Solve without a calculator: If $x+\sqrt{x}=13$ then $x+\frac{13}{\sqrt{x}}=?$

Question

$$x+\sqrt{x}=13$$
$$x+\frac{13}{\sqrt{x}}=?$$

I tried to square(and also triple in another attempt) both sides of both of the equations hoping that I would find some expression to plug in. It didn't help.

Then, I tried to simply bring the second equation to a common denominator.It didn't help neither.

Then I found the $x$ value ($9.86$) from the first equation by using a calculator and then plugged in to the second equation and got this expression
$$\frac{493}{50}+65\sqrt{\frac{2}{493}}$$

Now, Is this question solvable without a calculator?

Answer 1

Note that $$x+\frac{13}{\sqrt{x}} = x + \frac{x+\sqrt{x}}{\sqrt{x}} = x+\sqrt{x}+1=14.$$