Solve Using the Square Root Property (x-3)^2=48

${(x - 3)}^{2} = 48$

Step 1

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

$x - 3 = \pm \sqrt{48}$

Step 2

Simplify $\pm \sqrt{48}$ .

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x - 3 = \pm \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$x - 3 = \pm \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

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

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.

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

Add $3$ to both sides of the equation.

$x = 4 \sqrt{3} + 3$

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

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

Add $3$ to both sides of the equation.

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

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

$x = 4 \sqrt{3} + 3, - 4 \sqrt{3} + 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{3} + 3, - 4 \sqrt{3} + 3$

Decimal Form:

$x = 9.92820323 \dots, - 3.92820323 \dots$