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

$2 {(x - 7)}^{2} = 2$

Step 1

Divide each term in $2 {(x - 7)}^{2} = 2$ by $2$ and simplify.

Divide each term in $2 {(x - 7)}^{2} = 2$ by $2$ .

$\frac{2 {(x - 7)}^{2}}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x - 7)}^{2}}{2} = \frac{2}{2}$

Divide ${(x - 7)}^{2}$ by $1$ .

${(x - 7)}^{2} = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

${(x - 7)}^{2} = 1$

Step 2

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

$x - 7 = \pm \sqrt{1}$

Step 3

Any root of $1$ is $1$ .

$x - 7 = \pm 1$

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.

$x - 7 = 1$

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

Add $7$ to both sides of the equation.

$x = 1 + 7$

Add $1$ and $7$ .

$x = 8$

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

$x - 7 = - 1$

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

Add $7$ to both sides of the equation.

$x = - 1 + 7$

Add $- 1$ and $7$ .

$x = 6$

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

$x = 8, 6$