+2440 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. |
| \(x=\pm2i\sqrt{6}\) | |
