Solve for x (x-3)^4=21

${(x - 3)}^{4} = 21$

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

$x - 3 = \pm \sqrt[4]{21}$

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.

$x - 3 = \sqrt[4]{21}$

Add $3$ to both sides of the equation.

$x = \sqrt[4]{21} + 3$

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

$x - 3 = - \sqrt[4]{21}$

Add $3$ to both sides of the equation.

$x = - \sqrt[4]{21} + 3$

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

$x = \sqrt[4]{21} + 3, - \sqrt[4]{21} + 3$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[4]{21} + 3, - \sqrt[4]{21} + 3$

Decimal Form:

$x = 5.14069514 \dots, 0.85930485 \dots$