## Precalculus (6th Edition) Blitzer

$x=7.8\ in$ and $x=10\ in$
Step 1. Use the given formula $V=x(x+10)(30-2x)=x(30x-2x^2+300-20x)=-2x^3+10x^2+300x$ and letting $V=2000$, we have $x^3-5x^2-150x+1000=0$ Step 2. Using synthetic division, we can find a zero at $x=10$, as shown in the figure, and the above equation becomes $(x-10)(x^2+5x-100)=0$ Step 3. As $x\geq0$, the second solution can be found as $x=\frac{-5+5\sqrt {17}}{2}\approx7.8\ in$ Step 4. We conclude the two possible solutions are $x=7.8\ in$ and $x=10\ in$