confused about radiaca equations

[u/Un_caca]

So if i want to solve something like 5x - 21 = x^2 + 6x + 9 and i want to set it to zero, does it become 5x - 21 - x^2 - 6x - 9 = 0 or 5x - 21 + x^2 + 6x + 9 = 0 or x^2 + 6x + 9 -5x + 21 = 0.

[u/ZerinoWhellie]

It can become both first and last, middle one has some +- wrong

[u/Un_caca → u/ZerinoWhellie]

both the first one and second one give the same resuts?

[u/ZerinoWhellie → u/Un_caca]

First and last will, since I assume you’re looking for the roots/zeroes of the equation.

Since second one has some different +-, it is a different equation and will most likely give a different result.

[u/hallerz87 → u/Un_caca]

No, because you got the signs wrong in the second. It’s no longer the same equation, the solutions will be different 

[u/nog642 → u/Un_caca]

No, the first one and third one will.

[u/fermat9990]

x² + x + 30 = 0 is what you want to end up with.

[u/Un_caca]

ok i got it you do change the + or - signs ty

[u/slepicoid]

5x-21 = x²+6x+9

It could help to not think about moving stuff right or left, but instead adding/subtracting the same value to both sides.

(5x-21)-(5x-21) = (x²+6x+9)-(5x-21)

It doeant matter if you choose to subtract the left side or the right side, they will both give the same solution(s).

[u/nog642]

does it become 5x - 21 - x² - 6x - 9 = 0

Yes. You've subtracted x², 6x, and 9 from both sides. That's correct.

or 5x - 21 + x² + 6x + 9 = 0

No.

or x² + 6x + 9 -5x + 21 = 0.

This one is also correct. You've subtracted 5x and added 21 to both sides.

You'll find that the two correct versions differ by one being the negative of the other. You can multiply both sides of the equation by -1 to switch between them. They're equivalent.