Solve for x (x-2)^3=-14

${(x - 2)}^{3} = - 14$

Step 1

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$x - 2 = \sqrt[3]{- 14}$

Step 2

Simplify $\sqrt[3]{- 14}$ .

Rewrite $- 14$ as ${(- 1)}^{3} \cdot 14$ .

Rewrite $- 14$ as $- 1 (14)$ .

$x - 2 = \sqrt[3]{- 1 (14)}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$x - 2 = \sqrt[3]{{(- 1)}^{3} \cdot 14}$

Pull terms out from under the radical.

$x - 2 = - 1 \sqrt[3]{14}$

Rewrite $- 1 \sqrt[3]{14}$ as $- \sqrt[3]{14}$ .

$x - 2 = - \sqrt[3]{14}$

Step 3

Add $2$ to both sides of the equation.

$x = - \sqrt[3]{14} + 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt[3]{14} + 2$

Decimal Form:

$x = - 0.41014226 \dots$