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What is the solution of the equation over the complex numbers?

x^2+24=0

 Oct 9, 2017
 #1
avatar+637 
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Subtract 24 from both sides. 

 

x ^ 2 = -24

 

x = 24i

 Oct 9, 2017
 #2
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It's asking for 2 answers

Guest Oct 9, 2017
 #3
avatar+2340 
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By definition, \(\sqrt{x^2}=|x|\). I know this because if you graph both functions, the output will be the same.

 

\(x^2+24=0\) Subtract 24 from both sides.
\(x^2=-24\) Take the square root from both sides.
\(|x|=\sqrt{-24}\) The absolute value symbol means that the answer is in its positive and negative forms.
\(x=\pm\sqrt{-24}\) Now, let's change the square root to an imaginary form. We can apply the radical rule that \(\sqrt{-a}=\sqrt{-1}\sqrt{a}\)
\(x=\pm\sqrt{24}\sqrt{-1}\) We know that by definition, \(i=\sqrt{-1}\)
\(x=\pm i\sqrt{24}\) We can simplify the square root of 2 to its simplest radical form.
\(x=\pm2i\sqrt{6}\)  
   
 Oct 9, 2017

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