[Tex/LaTex] Increasing the Size of Beamer Footer

beamer

I work in Beamer extensively (specifically the Madrid theme). Sometimes, my "title" is quite long. Beamer puts this title at the bottom, but when it's too long it cuts it off. I'd really like to know how to increase the size of the bottom middle rectangular footer.
enter image description here

Here's the code (sorry for all of the packages and commands):

\documentclass[t]{beamer} %Add "mathserif" to script math lettering. "t" places all text to start at the top of each slide
\usetheme{Madrid}

%Packages 
\usepackage{amsmath} %Math mode
\usepackage{amssymb} %Math mode
\usepackage{commath}
\usepackage{graphicx} %Including pictures
\usepackage{color} %Define colours
\usepackage{setspace} %Enables double-spacing/variable spacing
\usepackage{pgfplots} %Draw graphs
\usepackage{upgreek} %Insert theta symbol as unitalicized 
\usepackage[version=3]{mhchem} %Chemistry equation mode \ce{}
\usepackage[export]{adjustbox} %Place black borders around images
\usepackage{scrextend} %Used to change font size
\usepackage{caption} %Used to utilize * in caption function
\usepackage{subfig} %Used to place figures side-by-side with sub-captions
\usepackage{siunitx} %SI Units (+ scientific notation)
\usepackage{cancel}
\usepackage{fancybox}
%\usepackage{enumitem} %Making lists
%\usepackage[english]{babel} %Lists with letters

%Erases Beamer Navigation Symbols on the bottom left
\setbeamertemplate{navigation symbols}{} 
%\setbeamertemplate{footline}{}
\captionsetup[subfigure]{labelformat=empty}

%Defined Colours
\definecolor{orangered}{RGB}{255,69,0}
\definecolor{darkgreen}{RGB}{0,100,0} 
\definecolor{firebrick}{RGB}{178, 34, 34}
\definecolor{navy}{RGB}{0,0,128}
\definecolor{lightsteelblue}{RGB}{176,196,222}
\definecolor{steelblue}{RGB}{70,130,180}
\definecolor{darkslateblue}{RGB}{72, 61, 139}
\definecolor{forestgreen}{RGB}{34, 139, 34}
\definecolor{Gold}{RGB}{218,165,32}

%Defined Colour Theme and List Sizing
\setbeamercolor{structure}{fg = Gold}
\setbeamertemplate{navigation symbols}{} 
\setbeamerfont*{itemize/enumerate body}{size=\normalsize}
\setbeamerfont*{itemize/enumerate subbody}{parent=itemize/enumerate body}
\setbeamerfont*{itemize/enumerate subsubbody}{parent=itemize/enumerate body}

%Opening Title Page
\title{Chapter 7 - Absolute Value and Reciprocal Functions}
\subtitle{Section 7.3 - Absolute Value Equations}
\date{}

\begin{document}
    %Slide 1
    \maketitle
\end{document}

Best Answer

The footline template used in beamer's Madrid theme is taken from the infolines outer theme and is defined by the following code:

\defbeamertemplate*{footline}{infolines theme}
{
  \leavevmode%
  \hbox{%
  \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
    \usebeamerfont{author in head/foot}\insertshortauthor\expandafter\beamer@ifempty\expandafter{\beamer@shortinstitute}{}{~~(\insertshortinstitute)}
  \end{beamercolorbox}%
  \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
    \usebeamerfont{title in head/foot}\insertshorttitle
  \end{beamercolorbox}%
  \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
    \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
\insertframenumber{} / \inserttotalframenumber\hspace*{2ex} 
  \end{beamercolorbox}}%
  \vskip0pt%
}

There are three beamercolorboxes with the width of one third of the \paperwidth each. If you want to modify the width of the boxes you can define a different template by copying this code in your file and change the wd parameters. You can choose the widths according to your needs, but you shoud make sure that the their sum is equal to \paperwidth. Moreover, you must enclose the definition between \makeatletter and \makeatother because @ is used in the code. An example is given by the following MWE (where the unused packaged of your example have been removed).

\documentclass[t]{beamer}
\usetheme{Madrid}

\definecolor{Gold}{RGB}{218,165,32}

%Defined Colour Theme and List Sizing
\setbeamercolor{structure}{fg = Gold}
\setbeamertemplate{navigation symbols}{}

\makeatletter
\defbeamertemplate*{footline}{Dan P theme}
{
  \leavevmode%
  \hbox{%
  \begin{beamercolorbox}[wd=.2\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
    \usebeamerfont{author in head/foot}\insertshortauthor\expandafter\beamer@ifempty\expandafter{\beamer@shortinstitute}{}{~~(\insertshortinstitute)}
  \end{beamercolorbox}%
  \begin{beamercolorbox}[wd=.6\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
    \usebeamerfont{title in head/foot}\insertshorttitle
  \end{beamercolorbox}%
  \begin{beamercolorbox}[wd=.2\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
    \usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
\insertframenumber{} / \inserttotalframenumber\hspace*{2ex} 
  \end{beamercolorbox}}%
  \vskip0pt%
}
\makeatother
%Opening Title Page
\title{Chapter 7 - Absolute Value and Reciprocal Functions}
\subtitle{Section 7.3 - Absolute Value Equations}
\date{}

\begin{document} %Slide 1
\maketitle
\end{document}

Output

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