# Why ${x = 2a^2}$ becomes ${a = \pm \sqrt{x/2}}$ when want to get ${a}$

Backstory: I've never had great math classes in school but college will require me to know everything from basics to what I guess is the more advanced stuff, I have 1.5 years to do this.

All I was tought were little memory tricks to remember how to solve simple "elementary algebra", as I'm giving an example below.

${x = 2a^2}$ in order to get ${x}$ you need to "reverse" the formula, so ${a = \pm \sqrt{x/2}}$

though I've never been tought why this is, or how to apply it to other things, and I can't seem to get the hang of it on my own with google searches.

It'd be great is someone could explain how and/or why this is.

sorry if this is a bad question.

• If $x=2a^2$ then it is not true that $a=\sqrt{x/2}$ in general. Jan 24, 2017 at 9:18
• $\pm \sqrt{\frac{x}{2}}$ Jan 24, 2017 at 9:19
• Am I the only one wondering how OP knows LaTeX but doesn't know pre-algebra? Jan 24, 2017 at 9:26
• @Nameless oh, well, there is a community post in the meta that explains how it works in great detail
– Grey
Jan 24, 2017 at 9:46

You solve equations step by step. So, if you start with $x=2a^2$, and you want to get to an expression for $a$, you start by "isolating" $a$ to one side. In this case, it's best to divide the equation by $2$ to get

$$a^2=\frac x2.$$

Once here, you need to remember that $a^2=b$ if and only if $a=\pm\sqrt b$, and you are done.

The important question here is "How do I remember the important things", and there are several things that help with that. The most important things are:

1. Practice
2. A little more practice
3. A touch of practice to top it off.

What I want to point out is that it takes hard work to learn math. It's worth it, of course, but there's no other way. And there's no such thing as "bad at math", there's just something like "never got around to actually practice math". I promise you that if you work on calculus problems for 2 hours each day, you will see a huge difference in a month or two.

Try to be systematic about these things. This means, grab a textbook, and work through it cover to cover. Read a chapter, then solve the exercises before moving on.

Edit:

Other users suggested other important points in learning:

1. Making sure what you learn is true - this comes with practice (non-true things will be useless to you) and from using common textbooks.
2. Remember arguments and ideas instead of results or formulas. - again, practice helps here, because if you only remember results and formulas, you won't be able to solve harder practice problems.
• It would help the OP if he remembered important true things!! So trying to understand what you memorize before memorizing it can't hurt. Jan 24, 2017 at 9:21
• 4. Remember arguments and ideas instead of results and formulas.
– user378947
Jan 24, 2017 at 9:22