i need to solve this graphically but i forgot my graphing calculator at school x^3+2x=12x
You can solve x^3 + 2x = 12x using the following steps.
x^3 + 2x = 12x
take all the terms to one side
=> x^3 + 2x - 12x = 0
subtract the common terms
=> x^3 - 10 x =0
=> x (x^2 -10) =0
this gives either x = 0 or x^2 - 10 =0
For x^2 - 10 =0
x can be equal to sqrt 10 and - sqrt 10
So we have three values of x that solve the equation x = 0, x = sqrt 10 and x = -sqrt 10
The required values of x are 0, sqrt 10 and - sqrt 10
To solve x^3+2x=12x
Subtract 12x from both sides:
x^3+2x-12x = 0
x^3-10x = 0
x (x - sqrt10) (x+sqrt10 ) = 0
Equate the terms to zero.
x =0 or x- sqrt10 = 0 or x+sqrt10 =0
x = 0,
x-sqrt10 gives x = sqrt10.
x +sqrt10 gives x = -sqrt10.
Therefore we get 3 solutions of the cubic are x =0, x = -sqt10 and x= sqrt10.