Solve Using the Square Root Property (x+4)^2=100

${(x + 4)}^{2} = 100$

Step 1

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

$x + 4 = \pm \sqrt{100}$

Step 2

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

$x + 4 = \pm \sqrt{10^{2}}$

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

$x + 4 = \pm 10$

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.

$x + 4 = 10$

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

Subtract $4$ from both sides of the equation.

$x = 10 - 4$

Subtract $4$ from $10$ .

$x = 6$

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

$x + 4 = - 10$

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

Subtract $4$ from both sides of the equation.

$x = - 10 - 4$

Subtract $4$ from $- 10$ .

$x = - 14$

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

$x = 6, - 14$