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

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

Step 1

Divide each term in $7 {(x - 2)}^{2} = 56$ by $7$ and simplify.

Divide each term in $7 {(x - 2)}^{2} = 56$ by $7$ .

$\frac{7 {(x - 2)}^{2}}{7} = \frac{56}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 {(x - 2)}^{2}}{7} = \frac{56}{7}$

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

${(x - 2)}^{2} = \frac{56}{7}$

Simplify the right side.

Divide $56$ by $7$ .

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

Step 2

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

$x - 2 = \pm \sqrt{8}$

Step 3

Simplify $\pm \sqrt{8}$ .

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$x - 2 = \pm \sqrt{4 (2)}$

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

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

Pull terms out from under the radical.

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

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.

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

Add $2$ to both sides of the equation.

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

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

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

Add $2$ to both sides of the equation.

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.82842712 \dots, - 0.82842712 \dots$