\documentclass{report}
% Change "report" to "article" to get a page number on title page
\usepackage{amsmath,amsfonts,amsthm,amssymb}
\usepackage{setspace}
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{extramarks}
\usepackage{chngpage}
\usepackage{soul,color}
\usepackage{graphicx,float,wrapfig}

% Homework Specific Information
\newcommand{\hmwkTitle}{Test 2 Review Answers}
\newcommand{\hmwkDueDate}{Fall 2018}
\newcommand{\hmwkClass}{MAT 1275}
\newcommand{\hmwkClassTime}{}
\newcommand{\hmwkClassInstructor}{Prof. Shaver}
\newcommand{\hmwkAuthorName}{}

% In case you need to adjust margins:
\topmargin=-0.45in      %
\evensidemargin=0in     %
\oddsidemargin=0in      %
\textwidth=6.5in        %
\textheight=9.0in       %
\headsep=0.25in         %

% Setup the header and footer
\pagestyle{fancy}                                                       %
%\lhead{\hmwkAuthorName}                                                 %
\lhead{\hmwkClass\ (\hmwkClassInstructor): \hmwkTitle}  %
\rhead{\firstxmark}                                                     %
\lfoot{\lastxmark}                                                      %
\cfoot{}                                                                %
\rfoot{Page\ \thepage\ of\ \protect\pageref{LastPage}}                          %
\renewcommand\headrulewidth{0.4pt}                                      %
\renewcommand\footrulewidth{0.4pt}                                      %

% This is used to trace down (pin point) problems
% in latexing a document:
%\tracingall

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Some tools
\newcommand{\enterProblemHeader}[1]{\nobreak\extramarks{#1}{#1 continued on next page\ldots}\nobreak%
                                    \nobreak\extramarks{#1 (continued)}{#1 continued on next page\ldots}\nobreak}%
\newcommand{\exitProblemHeader}[1]{\nobreak\extramarks{#1 (continued)}{#1 continued on next page\ldots}\nobreak%
                                   \nobreak\extramarks{#1}{}\nobreak}%

\newlength{\labelLength}
\newcommand{\labelAnswer}[2]
  {\settowidth{\labelLength}{#1}%
   \addtolength{\labelLength}{0.25in}%
   \changetext{}{-\labelLength}{}{}{}%
   \noindent\fbox{\begin{minipage}[c]{\columnwidth}#2\end{minipage}}%
   \marginpar{\fbox{#1}}%

   % We put the blank space above in order to make sure this
   % \marginpar gets correctly placed.
   \changetext{}{+\labelLength}{}{}{}}%

\newcommand{\homeworkProblemName}{}%
\newcounter{homeworkProblemCounter}%
\newenvironment{homeworkProblem}[1][Part \arabic{homeworkProblemCounter}]%
  {\stepcounter{homeworkProblemCounter}%
   \renewcommand{\homeworkProblemName}{#1}%
   \section*{\homeworkProblemName}%
   \enterProblemHeader{\homeworkProblemName}}%
  {\exitProblemHeader{\homeworkProblemName}}%

\newcommand{\problemAnswer}[1]
  {\noindent\fbox{\begin{minipage}[c]{\columnwidth}#1\end{minipage}}}%

\newcommand{\problemLAnswer}[1]
  {\labelAnswer{\homeworkProblemName}{#1}}

\newcommand{\homeworkSectionName}{}%
\newlength{\homeworkSectionLabelLength}{}%
\newenvironment{homeworkSection}[1]%
  {% We put this space here to make sure we're not connected to the above.
   % Otherwise the changetext can do funny things to the other margin

   \renewcommand{\homeworkSectionName}{#1}%
   \settowidth{\homeworkSectionLabelLength}{\homeworkSectionName}%
   \addtolength{\homeworkSectionLabelLength}{0.25in}%
   \changetext{}{-\homeworkSectionLabelLength}{}{}{}%
   \subsection*{\homeworkSectionName}%
   \enterProblemHeader{\homeworkProblemName\ [\homeworkSectionName]}}%
  {\enterProblemHeader{\homeworkProblemName}%

   % We put the blank space above in order to make sure this margin
   % change doesn't happen too soon (otherwise \sectionAnswer's can
   % get ugly about their \marginpar placement.
   \changetext{}{+\homeworkSectionLabelLength}{}{}{}}%

