この配置の何が問題になっていますか？

Question

この配置の何が問題になっていますか？

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環境：

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まず、長い投稿をお詫びします。

そのため、LaTexの記事ドキュメントで初めてアライメント環境を使用していますが、あまり成功していません。これが私の記事文書の前文です：

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質問

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この記事では、いくつかの方程式を調整したかったので、オンラインのいくつかのガイドに基づいて次のコードを使用しました。

We can now use the Pythagorean Theorem to find PE in two different equations which utilise $x$ and hence solve for $x$:

\emph{From $\triangle$PEB:}

\begin{align*}
PE &= $\sqrt{BP^2 - x^2}$ \\
&= $\sqrt{10^2 - x^2}$ \\
&= $\sqrt{100 - x^2}$
\end{align*}

しかし、私は結果としてこれを取得します：

そして、エラーログも自分自身を修正しているようです（つまり、何かを修正してから、間違っていると思われる修正を修正しようとします...あなたは何を知っていますか？ログを見てください:)

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing { inserted.
<inserted text> 
                {
l.65 \end{align*}
                 
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Extra }, or forgotten $. <recently read> } l.65 \end{align*} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing { inserted. <inserted text> { l.65 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. ! Extra }, or forgotten $.
<recently read> }
                 
l.65 \end{align*}
                 
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing { inserted.
<inserted text> 
                {
l.65 \end{align*}
                 
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Extra }, or forgotten $. <recently read> } l.65 \end{align*} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $.
<recently read> }
                 
l.65 \end{align*}
                 
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \omit.
\math@cr@@@ ...@ \@ne \add@amps \maxfields@ \omit 
                                                  \kern -\alignsep@ \iftag@ ...
l.65 \end{align*}
                 
I expect to see \omit only after tab marks or the \cr of
an alignment. Proceed, and I'll ignore this case.

! Missing { inserted.
<inserted text> 
                {
l.65 \end{align*}
                 
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Extra }, or forgotten $. <recently read> } l.65 \end{align*} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing \endgroup inserted. <inserted text> \endgroup l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Misplaced \omit. \math@cr@@@ ...@ \@ne \add@amps \maxfields@ \omit \kern -\alignsep@ \iftag@ ... l.65 \end{align*} I expect to see \omit only after tab marks or the \cr of an alignment. Proceed, and I'll ignore this case. ! Missing { inserted. <inserted text> { l.65 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. ! Missing } inserted. <inserted text> } l.65 \end{align*} I've inserted something that you may have forgotten. (See the <inserted text> above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing $ inserted.
<inserted text> 
                $ l.65 \end{align*} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $.
<recently read> }
                 
l.65 \end{align*}
                 
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'.

! Missing $ inserted. <inserted text> $
l.65 \end{align*}
                 
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing \endgroup inserted.
<inserted text> 
                \endgroup 
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
l.65 \end{align*}
                 
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced \omit.
\math@cr@@@ ...@ \@ne \add@amps \maxfields@ \omit 
                                                  \kern -\alignsep@ \iftag@ ...
l.65 \end{align*}
                 
I expect to see \omit only after tab marks or the \cr of
an alignment. Proceed, and I'll ignore this case.

! Missing { inserted.
<inserted text> 
                {
l.65 \end{align*}
                 
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

したがって、基本的にエラーログが行ったのは私を混乱させることだけであり、何をすべきかよくわかりません。これを修正するために感謝します！

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ありがとう！

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Answer 1

したがって、コメントで指摘されているように、これは比較的簡単な修正です-言い換えれば、長い投稿に対する比較的短い答えです:)：

align環境は、その性質上、すでに数式モードであるので、使用しないで、$その中に。削除する$と、目的の出力が得られます。

すなわち

We can now use the Pythagorean Theorem to find PE in two different equations which utilise $x$ and hence solve for $x$:

\emph{From $\triangle$PEB:}

\begin{align*} PE &= \sqrt{BP^2 - x^2} \\ &= \sqrt{10^2 - x^2} \\ &= \sqrt{100 - x^2} \end{align*}