Answer
The solution is $s=-18$.
Work Step by Step
The given equation is
$\Rightarrow \sqrt[3]{2s+9}=-3$
Cube each side of the equation.
$\Rightarrow (\sqrt[3]{2s+9})^3=(-3)^3$
Simplify.
$\Rightarrow 2s+9=-27$
Subtract $9$ from each side.
$\Rightarrow 2s+9-9=-27-9$
Simplify.
$\Rightarrow 2s=-36$
Divide each side by $2$.
$\Rightarrow s=-18$
Check $s=-18$.
$\Rightarrow \sqrt[3]{2s+9}=-3$
$\Rightarrow \sqrt[3]{2(-18)+9}=-3$
$\Rightarrow \sqrt[3]{-36+9}=-3$
$\Rightarrow \sqrt[3]{-27}=-3$
$\Rightarrow \sqrt[3]{(-3)^3}=-3$
$\Rightarrow -3=-3$
True.
Hence, the solution is $s=-18$.