\newcommand{\sectionAnswer}[1]
  {% We put this space here to make sure we're disconnected from the previous
   % passage

   \noindent\fbox{\begin{minipage}[c]{\columnwidth}#1\end{minipage}}%
   \enterProblemHeader{\homeworkProblemName}\exitProblemHeader{\homeworkProblemName}%
   \marginpar{\fbox{\homeworkSectionName}}%

   % We put the blank space above in order to make sure this
   % \marginpar gets correctly placed.
   }%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Make title
\title{\vspace{2in}\textmd{\textbf{\hmwkClass:\ \hmwkTitle}}\\\normalsize\vspace{0.1in}\small{Due\ on\ \hmwkDueDate}\\\vspace{0.1in}\large{\textit{\hmwkClassInstructor\ \hmwkClassTime}}\vspace{3in}}
\date{}
\author{\textbf{\hmwkAuthorName}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}
\begin{spacing}{1.1}

% \maketitle

% \newpage

The references to examples in the textbook are given as well: review as needed before you repeat the self-test. The test could include any of the similar homework problems from these sections: it will NOT just change the numbers in these problems.\\\\
Also, remember that you are graded on your work. I have only indicated what should be done in these problems: you must show complete work to justify your answers in order to receive credit.\\
\textbf{NOTE: Please DO NOT use set notation when reporting your solutions to equations: just write the solutions as I have done below.}
\large
\textbf{Self-Test:} %allow 50 minutes\\\\
For each of problems 1-5:  Use the special products patterns (the square of a binomial, difference of squares pattern, or the pattern for the product of a complex number with its conjugate) where appropriate: \textbf{failure to do so will reduce your score.}\\\\

\textbf{Perform the indicated operation: and simplify your answer, using fractions in lowest terms (no decimals). Write the final result in the standard form $a+bi$.}

\begin{description}
\item[1)] $3i(2+5i) = 6i + 15i^{2} = -15 + 6i$
\item[2)] $(3-5i)+(8+6i) = 11 + i$

\item[3)] $(3-5i)(8+6i) = 24 +18i - 40i - 30i^{2} = -6 - 22i$

\item[4)] 
$(2-5i)^{2}$ Use the perfect square pattern $(A-B)^{2} = A^{2} - 2AB + B^{2}$: you get $-21 -20i$

\item[5)] 
\Large
 $\frac{3+i}{3-4i}$ Multiply by the conjugate of the denominator on top and bottom, and use the pattern $(a+bi)(a-bi) = a^{2} + b^{2}$: you get $\frac{1}{5} + \frac{3}{5}i$
 \normalsize


\item[6)] \textbf{Solve the equation: make sure to indicate your final answer clearly}\\
\large $2+\sqrt{3x-2}=x$\\
Isolate the radical, then square both sides and solve the resulting quadratic equation using the Zero Product Property. Make sure to check for. ``extraneous solutions''!  The final result is $x=6$.
\normalsize

\item[7)] \textbf{Solve the equation using the Square Root Property:}\\
$5x^{2} + 100 = 0$\\
Isolate the $x^{2}$: this gives $x^{2} = -20 \implies x = \pm\sqrt{-20}$\\
Simplify the radical: $x = 2i\sqrt{5}$ or $x= -2i\sqrt{5}$

\item[8)] \textbf{Solve the equation using the Square Root Property:}\\
$(x-7)^{2} = 12 \implies x-7 = \pm\sqrt{12}$\\
Solve for x: $x = 7 + 2\sqrt{3}$ or $x = 7 - \sqrt{3}$

\item[9)] \textbf{Solve the equation by completing the square and using the Square Root Property:}\\
$x^{2} + x + 1 = 0$\\
Move the term +1 to the right-hand side and complete the square:\\
$x^{2} + x + \frac{1}{4} = -1 + \frac{1}{4}$\\
$\left(x + \frac{1}{2}\right)^{2} = -\frac{3}{4}$\\
Use the Square Root Property and solve, you get as final result $x = -\frac{1}{2} + \frac{\sqrt{3}}{2} i$ or $x = -\frac{1}{2} - \frac{\sqrt{3}}{2} i$

\item[10)] \textbf{Solve the equation using the Quadratic Formula:}\\
$2x^{2} - 3x - 1 = 0$\\
You get $x = 1$ or $x = \frac{1}{2}$

\end{description}



\end{spacing}
\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
