Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 3 - Quadratic Functions - Exercises for Skills for Factoring - Page 135: 91

Answer

$x=\{0,36\}$

Work Step by Step

Let $u=\sqrt{x}$ for this example. Therefore, $u^2=x$. This means that the equation becomes $3u=\frac{1}{2}u^2$. Multiply both sides by $2$ and bring the $3u$ term to the other side to get $$u^2-6u=0$$ Since both terms have $u$, it can be factored out. $$u(u-6)=0$$ Therefore, set both expressions to zero to find a solution. $$u=0$$ $$u-6=0 \implies u=6$$ However, $u=\sqrt{x}$, so $x=u^2$. That means that the solutions for $x$ are $x=0^2=0$ and $x=6^2=36$.
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