Solve Using the Square Root Property 2(x-3)^2=4

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

Step 1

Divide each term in $2 {(x - 3)}^{2} = 4$ by $2$ and simplify.

Divide each term in $2 {(x - 3)}^{2} = 4$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $4$ by $2$ .

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

Step 2

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

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

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.

$x - 3 = \sqrt{2}$

Add $3$ to both sides of the equation.

$x = \sqrt{2} + 3$

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

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

Add $3$ to both sides of the equation.

$x = - \sqrt{2} + 3$

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

$x = \sqrt{2} + 3, - \sqrt{2} + 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{2} + 3, - \sqrt{2} + 3$

Decimal Form:

$x = 4.41421356 \dots, 1.58578643 \dots$