Answer
$s=25$
Work Step by Step
$ s+3\sqrt{s}-40=0\qquad$...substitute $\sqrt{s}$ for $u$ so that $u^{2}=s$
Note that $s$ and $\sqrt{s}$ are positive.
.
$ u^{2}+3u-40=0\qquad$... solve with the Quadractic formula.
$u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$u=\displaystyle \frac{-3\pm\sqrt{9+160}}{2}$
$u=\displaystyle \frac{-3\pm\sqrt{169}}{2}$
$u=\displaystyle \frac{-3\pm 13}{2}$
$u=\displaystyle \frac{-3+13}{2}=\frac{10}{2}=5$ or $u=\displaystyle \frac{-3-13}{2}=\frac{-16}{2}=-8$
Bring back $\sqrt{s}=u$.
$\sqrt{s}=5$ or $\sqrt{s}=-8$
$\sqrt{s}$ is a positive number which is why we discard $-8$.
$s=5^{2}=25$
