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Added labels to equation 6

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Kenneth John Odle 2023-07-16 15:48:49 -04:00
parent 754cf7230a
commit 4cd3b57761
1 changed files with 13 additions and 12 deletions
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complete-the-square.tex
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@ -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: 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} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\end{equation} \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: \noindent{}Here is the entire sequence all together:
\begin{align}\label{eq5} \begin{equation}\label{eq6}
\begin{split} \begin{aligned}
x^2+4x+1 &= 0 \\ x^2+4x+1 &= 0 && && &&\text{Original equation}\\
x^2+4x &= -1 \\ x^2+4x &= -1 && && &&\text{Step 2}\\
x^2+4x &= 3 \\ x^2+4x &= 3 && && &&\text{Step 3}\\
(x+2)^2 &= 3 \\ (x+2)^2 &= 3 && && && \text{Step 4}\\
\sqrt{(x+2)^2} &= \pm\sqrt{3} \\ \sqrt{(x+2)^2} &= \pm\sqrt{3} && && && \text{Step 5}\\
x+2 &= \pm\sqrt{3} \\ x+2 &= \pm\sqrt{3} && && && \text{Step 5}\\
x &= -2\pm\sqrt{3} x &= -2\pm\sqrt{3} && && &&\text{Step 6}
\end{split} %\end{split}
\end{align} \end{aligned}
\end{equation}
\pagestyle{lastpage}% Remove the header from the last page; comment this out if the document ends on an odd-numbered page \pagestyle{lastpage}% Remove the header from the last page; comment this out if the document ends on an odd-numbered page