Solve the equation.
-$$x ^ { 3 } - x = - 6 x ^ { 2 } + 6$$
A) $\{ 36 \}$
B) $\{ - 1,1 , - 6 \}$
C) $\{ 1 , - 6,6 \}$
D) $\{ - 6,6 \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^3 - x = -6x^2 + 6$, we first bring all terms to one side to get a polynomial equation: $x^3 + 6x^2 - x - 6 = 0$. Factoring by grouping, we get $x^2(x + 6) - 1(x + 6) = 0$, which simplifies to $(x^2 - 1)(x + 6) = 0$. This further factors into $(x - 1)(x + 1)(x + 6) = 0$, giving the roots $x = 1$, $x = -1$, and $x = -6$.

Solve the Equation x3−x=−6x2+6x ^ { 3 } - x = - 6 x ^ { 2 } + 6x3−x=−6x2+6

Solve the Equation $x ^ { 3 } - x = - 6 x ^ { 2 } + 6$