#### Answer

$x=5$

#### Work Step by Step

$x^{3/2}-10x^{1/2}+25x^{-1/2}=0$
$x^{-1/2}(x^{2}-10x+25)=0$
$x^{-1/2}(x-5)^{2}=0$
$x^{-1/2}=0$ or $(x-5)^{2}=0$
$\frac{1}{\sqrt{x}}=0$ or $x=\sqrt{0}+5=5$
The left equation has no solution, so the only solution is $x=5$