College Algebra, Chapter 1, 1.3, Section 1.3, Problem 82

Find the width of the room, suppose it has an area of $228 ft^2$ and its length is $7 ft$ longer than its width.

Recall that the area


$
\begin{equation}
\begin{aligned}

A & L x W
&& \text{Model}
\\
\\
228 =& L x W
&& \text{Substitute the given}
\\
\\
228 =& (W + 7)(W)
&& \text{Perform the condition}
\\
\\
228 =& W^2 + 7W
&& \text{Distribute } W
\\
\\
W^2 + 7W - 228 =& 0
&& \text{Subtract 228}
\\
\\
(x + 19)(x - 12) =& 0
&& \text{Factor}
\\
\\
x + 19 =& 0 \text{ and } x - 12 = 0
&& \text{Zero Product Property}
\\
\\
x =& -19 \text{ and } x = 12
&& \text{Solve for } x
\\
\\
x =& 12 ft
&& \text{Choose } x > 0

\end{aligned}
\end{equation}
$