Solve the equation −x2−3x=5−3x
and re-express the answer as a complex number with the imaginary unit.
explain how you get the answer and the answer is √5
To solve the equation −x^2−3x=5−3x, we can start by simplifying both sides. We notice that both sides have a −3x term, so we can subtract it from both sides to simplify the equation:
−x^2 − 3x + 3x = 5 − 3x + 3x
Simplifying further:
−x^2 = 5
Now, we want to solve for x. To do this, we'll isolate x^2 by multiplying both sides of the equation by -1:
x^2 = -5
Finally, to find x, we take the square root of both sides:
√(x^2) = √(-5)
Since we want to express the answer as a complex number, we know that the square root of a negative number is an imaginary number. Therefore, we can express the answer as:
x = ±√5 i
So, the solution to the equation −x^2−3x=5−3x as a complex number is ±√5 i.