Solve Using the Square Root Property (x-3)^2=20

${(x - 3)}^{2} = 20$

Step 1

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

$x - 3 = \pm \sqrt{20}$

Step 2

Simplify $\pm \sqrt{20}$ .

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x - 3 = \pm \sqrt{4 (5)}$

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

$x - 3 = \pm \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$x - 3 = \pm 2 \sqrt{5}$

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.

$x - 3 = 2 \sqrt{5}$

Add $3$ to both sides of the equation.

$x = 2 \sqrt{5} + 3$

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

$x - 3 = - 2 \sqrt{5}$

Add $3$ to both sides of the equation.

$x = - 2 \sqrt{5} + 3$

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

$x = 2 \sqrt{5} + 3, - 2 \sqrt{5} + 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{5} + 3, - 2 \sqrt{5} + 3$

Decimal Form:

$x = 7.47213595 \dots, - 1.47213595 \dots$