College Algebra, Chapter 1, 1.5, Section 1.5, Problem 52

Find all real solutions of the equation $\displaystyle x - 5 \sqrt{x} + 6 = 0$


$
\begin{equation}
\begin{aligned}

x - 5 \sqrt{x} + 6 =& 0
&& \text{Given}
\\
\\
(\sqrt{x})^2 - 5 \sqrt{x} + 6 =& 0
&& \text{Let } w = \sqrt{x}
\\
\\
w^2 - 5w + 6 =& 0
&& \text{Factor}
\\
\\
(w - 3)(w - 2) =& 0
&& \text{Zero Product Property}
\\
\\
w - 3 =& 0 \text{ and } w - 2 = 0
&& \text{Solve for } w
\\
\\
w =& 3 \text{ and } w = 3
&& \text{Substitute } w = \sqrt{x}
\\
\\
\sqrt{x} =& 3 \text{ and } \sqrt{x} = 2
&& \text{Solve for } x
\\
\\
x =& 9 \text{ and } x = 4
&&

\end{aligned}
\end{equation}
$