[Tex/LaTex] Explaining equation steps (multiple line \text)

amsmathequations

I'm trying to explain my steps in an equation. The problem is that the text is longer than the line in the \flalign* environment, is there any way to make the text span over multiple lines while maintaining alignment?

Instead of just this:
enter image description here

I want it to look something like this:

enter image description here
This is my code:

\documentclass[a4paper,oneside,article,leqno]{memoir}
\pagestyle{title}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[danish]{babel}\renewcommand{\danishhyphenmins}{22}
\renewcommand{\danishhyphenmins}{22}
\usepackage{sistyle, amsmath}
\usepackage{mathtools,amssymb}
\usepackage[margin=1.0in]{geometry}
\begin{document}
\begin{flalign*}
GKA(a,b)&=\frac{1}{n}\sum\limits_{i=1}^{n}(y_i-(ax_i+b))^2 &&\text{Anvend hjælpesætning b.}\\
&=\frac{1}{n}\sum\limits_{i=1}^{n}(\underbrace{(y_i-\bar{y})}_\text{s}-\underbrace{a(x_i-\bar{x})}_\text{t}+\underbrace{(\bar{y}-(a\bar{x}+b)}_\text{u})^2&&\text{Anvend omskrivning 2.}\\
&=\frac{1}{n}\sum\limits_{i=1}^{n} 
\begin{pmatrix*}[l]
\vphantom{\frac{1}{n}\sum\limits_{i=1}^{n}}\underbrace{(y_i-\bar{y})^2}_\text{$s^2$}+\underbrace{a^2(x_i-\bar{x})^2}_\text{$t^2$}+\underbrace{(\bar{y}-(a\bar{x}+b))^2}_\text{$u^2$}\\
\vphantom{\frac{1}{n}\sum\limits_{i=1}^{n}}-\underbrace{2a(y_i-\bar{y})(x_i-\bar{x})}_\text{2st}+\underbrace{2(y_i-\bar{y})(\bar{y}-(a\bar{x}+b))}_\text{2su}\\
\vphantom{\frac{1}{n}\sum\limits_{i=1}^{n}}-\underbrace{2a(x_i-\bar{x})(\bar{y}-(a\bar{x}+b))}_\text{2tu}
\end{pmatrix*}&&\text{Gang med $\frac{1}{n}\sum\limits_{i=1}^{n}$ og brug hjælpesætning a.}\\ 
&=\frac{1}{n}\sum\limits_{i=1}^{n}(y_i-\bar{y})^2+\frac{1}{n}a^2\sum\limits_{i=1}^{n}(x_i-\bar{x})^2+\frac{1}{n}\sum\limits_{i=1}^{n}(\bar{y}-(a\bar{x}+b))^2&&\text{Brug at $V_1=$ gennemsnittet af $x_i$-erne}\\
&\quad-2a\cdot\frac{1}{n}\sum\limits_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})+2(\bar{y}-(a\bar{x}+b))\cdot\frac{1}{n}\sum\limits_{i=1}^{n}(y_i-\bar{y})\\
&\quad-2a(\bar{y}-(a\bar{x}+b))\cdot\frac{1}{n}\sum\limits_{i=1}^{n}(x_i-\bar{x})\\
&=V_2+a^2V_1+\frac{1}{n}\cdot n(\bar{y}-a\bar{x}-b)^2-2Ca+0-0\\
&=V_1\cdot a^2-2Ca+V_2+(\bar{y}-a\bar{x}-b)^2\\
&=f(a)+g(a,b)
\end{flalign*}
\end{document}

Best Answer

In addition to placing the explanatory text that is supposed to be automatically wrapped in a \parbox of a suitably chosen width (in the code below, I've chosen 4.5cm) that sets its material in ragged-right mode (in order to avoid big interword gaps), you may also want to eliminate all unneeded \text directives as well as get rid of all but one of the \limits modifiers; in display-math mode, \sum and \sum\limits produce the exact same output. Separately, since GKA presumably doesn't represent the product of variables named G, K, and A, you should write that term as either \mathit{GKA} or \mathrm{GKA}.

enter image description here

\documentclass[a4paper,oneside,article,leqno]{memoir}
\pagestyle{title}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\usepackage[danish]{babel}
\renewcommand{\danishhyphenmins}{22}

\usepackage{sistyle, mathtools, amssymb}
\usepackage[margin=1.0in]{geometry}

\newcommand\textbox[2]{\parbox{#1}{\raggedright #2}}
\newcommand\tallstrut{\vphantom{\sum\limits_{i=1}^{n}}} % tall typographic strut

\begin{document}
\begin{flalign*}
\mathit{GKA}(a,b)
&=\frac{1}{n}\sum_{i=1}^{n}(y_i-(ax_i+b))^2 
&&\text{Anvend hjælpesætning b.}\\
&=\frac{1}{n}\sum_{i=1}^{n} \bigl(\,
    {\underbrace{(y_i-\bar{y})}_{s}} 
   -{\underbrace{a(x_i-\bar{x})}_{t}} 
   +{\underbrace{(\bar{y}-(a\bar{x}+b)}_{u}}\,\bigr)^2
&&\text{Anvend omskrivning 2.}\\
&=\frac{1}{n}\sum_{i=1}^{n} 
\begin{pmatrix*}[l]
{\underbrace{(y_i-\bar{y})^2}_{s^2}}+
{\underbrace{a^2(x_i-\bar{x})^2}_{t^2}}+
{\underbrace{(\bar{y}-(a\bar{x}+b))^2}_{u^2}}\\
\tallstrut-{\underbrace{2a(y_i-\bar{y})(x_i-\bar{x})}_{2st}}
+{\underbrace{2(y_i-\bar{y})(\bar{y}-(a\bar{x}+b))}_{2su}}\\
\tallstrut-{\underbrace{2a(x_i-\bar{x})(\bar{y}-(a\bar{x}+b))}_{2tu}}
\end{pmatrix*}
&&\textbox{4.5cm}{Gang med $\frac{1}{n}\sum_{i=1}^{n}$ 
                  og brug hjælpesætning a.}\\ 
&=\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})^2+
  \frac{1}{n}a^2\sum_{i=1}^{n}(x_i-\bar{x})^2+
  \frac{1}{n}\sum_{i=1}^{n}(\bar{y}-(a\bar{x}+b))^2
&&\textbox{4.5cm}{Brug at $V_1=$ gennemsnittet af $x_i$-erne}\\
&\quad-2a\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})
 +2(\bar{y}-(a\bar{x}+b))\frac{1}{n}\sum_{i=1}^{n}(y_i-\bar{y})\\
&\quad-2a(\bar{y}-(a\bar{x}+b))\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})\\
&=V_2+a^2V_1+\frac{1}{n} n(\bar{y}-a\bar{x}-b)^2-2Ca+0-0\\
&=V_1 a^2-2Ca+V_2+(\bar{y}-a\bar{x}-b)^2\\
&=f(a)+g(a,b)
\end{flalign*}
\end{document}
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