Find all Real number Solutions.
2x^3-6x^2=0

Question

Find all Real number Solutions.
2x^3-6x^2=0

hero · Answer

2x^3 - 6x^2=0

Factor out 2x^2 to get:
2x^2(x - 3) = 0

Divide both sides by 2:
x^2(x - 3) = 0

Use zero product property:
x^2 = 0
x - 3 = 0

Finish solving for x

anonymous · Answer

why do you divide both sides by 2?

hero · Answer

To reduce the expression on the left to a simpler form so that we only deal with what is relevant to solve for x in the next step.

anonymous · Answer

i got x=3 and x=+-o, is that right?

hero · Answer

There's no such thing as ±0 since zero is neither positive or negative, but neutral. Therefore, x = 0 or x = 3 is the correct answer, but great job either way.

hero · Answer

Furthermore, square root and square are inverses of each other, so they cancel. Therefore you are only taking the square root of zero on the other side. You don't have to write ± in front of the square root symbol.

anonymous · Answer

Okay, but if there was a number that wasn't a perfect square in the same place as the zero, the +- would be there right?

hero · Answer

I just addressed that just a second ago if you want to read what I posted.

hero · Answer

$$\sqrt{x^2} = x$$

hero · Answer

Anytime you have a perfect square, it will cancel evenly with its root, leaving only the number remaining.