Answer
The solutions are $x=64$ and $x=25$
Work Step by Step
$x-13\sqrt{x}+40=0$
Rewrite $\sqrt{x}$ as $x^{1/2}$:
$x-13x^{1/2}+40=0$
Let $u$ be equal to $x^{1/2}$
If $u=x^{1/2}$, then $u^{2}=x$
Rewrite the equation using the new variable $u$:
$u^{2}-13u+40=0$
Solve by factoring:
$(u-8)(u-5)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$u-8=0$
$u=8$
$u-5=0$
$u=5$
Substitute $u$ back to $x^{1/2}$ and solve for $x$:
$x^{1/2}=8$
$(x^{1/2})^{2}=8^{2}$
$x=64$
$x^{1/2}=5$
$(x^{1/2})^{2}=5^{2}$
$x=25$
The solutions are $x=64$ and $x=25$
