Solve Using the Square Root Property 2(x+5)^2+37=39

$2 {(x + 5)}^{2} + 37 = 39$

Step 1

Subtract $37$ from both sides of the equation.

$2 {(x + 5)}^{2} = 39 - 37$

Step 2

Subtract $37$ from $39$ .

$2 {(x + 5)}^{2} = 2$

Step 3

Divide each term in $2 {(x + 5)}^{2} = 2$ by $2$ and simplify.

Divide each term in $2 {(x + 5)}^{2} = 2$ by $2$ .

$\frac{2 {(x + 5)}^{2}}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x + 5)}^{2}}{2} = \frac{2}{2}$

Divide ${(x + 5)}^{2}$ by $1$ .

${(x + 5)}^{2} = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

${(x + 5)}^{2} = 1$

Step 4

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

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

Step 5

Any root of $1$ is $1$ .

$x + 5 = \pm 1$

Step 6

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.

$x + 5 = 1$

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

Subtract $5$ from both sides of the equation.

$x = 1 - 5$

Subtract $5$ from $1$ .

$x = - 4$

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

$x + 5 = - 1$

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

Subtract $5$ from both sides of the equation.

$x = - 1 - 5$

Subtract $5$ from $- 1$ .

$x = - 6$

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

$x = - 4, - 6$