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

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


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