Question

Please help me solve x^3-6x^2+6x=0.

Answer 1

Could I help you?

Answer 2

Hint:

\[x = \frac{ -b ± \sqrt{b^2 - 4ac} }{ 2a }\]

Answer 3

Hey, @Kira_Yamato!
It is a cubic equation, not quadratic!

Answer 4

Could I perhaps split the middle term so that I can solve the equation by grouping? I'm open to any other suggestions.

Answer 5

I don't think so.
But what I am sure about is that you can take xa s a common factors from all three terms!
agree with me?

Answer 6

Yes, so I get x(x^2-6x+6)=0. What now?

Answer 7

You are Awesome!

Answer 8

Now you have a quadratic equation which could be solved by the quadratic formula!
Are you familiar with it?

Answer 9

I used the quadratic formula to find that x=3+sqrt(3) and x=3-sqrt(3), so can x=0 be a solution?

Answer 10

Technically I'll say factorization of x yields a quadratic equation

Answer 11

yes, when you write
x (x^2-6x+6)=0
that is like A*B=0
if A is 0 you will get 0
if B is 0 you get 0

in this case if x=0 you get 0, so x=0 is a solution.

and of course of
x^2-6x+6=0
gives two more solutions

Answer 12

"so can x=0 be a solution?"
Yes, Of course, in addition to the two solutions you have gotten from the qu.formula!

Answer 13

Thank you all for helping me solve this equation!

Answer 14

That is with my pleasure!
Any Help... Any Time...
Are you persuaded?

Answer 15

Of course!

Answer 16

I am happy to hear that.
Thank you for learning!