Find All Complex Solutions 7x^4=56

$7 x^{4} = 56$

Subtract $56$ from both sides of the equation.

$7 x^{4} - 56 = 0$

Factor $7$ out of $7 x^{4} - 56$ .

Factor $7$ out of $7 x^{4}$ .

$7 (x^{4}) - 56 = 0$

Factor $7$ out of $- 56$ .

$7 x^{4} + 7 \cdot - 8 = 0$

Factor $7$ out of $7 x^{4} + 7 \cdot - 8$ .

$7 (x^{4} - 8) = 0$

Divide each term in $7 (x^{4} - 8) = 0$ by $7$ and simplify.

Divide each term in $7 (x^{4} - 8) = 0$ by $7$ .

$\frac{7 (x^{4} - 8)}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (x^{4} - 8)}{7} = \frac{0}{7}$

Divide $x^{4} - 8$ by $1$ .

$x^{4} - 8 = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$x^{4} - 8 = 0$

Add $8$ to both sides of the equation.

$x^{4} = 8$

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

$x = \pm \sqrt[4]{8}$

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.

$x = \sqrt[4]{8}$

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

$x = - \sqrt[4]{8}$

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

$x = \sqrt[4]{8}, - \sqrt[4]{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[4]{8}, - \sqrt[4]{8}$

Decimal Form:

$x = 1.68179283 \dots, - 1.68179283 \dots$