1. ## x^2+75=0

What can I do to simplify $\displaystyle x^2+75=0$ ?
I could switch it around to equal $\displaystyle x^2=-75$, but any number times itself is going to equal a positive, so what can I do?! Will I end up with imaginary numbers?

2. Originally Posted by deathtolife04
Will I end up with imaginary numbers?
yes

3. Originally Posted by Jhevon
yes
OK so I could change x^2=-75 to x= + or - √-75

Then it would be:
√-75 = √75 * √-1 = + or - i√75

Could I take it any further than that or is that my final answer?

4. Originally Posted by deathtolife04
OK so I could change x^2=-75 to x= + or - √-75

Then it would be:
√-75 = √75 * √-1 = + or - i√75

Could I take it any further than that or is that my final answer?
that's good enough

5. Originally Posted by Jhevon
that's good enough

Could I simplify it to 5i√3 or would that be wrong?

6. Originally Posted by deathtolife04
Could I simplify it to 5i√3 or would that be wrong?
that's fine, except it's weird to have the i in the middle, put it in front (the archaic way to do it) or in the back: $\displaystyle 5 \sqrt {3}~i$