Answer
$x=4$ and $x=9$
Work Step by Step
$x-5\sqrt{x}+6=0$
Let $\sqrt{x}$ be equal to $u$:
$u=\sqrt{x}$
$u^{2}=x$
Rewrite the original equation using the new variable $u$:
$u^{2}-5u+6=0$
Solve this equation by factoring:
$(u-3)(u-2)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$u-3=0$
$u=3$
$u-2=0$
$u=2$
Substitute $u$ back to $\sqrt{x}$ and solve for $x$:
$u=3$
$\sqrt{x}=3$
$x=9$
$u=2$
$\sqrt{x}=2$
$x=4$
The two solutions found are $4$ and $9$ and the original equation is true for both of them. The final answer is:
$x=4$ and $x=9$
