# Mixing bracket types when writing solutions?

Gold Member
Is it okay to mix the types of brackets you use when writing out a solution to help make it a bit clearer?

For example:

If I was completeing the square with:

$$3x^{2} + 5x -2 = 0$$

I would factor out the 3 onto square brackets like this:

$3 \left[x^{2} + \frac{5}{3}x - \frac{2}{3} \right] = 0$

Then do my competing the square with round brackets:

$$3 \left[ \left( x + \frac{5}{6} \right)^{2} -\left(\frac{5}{6}\right)^{2} - \frac{2}{3} \right] = 0$$

Last edited:

Yes, that is perfectly ok. It is even recommended.

Also, I think you made some calculations errors when completing the square.

Gold Member
Yes, that is perfectly ok. It is even recommended.

Also, I think you made some calculations errors when completing the square.

Thanks,

There probably are errors as I was about ready to punch my tv trying to get latex to put in the brackets, turns out I had spelled right as rigt.

Edit: I think fixed the mistake.

mfb
Mentor
In your example, I would divide both sides by 3, then you do not need the big brackets at all.
If that is not possible, [ ] are fine.

Gold Member
In your example, I would divide both sides by 3, then you do not need the big brackets at all.
If that is not possible, [ ] are fine.

In some questions they ask for the answer in the form, $$a(x - b)^{2} + c$$

But yeah if I was just solving to find x I'd divide through, I probably have a few better examples here of where you could use multiple brackets but that was what came to mind first.

dextercioby
Homework Helper
If the question is indeed about 'bracketing' and not about completing the square, then I can only say that what you're doing is not right in my book, brackets 'evolve', as the expression gets more complicated. First you place a round bracket, then if you need to put a round bracket into the first round bracket, the initial round brackets become square. If furthermore, you need a new round bracket into the newly created round bracket, the square one will become a brace, the previously existing round bracket will become square. And more, well, the number of braces will increase, since we don't have new types anymore.

Mark44
Mentor
Maybe it's a British English vs. American English thing, but as I learned them, there are
• brackets - [] (AKA "square brackets", which IMO is redundant, since brackets already are square)
• braces - {} (AKA "curly" brackets)
• parentheses - () (AKA "round" brackets)

dextercioby
Homework Helper
Apparently Dirac called these things <> brackets, else he would not have coined the words bra for <| and ket for |>.

Mark44
Mentor
They're also called angle brackets. They're not normally used for grouping mathematical expressions, I don't believe.

Not to mention those things that hold your trousers up.

Mark44
Mentor
Belts? :tongue:

NascentOxygen
Staff Emeritus