Solve the equation -x^2 -3x=5-3x and re-express the answer a complex number with the imaginary unit.
To solve the equation -x^2 - 3x = 5 - 3x, we can start by simplifying both sides of the equation:
-x^2 - 3x = 5 - 3x
Adding 3x to both sides, we get:
-x^2 = 5
To solve for x, we need to isolate the x term. We can do this by multiplying both sides by -1:
x^2 = -5
From here, we can take the square root of both sides to solve for x:
x = ±√(-5)
Since taking the square root of a negative number results in an imaginary number, we can express the answer as a complex number. In this case, the answer would be:
x = ± √5i
So the solution to the equation -x^2 - 3x = 5 - 3x, expressed as a complex number, is x = ± √5i.