{-}2.$ We can imagine that this will be some combination of $\pm 1$ and $\pm 2.$

Factor $m$	Factor $n$	$m+n$	$mn$
$2$	$1$	$3$	$2$
$2$	$\text{-}1$	$1$	$\text{-}2$
$\text{-}2$	$1$	$\text{-}1$	$\text{-}2$
$\text{-}2$	$\text{-}1$	$\text{-}3$	$2$

The factors that allow for this are $\text{-}2$ and $1.$ Now we can write the factored form of the equation. In order to have the entire equation equal $0,$ one of the factors must be equal to $0$ by the Zero Product Property. Since the measure of any length cannot be negative, $x$ must be $2.$