To solve the equation \(-x^2 - 3x = 5 - 3x\), we first want to rearrange the equation to set it to zero:
- Start by adding \(3x\) to both sides:
\[ -x^2 - 3x + 3x = 5 \]
This simplifies to:
\[ -x^2 = 5 \]
- Next, multiply both sides by \(-1\):
\[ x^2 = -5 \]
- Now, take the square root of both sides. Remember that when you take the square root of a negative number, you will use the imaginary unit \(i\):
\[ x = \pm \sqrt{-5} \]
This can be rewritten as:
\[ x = \pm i\sqrt{5} \]
Thus, the solution to the equation expressed as a complex number with the imaginary unit is:
\[ x = \pm i\sqrt{5} \]
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