Align multiple equations under longer equation

Question

I want to do what this MWE would do if the hspace{-1in} actually moved that second alignment column to the left, underneath the big quadratic formula.

\documentclass{article}

\usepackage{amsmath}

\begin{document}
    \begin{alignat*}{2}
        x &= \frac{-(-13) \pm \sqrt{(-13)^2 - 4(7)(0)}}{2(7)}\\
          &= \frac{13 \pm \sqrt{169}}{14}\\
          &= \frac{13 + 13}{14}& \hspace{-1in} &\phantom{=} \frac{13-13}{14}\\
          &= \frac{26}{14}& &= \frac{0}{14}\\
          &= \frac{13}{7}& &= 0
    \end{alignat*}
\end{document}

I'm trying to get rid of the unnecessary white space, and both equations in the third line are solutions of the equation in the first line, so it makes sense to have them underneath. But I still want the left one aligned vertically with the first two equal signs and the second one aligned vertically.

Any ideas?

Answer 1

You could enclose the quadratic in an rlap:

you could also add a horizontal space to separate out the two equations:

Notes:

• See Can I use \clap, \rlap and \llap in math mode? for info on rlap.

• The mathtools package provides math equivalent macros so you don't need to go back into math mode.

Code:

\documentclass{article}

\usepackage{amsmath}

\begin{document}
    \begin{alignat*}{2}
        x &= \rlap{$\displaystyle \frac{-(-13) \pm \sqrt{(-13)^2 - 4(7)(0)}}{2(7)}$}\\
        &= \frac{13 \pm \sqrt{169}}{14}\\
        &= \frac{13 + 13}{14} &&\phantom{=} \frac{13-13}{14}\\
        &= \frac{26}{14}      &&= \frac{0}{14}\\
        &= \frac{13}{7}       &&= 0
    \end{alignat*}
    \begin{alignat*}{2}
        x &= \rlap{$\displaystyle \frac{-(-13) \pm \sqrt{(-13)^2 - 4(7)(0)}}{2(7)}$}\\
        &= \frac{13 \pm \sqrt{169}}{14}\\
        &= \frac{13 + 13}{14} &\qquad&\phantom{=} \frac{13-13}{14}\\
        &= \frac{26}{14}      &&= \frac{0}{14}\\
        &= \frac{13}{7}       &&= 0
    \end{alignat*}
\end{document}

Code: (with mathtools):

\documentclass{article}

\usepackage{mathtools}% includes amsmath

\begin{document}
    \begin{alignat*}{2}
        x &= \mathrlap{\frac{-(-13) \pm \sqrt{(-13)^2 - 4(7)(0)}}{2(7)}}\\
        &= \frac{13 \pm \sqrt{169}}{14}\\
        &= \frac{13 + 13}{14} &\qquad&\phantom{=} \frac{13-13}{14}\\
        &= \frac{26}{14}      &&= \frac{0}{14}\\
        &= \frac{13}{7}       &&= 0
    \end{alignat*}
\end{document}