i need to solve this graphically but i forgot my graphing calculator at school x^3+2x=12x

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william1941 | College Teacher | (Level 3) Valedictorian

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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

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve x^3+2x=12x

Subtract 12x from both sides:

x^3+2x-12x = 0

x^3-10x = 0

x(x^2-10)

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.

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