Solve Using the Square Root Property (x+1)^2-25=0

${(x + 1)}^{2} - 25 = 0$

Step 1

Add $25$ to both sides of the equation.

${(x + 1)}^{2} = 25$

Step 2

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

$x + 1 = \pm \sqrt{25}$

Step 3

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x + 1 = \pm \sqrt{5^{2}}$

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

$x + 1 = \pm 5$

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.

$x + 1 = 5$

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.

$x = 4, - 6$