solve X^2=-9

Question

solve X^2=-9

bibby · Answer

underfined. Nothing squared will ever give you a negative number.
for example if it was 9. You could take the square roots and get 3. but -3^2 will give you positive 9

zepdrix · Answer

Taking the square root of both sides gives us,$$\huge x= \pm \sqrt{-9}$$We can rewrite this, factoring out a negative 1 like so,$$\huge x= \pm \sqrt9 \color{cadetblue}{\sqrt{-1}}$$From here we need to recall an important identity. The imaginary unit i.$$\huge \color{cadetblue}{i=\sqrt{-1}}$$Which will allow us to write our problem as such,$$\huge x= \pm \sqrt9 \color{cadetblue}{i}$$Taking the square root of 9 gives us,$$\huge x=3i, \qquad x=-3i$$
These two solutions.

Bibby is certainly correct that there are no real solutions. But these are your two complex solutions for x. Hope that helps! :)

bibby · Answer

Based off of his other questions I didn't think he was doing complex numbers, gah

zepdrix · Answer

Ah fair enough! :) My long-winded response was really just so I could get some practice using the \color function in LaTeX, hehe.

anonymous · Answer

lol im so lost so is bibby right?

zepdrix · Answer

I would hope you would know that based on whatever math class you're taking :D Have you learned about complex numbers yet? The number i?

anonymous · Answer

yea thats why i asked and if i need the help im gonna ask for it

zepdrix · Answer

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