Get rid of R formulas outside the rmarkdown pdf borders - r

Question

I have a following problem. I prepare a project in R and always get a problem that after knitting formulas are partially outside of pdf document.
Formula issue formatting description
There is a post with similar problem, but it didn't help (R Markdown Knitr to PDF Code Outside Margin)
I have also tried adding "\\", but it also didn't help.
Is there any easy solution about how to organize auto line breaks in formulas in Rmarkdown? I don't want to convert html to pdf since I would lose all internal references then.
I will be very grateful if someone would help!!!
Update:
Here is a sample formula for rmarkdown:
---
title: "Code Sample"
output:
pdf_document: default
html_document: default
---
1) $$ (\sum_{i = 1}^{N} \|x_i - \mu - V_q \lambda_i\|^2)'_\mu = \\
(\sum_{i = 1}^{N} (x_i - \mu - V_q \lambda_i)^T (x_i - \mu - V_q \lambda_i))'_\mu = \\
= \sum_{i = 1}^{N} ((x_i - \mu - V_q \lambda_i)^T (x_i - \mu - V_q \lambda_i))'_\mu = \\
= \sum_{i = 1}^{N} 2 (x_i - \mu - V_q \lambda_i) \cdot (-1) = \\
= \sum_{i = 1}^{N} -2 \cdot (x_i - \mu - V_q \lambda_i) \\
\text{since the degree was 2 and the sign of $\mu$ was '-' (minus)} $$

Answer 1

Welcome to SO, #Irina Mironova!
You could try this, using & to align and \\ to break lines:
---
title: "Aligned equations"
author: "bttomio"
date: "4/7/2021"
output: pdf_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
\begingroup\small
\begin{equation}
\begin{aligned}
ER_t
= & \lambda_1 + \sum_{i=0}^k\alpha_{11i}ER_{t-1} + \sum_{j=k+1}^p\alpha_{12j}ER_{t-j} + \sum_{i=0}^k\beta_{11i}CT_{t-1} + \sum_{j=k+1}^p\beta_{12j}CT_{t-j} \\
+ & \sum_{i=0}^k\gamma_{11i}IRD_{t-1} + \sum_{j=k+1}^p\gamma_{12j}IRD_{t-j} + \sum_{i=0}^k\delta_{11i}VIX_{t-1} + \sum_{j=k+1}^p\delta_{12j}VIX_{t-j} \\
+ & \sum_{i=0}^k\phi_{11i}SM_{t-1} + \sum_{j=k+1}^p\phi_{12j}SM_{t-j} + \sum_{i=0}^k\psi_{11i}SMUS_{t-1} + \sum_{j=k+1}^p\psi_{12j}SMUS_{t-j} +\varepsilon_{1t}
\end{aligned}
\end{equation}
\endgroup
-output
UPDATE
Following the equation supplied by the OP, here is a working example:
---
title: "Code example"
author: "bttomio"
date: "4/9/2021"
output: pdf_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
\begingroup
\begin{equation}
\begin{aligned}
(\sum_{i = 1}^{N} \|x_i - \mu - V_q \lambda_i\|^2)'_\mu = \\
(\sum_{i = 1}^{N} (x_i - \mu - V_q \lambda_i)^T (x_i - \mu - V_q \lambda_i))'_\mu = \\
\sum_{i = 1}^{N} ((x_i - \mu - V_q \lambda_i)^T (x_i - \mu - V_q \lambda_i))'_\mu = \\
\sum_{i = 1}^{N} 2 (x_i - \mu - V_q \lambda_i) \cdot (-1) = \\
\sum_{i = 1}^{N} -2 \cdot (x_i - \mu - V_q \lambda_i) \\
\text{since the degree was 2 and the sign of $\mu$ was '$-$' (minus)}
\end{aligned}
\end{equation}
\endgroup
-output

Answer 2

What happens when you use specific margins in PDF output?
---
title: "Habits"
author: John Doe
date: March 22, 2005
geometry: "left=3cm,right=3cm,top=2cm,bottom=2cm"
output: pdf_document
---