Solve for x (x+3)^4=362

${(x + 3)}^{4} = 362$

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$x + 3 = \pm \sqrt[4]{362}$

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.

$x + 3 = \sqrt[4]{362}$

Subtract $3$ from both sides of the equation.

$x = \sqrt[4]{362} - 3$

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

$x + 3 = - \sqrt[4]{362}$

Subtract $3$ from both sides of the equation.

$x = - \sqrt[4]{362} - 3$

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

$x = \sqrt[4]{362} - 3, - \sqrt[4]{362} - 3$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[4]{362} - 3, - \sqrt[4]{362} - 3$

Decimal Form:

$x = 1.36191444 \dots, - 7.36191444 \dots$