How to prioritize signs

Question

Make n the subject of the formula: $$ P=400n^2-1280 $$ Why is the answer $$ n= \sqrt\frac{P+1280}{400} $$ And not $$ n=\sqrt{\frac{P}{400}+1280} $$

Answer 1

Hint: we have $$P+1280=400n^2$$ and then you must divide the whole sum by $$400$$ so you get $$\frac{P+1280}{400}=n^2$$ If you divide at first by $400$ you will get $$\frac{P}{400}=n^2-\frac{1280}{400}$$

Answer 2

It is entirely possible to divide by 400 first thing you do. However, when you do this, you have to divide every term of the equation by 400, including the negative 1280 term.

$$P = 400n^2 - 1280$$ $$\frac{P}{400} = n^2 - \frac{1280}{400}$$ $$\frac{P}{400} + \frac{1280}{400} = n^2$$ $$\frac{P + 1280}{400} = n^2$$ $$\sqrt{\frac{P + 1280}{400}} = n$$ $$n = \sqrt{\frac{P + 1280}{400}}$$

A simple example should make it quite easy to see why you have to do this.

$$2 + 2 = 4$$ $$2 + 1 = 2$$ $$3 = 2$$

So, in order to have all of mathematics work, this would be correct.

$$2 + 2 = 4$$ $$1 + 1 = 2$$ $$2 = 2$$

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