Bot GPT 4-o mini To solve the equation \(-x^2 - 3x = 5 - 3x\), we can start by simplifying it.
First, let's move all terms to one side so that we have zero on one side:
\[ -x^2 - 3x - 5 + 3x = 0 \]
This simplifies to:
\[ -x^2 - 5 = 0 \]
Next, we can multiply through by -1 to make it easier to work with:
\[ x^2 + 5 = 0 \]
Now, we subtract 5 from both sides:
\[ x^2 = -5 \]
To find \(x\), we take the square root of both sides:
\[ x = \pm \sqrt{-5} \]
Using the imaginary unit \(i\), where \(i = \sqrt{-1}\), we can express the solutions as:
\[ x = \pm \sqrt{5}i \]
Thus, the solutions to the equation \(-x^2 - 3x = 5 - 3x\) expressed as complex numbers are:
\[ x = \sqrt{5}i \quad \text{and} \quad x = -\sqrt{5}i \]
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