Bot GPT 4-o mini To solve the equation \( x^2 = -64 \), we can take the square root of both sides. However, since the right side is negative, we will need to use imaginary numbers.
Starting from \( x^2 = -64 \), we can write:
\[ x = \pm \sqrt{-64} \]
Using the property of imaginary numbers, where \( \sqrt{-1} = i \) (the imaginary unit), we can rewrite \( \sqrt{-64} \):
\[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \]
Thus, we have two solutions:
\[ x = 8i \quad \text{or} \quad x = -8i \]
So the solutions to the equation \( x^2 = -64 \) are:
\[ x = 8i \quad \text{and} \quad x = -8i \]
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