From 4cd3b57761e5917ce82f45ed840261ccc529e8c8 Mon Sep 17 00:00:00 2001
From: Kenneth Odle <kenneth.odle@kjodle.net>
Date: Sun, 16 Jul 2023 15:48:49 -0400
Subject: [PATCH] Added labels to equation 6

---
 complete-the-square.tex | 25 +++++++++++++------------
 1 file changed, 13 insertions(+), 12 deletions(-)

diff --git a/complete-the-square.tex b/complete-the-square.tex
index af60cc5..7832c26 100644
--- a/complete-the-square.tex
+++ b/complete-the-square.tex
@@ -111,7 +111,7 @@ For equations that are not easily factored, a general solution called ``the 	qua
 
 For any equation of the form $ax^2+bx+c=0$, the solution can be found by using:
 
-\begin{equation}
+\begin{equation}\label{eq5}
 x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
 \end{equation}
 
@@ -156,17 +156,18 @@ Conventionally, we would write this as $x=-2+\sqrt{3}$ or $x=-2-\sqrt{3}$.
 
 \noindent{}Here is the entire sequence all together:
 
-\begin{align}\label{eq5}
-\begin{split}
-x^2+4x+1 &= 0 \\
-x^2+4x &= -1 \\
-x^2+4x &= 3 \\
-(x+2)^2 &= 3 \\
-\sqrt{(x+2)^2} &= \pm\sqrt{3} \\
-x+2 &= \pm\sqrt{3} \\
-x &= -2\pm\sqrt{3}
-\end{split}
-\end{align}
+\begin{equation}\label{eq6}
+\begin{aligned}
+x^2+4x+1 &= 0 && && &&\text{Original equation}\\
+x^2+4x &= -1 && && &&\text{Step 2}\\
+x^2+4x &= 3  && && &&\text{Step 3}\\
+(x+2)^2 &= 3 && && && \text{Step 4}\\
+\sqrt{(x+2)^2} &= \pm\sqrt{3} && && && \text{Step 5}\\
+x+2 &= \pm\sqrt{3} && && && \text{Step 5}\\
+x &= -2\pm\sqrt{3} && && &&\text{Step 6}
+%\end{split}
+\end{aligned}
+\end{equation}
 
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