Solve for x 2x^6=1458

$2 x^{6} = 1458$

Step 1

Divide each term in $2 x^{6} = 1458$ by $2$ and simplify.

Divide each term in $2 x^{6} = 1458$ by $2$ .

$\frac{2 x^{6}}{2} = \frac{1458}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{6}}{2} = \frac{1458}{2}$

Divide $x^{6}$ by $1$ .

$x^{6} = \frac{1458}{2}$

Simplify the right side.

Divide $1458$ by $2$ .

$x^{6} = 729$

Step 2

Take the 6th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[6]{729}$

Step 3

Simplify $\pm \sqrt[6]{729}$ .

Rewrite $729$ as $3^{6}$ .

$x = \pm \sqrt[6]{3^{6}}$

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

$x = \pm 3$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$