Solve the equation -x^2 - 3x = 5 - 3x and re-express the answer as a complex number with the imaginary unit.
To solve the equation -x^2 - 3x = 5 - 3x, we can first combine like terms and move all terms to one side to get:
-x^2 - 3x + 3x = 5 - 3x + 3x
-x^2 = 5
Next, we can multiply both sides of the equation by -1 to isolate x^2:
(-1)(-x^2) = (-1)(5)
x^2 = -5
Finally, we take the square root of both sides, remembering to include the ± sign since we are dealing with complex numbers:
x = ±√(-5)
This simplifies to:
x = ±√5i
Therefore, the solution to the equation -x^2 - 3x = 5 - 3x expressed as a complex number with the imaginary unit is x = ±√5i.