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\problemgrouptitle{Solving Equations}

\begin{problemblock}[2]{Solve the given equations.}

\item $\displaystyle x^2-6x+9=0$
\answer{$\displaystyle x=3$}

\item $\displaystyle 2x^2-5x-3=0$
\answer{$\displaystyle x=3$ or $\displaystyle x=-\frac{1}{2}$.  Written as a \emph{solution set} it is $\displaystyle \{3,-1/2\}$}

\item $\displaystyle 4x^2+3x+1=0$
\answer{$\displaystyle x=\frac{-3\pm\sqrt{-7}}{8}$, so no real solution.}

\item $\displaystyle x^3-2x-4=0$
\answer{$\displaystyle x=2$}

\item $\displaystyle x^3-4x^2-4x+16=0$
\answer{$\displaystyle \{-2,2,4\}$}

\item $\displaystyle x^3+4x-5=0$
\answer{$\displaystyle x=1$}

\item $\displaystyle 2x^4-3x^2=0$
\answer{$\displaystyle \left\{0,\pm\sqrt{\frac{3}{2}}\right\}$}

\item $\displaystyle x^4-3x^2+2=0$
\answer{$\displaystyle \left\{\pm 1,\pm\sqrt{2}\right\}$}

\item $\displaystyle 3x^5-2x^3+3x^2-2=0$
\answer{$\displaystyle \left\{-1,\pm\sqrt{\frac{2}{3}}\right\}$}

\item $\displaystyle 2x^5+5x^4-3x^2=0$
\answer{$\displaystyle \left\{-1,0,\frac{-3\pm\sqrt{33}}{4}\right\}$}

\end{problemblock}


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