Final answer:
The real number solutions to the equation 5x³=45x are x = -3, 0, 3, found by simplifying the equation and then taking the square root of both sides.
Step-by-step explanation:
To find all real number solutions for the equation 5x³=45x, we first simplify the equation by dividing both sides by 5x, assuming that x is not equal to 0:
x² = 9
Next, we take the square root of both sides to find the solutions for x:
x = ± 3
We also need to consider the solution x=0, which was assumed in our initial step to avoid division by zero. Therefore, the complete set of real number solutions to the equation 5x³=45x is x = -3, 0, 3.