Question

i need to solve the equation x^3=9x.
it looks like it's supposed to be simple? but im lost...

Answer 1

write it as
x^3 - 9x = 0
now can you factor the left side?

Answer 2

what is common to x^3 and 9x?

Answer 3

x right?
so we have
x(x^2 - 9) = 0

can you continue/

Answer 4

if we have 2 functions multiplied together to give 0 then either of them will be 0

Answer 5

Im not sure how to continue from this point.. x(x^2-9)=0 but then what? I'm not sure how the final answer is supposed to look

Answer 6

Why did you stop factoring? Go!!

Answer 7

x^2 - 9

Answer 8

- do you recall the difference of 2 squares?

Answer 9

wait... where did you get x6-9 from i feel like im missing something significant here

Answer 10

- that was a typo!
i meant x^2 - 9

Answer 11

oh okay phew-- so wait where we are now.. argh... I'm sorry I'm still confused... I don't know what i can factor out ?

Answer 12

x^2 - 9 is a difference of 2 squares x^2 is a perfect square and so is 9

Answer 13

so square root of x^2 is x and square root of 9 is 3
so we write these into 2 parentheses and + sign goes into one parenthese and - sign in the other
x^2 - 9 = (x + 3)(x - 3)

Answer 14

so now we have
x(x^2 - 9) = 0
x(x + 3)(x - 3) = 0

Answer 15

this means x and x + 3 and x- 3 can all be 0

Answer 16

so... okay that makes a bit more sense now.. so would that be the final answer?

Answer 17

no we need to find the values of x by solving 3 simple equations
x = 0 - that's one root

x + 3 = 0
and
x - 3 = 0

Answer 18

x + 3 = 0 so x = ?

Answer 19

x would equal 3 and -3 right?

Answer 20

yes
and dont forget the x = 0

Its a cubic equation ( as it hace x^3 in it) so there will be 3 solutions

the solution set is {0, -3 , 3}

Answer 21

okay, i think I have a bit more of a grip on it now. Thank you so much for your help, I appreciate it a lot

Answer 22

yw