%Template for doing 21-355 homework in LaTex.

\documentclass[leqno, fleqn]{article}
\usepackage{amsmath, amssymb, amsthm}%Standard AMS packages for most symbols and proof environments
\usepackage{hyperref}%Provides links to referenced equations.  

%Sets up theorem, lemma, corollary, proposition, definition, and remark environments.
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}{Corollary}
\newtheorem{proposition}{Proposition}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\theoremstyle{remark}
\newtheorem{remark}{Remark}

\title{Homework X--21-355 A}%Replace X with the assignment number
\author{Name}%Enter your name
\date{Due Date}%Enter the DUE date

\begin{document}
\maketitle

\begin{enumerate}
\item Statement of first problem.

\begin{proof}
Enter your proof here.
\end{proof}

\item Statement of second problem.

\begin{proof}[Solution:]
Use [Solution:] as above if the problem requires a calculated answer instead of a proof.
\end{proof}

%Add \item and \begin{proof}...\end{proof} for each problem on the assignment.

\item\begin{proposition}%You may use the theorem, lemma, proposition, etc. environments if you wish.
If $x\in\mathbb{C}$ such that
\begin{equation}\label{eqnquad}
ax^2+bx+c=0
\end{equation}
where $a\neq 0$, then 
\begin{equation*}%The * tells the compiler not to number this equation.
x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
\end{equation*}
\end{proposition}

\begin{proof}
We wish to solve \eqref{eqnquad} for $x$.  We note that \eqref{eqnquad} can be rewritten as
\begin{equation}
a\left( x^2 + \frac{b}{a} x + \frac{b^2}{4a^2} \right) + c - \frac{b^2}{4a} =0
\end{equation}
since $a\neq 0$.  Accordingly,
\begin{equation}
a\left(x + \frac{b}{2a}\right)^2 = \frac{b^2-4ac}{4a}
\end{equation} 
or
\[\left(x + \frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}.
\]

Solving for $x$ yields the result.
\end{proof}

\end{enumerate}

\end{document}