Question

What are the values of x in this equation?

Answer 1

Answer:

A. x = 0, x = -3, x = 2, and x = -2

Step-by-step explanation:

$x^{4} +12x=4x^{2} +3x^{3}$

by moving the terms on the left side to the right side

$x^{4} -3x^{3} -4x^{2} +12x = 0$

factor an $x^{3}$ from $x^{4} -3x^{3}$

and factor - 4$x$ from $-4x^{2} +12x$

the equation becomes :

$x^{3} (x - 3 )-4x (x - 3)$ = 0

take $(x - 3)$  as  a common factor the equation becomes :

$(x-3)(x^{3}-4x )$ = 0

thus

$x - 3 = 0$⇒$x = 3$

and

$x^{3} - 4x = 0$ by factoring an x we get :

$x(x^{2}-4 ) =0$ ⇒ $x$ = 0 and $x^{2} - 4 = 0$

$x^{2} - 4 =0$⇒$x = 2$ and $x = -2$

Thus

the values are :

x = 0, x = -3, x = 2, and x = -2