Answer
The solution is $x=36$
Work Step by Step
$2x-7\sqrt{x}-30=0$
Rewrite $\sqrt{x}$ as $x^{1/2}$:
$2x-7x^{1/2}-30=0$
Let $u$ be equal to $x^{1/2}$
If $u=x^{1/2}$, then $u^{2}=x$
Rewrite the equation using the new variable $u$:
$2u^{2}-7u-30=0$
Solve by factoring:
$(2u+5)(u-6)=0$
Set both factors equal to $0$ and solve each individual equation for $u$:
$2u+5=0$
$2u=-5$
$u=-\dfrac{5}{2}$
$u-6=0$
$u=6$
Substitute $u$ back to $x^{1/2}$ and solve for $x$:
$x^{1/2}=-\dfrac{5}{2}$
$(x^{1/2})^{2}=\Big(-\dfrac{5}{2}\Big)^{2}$
$x=\dfrac{25}{4}$
$x^{1/2}=6$
$(x^{1/2})^{2}=6^{2}$
$x=36$
Check the solutions found by plugging them into the original equation:
$x=\dfrac{25}{4}$
$2\Big(\dfrac{25}{4}\Big)-7\sqrt{\dfrac{25}{4}}-30=0$ False
$x=36$
$2(36)-7(\sqrt36)-30=0$ True
The solution is $x=36$
