Solve for x ((x-3)^3)/3+5=14

$\frac{{(x - 3)}^{3}}{3} + 5 = 14$

Step 1

Subtract $5$ from both sides of the equation.

$\frac{{(x - 3)}^{3}}{3} = 14 - 5$

Step 2

Subtract $5$ from $14$ .

$\frac{{(x - 3)}^{3}}{3} = 9$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{{(x - 3)}^{3}}{3} = 3 \cdot 9$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{{(x - 3)}^{3}}{3} = 3 \cdot 9$

Rewrite the expression.

${(x - 3)}^{3} = 3 \cdot 9$

Simplify the right side.

Multiply $3$ by $9$ .

${(x - 3)}^{3} = 27$

Step 5

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

$x - 3 = \sqrt[3]{27}$

Step 6

Simplify $\sqrt[3]{27}$ .

Rewrite $27$ as $3^{3}$ .

$x - 3 = \sqrt[3]{3^{3}}$

Pull terms out from under the radical, assuming real numbers.

$x - 3 = 3$

Step 7

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$x = 3 + 3$

Add $3$ and $3$ .

$x = 6$