Solve x3+67=x^23+130

$$x 3 + 67 = x ^ { 2 } 3 + 130$$

Solve for x_3

$$x_{3}=3\left(x^{2}+21\right)$$

Solution Steps

Subtract 67 from both sides.

$$x_{3}=x^{2}\times 3+130-67$$

Subtract 67 from 130 to get 63.

$$x_{3}=x^{2}\times 3+63$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3\left(x_{3}-63\right)}}{3}$$

$$x=\frac{\sqrt{3\left(x_{3}-63\right)}}{3}$$

Solve for x

$$x=\frac{\sqrt{3\left(x_{3}-63\right)}}{3}$$

$$x=-\frac{\sqrt{3\left(x_{3}-63\right)}}{3}\text{, }x_{3}\geq 63$$