Solve Using the Square Root Property (x+1)^2=400

${(x + 1)}^{2} = 400$

Step 1

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

$x + 1 = \pm \sqrt{400}$

Step 2

Simplify $\pm \sqrt{400}$ .

Rewrite $400$ as $20^{2}$ .

$x + 1 = \pm \sqrt{20^{2}}$

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

$x + 1 = \pm 20$

Step 3

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.

$x + 1 = 20$

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

Subtract $1$ from both sides of the equation.

$x = 20 - 1$

Subtract $1$ from $20$ .

$x = 19$

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

$x + 1 = - 20$

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

Subtract $1$ from both sides of the equation.

$x = - 20 - 1$

Subtract $1$ from $- 20$ .

$x = - 21$

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

$x = 19, - 21$