There appears to be a mistake in the LaTeX, so that the equation is supposed to be
[tex]x\sqrt{x}-5x-9\sqrt{x}=35[/tex]
If we let z=√x, then this is
[tex]z^{3}-5z^{2}-9z-35=0[/tex]
By Descartes' rule of signs, this will have one positive real root. The rational root theorem says it will be one of 1, 5, 7, or 35. It is actually z=7. The corresponding value of x is
x = z² = 7² = 49.
A graphing calculator finds the solution to the original equation easily. (I find it useful to put it in the form f(x)=0.)
x = 49
