Solve Using the Square Root Property 2(x-3)^2=8

$2 {(x - 3)}^{2} = 8$

Step 1

Divide each term in $2 {(x - 3)}^{2} = 8$ by $2$ and simplify.

Divide each term in $2 {(x - 3)}^{2} = 8$ by $2$ .

$\frac{2 {(x - 3)}^{2}}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(x - 3)}^{2}}{2} = \frac{8}{2}$

Divide ${(x - 3)}^{2}$ by $1$ .

${(x - 3)}^{2} = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

${(x - 3)}^{2} = 4$

Step 2

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

$x - 3 = \pm \sqrt{4}$

Step 3

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x - 3 = \pm \sqrt{2^{2}}$

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

$x - 3 = \pm 2$

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.

$x - 3 = 2$

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

Add $3$ to both sides of the equation.

$x = 2 + 3$

Add $2$ and $3$ .

$x = 5$

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

$x - 3 = - 2$

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

Add $3$ to both sides of the equation.

$x = - 2 + 3$

Add $- 2$ and $3$ .

$x = 1$

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

$x = 5, 1$