Solve Using the Square Root Property (x+3)^2+7=56

${(x + 3)}^{2} + 7 = 56$

Step 1

Subtract $7$ from both sides of the equation.

${(x + 3)}^{2} = 56 - 7$

Step 2

Subtract $7$ from $56$ .

${(x + 3)}^{2} = 49$

Step 3

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

$x + 3 = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

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

$x + 3 = \pm \sqrt{7^{2}}$

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

$x + 3 = \pm 7$

Step 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.

$x + 3 = 7$

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

Subtract $3$ from both sides of the equation.

$x = 7 - 3$

Subtract $3$ from $7$ .

$x = 4$

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

$x + 3 = - 7$

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

Subtract $3$ from both sides of the equation.

$x = - 7 - 3$

Subtract $3$ from $- 7$ .

$x = - 10$

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

$x = 4, - 10$