Solve Using the Square Root Property (x+7)^2-49=0

${(x + 7)}^{2} - 49 = 0$

Step 1

Add $49$ to both sides of the equation.

${(x + 7)}^{2} = 49$

Step 2

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

$x + 7 = \pm \sqrt{49}$

Step 3

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

$x + 7 = \pm \sqrt{7^{2}}$

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

$x + 7 = \pm 7$

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.

$x + 7 = 7$

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

Subtract $7$ from both sides of the equation.

$x = 7 - 7$

Subtract $7$ from $7$ .

$x = 0$

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

$x + 7 = - 7$

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

Subtract $7$ from both sides of the equation.

$x = - 7 - 7$

Subtract $7$ from $- 7$ .

$x = - 14$

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

$x = 0, - 14$