4

I am having an issue with my equations. I would like to align 3 equations within 3 columns.

Currently my text is as follows:

\begin{align*}
 & = x^2 -12x +67 & = 6x^2 +24x +18 & = 9x^2 +7x +18 \\
 & = (x^2-12x+36)-36-67 & x^2+4x+3 & = 9\left(x^2+\dfrac{9}{7}x+2\right) \\ 
 & = (x-6)^2+31 & = (x+2)^2-1 &=  9\left(x^2+2\cdot \dfrac{45}{70} + \dfrac{45}{70}^2 -\dfrac{45}{70}^2 +2\right) \\
 & & & = 9\left[\left(x+\dfrac{45}{70}\right)^2+\dfrac{311}{196}\right]
\end{align*}

and the result:

enter image description here

Please help me find out out to space and align correctly my equations.

Thank you so much

  • 1
    It is not clear what you want. What would you like to be different? – Pieter van Oostrum Nov 19 '16 at 16:06
  • Thank you for asking, I would like the equations to be equally spaced. As you can see, there are different equations. x^2 - 12x + 67 6x^2+24x+18 9x^2+7x+18 I would like them to be equally spaced in terms of the horizontal and also aligned with each other – Arthur PL Nov 19 '16 at 16:09
  • The first equation x^2-12x+67 is correctly placed and aligned with the rest of it. However, the 2 others are all together which I don't want. – Arthur PL Nov 19 '16 at 16:11
  • I would like it to be as 3 blocks of equations equally spaced in between them. – Arthur PL Nov 19 '16 at 16:12
  • Mathematically there would need to be a factor 6 in the second and third equation in the middle column :) – Pieter van Oostrum Nov 19 '16 at 16:19
4

The align environment requires two & per column from the second one: one to introduce the new column, one to set the alignment point within this column.

Maybe you might want to use the flalign environment in the present case. You can compare both solutions in the following code.

I also took the liberty to correct the calculations in the 3rd column.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage[showframe]{geometry}
\usepackage{amsmath}

\begin{document}

\begin{align*}
    & = x² -12x +67 & & = 6x² +24x +18 & & = 9x² +7x +18 \\
    & = (x²-12x+36)-36-67 & & = 6(x²+4x+3) & & = 9\left(x²+\dfrac{7}{9}x+2\right) \\
    & = (x-6)²+31 & & = 6[(x+2)²-1] & & = 9\Biggl[x²+2 · \frac{7}{18} +{ \biggl(\frac{7}{18}\biggr)}^{\!2} - \biggl(\frac{7}{18}\biggr)^{\!2} +2\Biggr] \\
    & & & & & = 9\Biggl[\biggl(x+\frac{7}{18}\biggr)²+\frac{599}{324}\Biggr]
\end{align*}

\begin{flalign*}
  & = x² -12x +67 & & = 6x² +24x +18 & & = 9x² +7x +18 \\
  & = (x²-12x+36)-36-67 & & = 6(x²+4x+3) & & = 9\left(x²+\dfrac{7}{9}x+2\right) \\
  & = (x-6)²+31 & & = 6[(x+2)²-1] & & = 9\Biggl[x²+2 · \frac{7}{18} +{ \biggl(\frac{7}{18}\biggr)}^{\!2} - \biggl(\frac{7}{18}\biggr)^{\!2} +2\Biggr] \\
  & & & & & = 9\Biggl[\biggl(x+\frac{7}{18}\biggr)²+\frac{599}{324}\Biggr]
\end{flalign*}

\end{document} 

enter image description here

|improve this answer|||||
  • I would like to thank you very much for your help ! Thank you for correcting my math, appreciated it ^ ^ ! – Arthur PL Nov 19 '16 at 16:58
  • 1
    You're welcome. I'm always glad when I can help! – Bernard Nov 19 '16 at 18:21
3

Like this?

enter image description here

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{align*}
 & = x^2 -12x +67       && = 6x^2 +24x +18   && = 9x^2 +7x +18 \\
 & = (x^2-12x+36)-36-67 && = x^2+4x+3        && = 9\left(x^2+\dfrac{9}{7}x+2\right) \\
 & = (x-6)^2+31         && = (x+2)^2-1       && =  9\left(x^2+2\cdot \dfrac{45}{70} 
                                            + \dfrac{45}{70}^2 -\dfrac{45}{70}^2 +2\right) \\
 &                      &&                   && = 9\left[\left(x+\dfrac{45}{70}\right)^2
                                                +\dfrac{311}{196}\right]
\end{align*}
\end{document}
|improve this answer|||||
  • The {3} should be removed. – Pieter van Oostrum Nov 19 '16 at 16:20
  • thank you, i forget to remove it when test alignat ... – Zarko Nov 19 '16 at 16:22

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