Solve for x 4(x+1)^4=2500

$4 {(x + 1)}^{4} = 2500$

Divide each term in $4 {(x + 1)}^{4} = 2500$ by $4$ and simplify.

Divide each term in $4 {(x + 1)}^{4} = 2500$ by $4$ .

$\frac{4 {(x + 1)}^{4}}{4} = \frac{2500}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(x + 1)}^{4}}{4} = \frac{2500}{4}$

Divide ${(x + 1)}^{4}$ by $1$ .

${(x + 1)}^{4} = \frac{2500}{4}$

Simplify the right side.

Divide $2500$ by $4$ .

${(x + 1)}^{4} = 625$

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

$x + 1 = \pm \sqrt[4]{625}$

Simplify $\pm \sqrt[4]{625}$ .

Rewrite $625$ as $5^{4}$ .

$x + 1 = \pm \sqrt[4]{5^{4}}$

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

$x + 1 = \pm 5$

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.

$x + 1 = 5$

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

Subtract $1$ from both sides of the equation.

$x = 5 - 1$

Subtract $1$ from $5$ .

$x = 4$

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

$x + 1 = - 5$

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

Subtract $1$ from both sides of the equation.

$x = - 5 - 1$

Subtract $1$ from $- 5$ .

$x = - 6$

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

$x = 4, - 6$