Solve Using the Square Root Property 3(x+6)^2=54

$3 {(x + 6)}^{2} = 54$

Step 1

Divide each term in $3 {(x + 6)}^{2} = 54$ by $3$ and simplify.

Divide each term in $3 {(x + 6)}^{2} = 54$ by $3$ .

$\frac{3 {(x + 6)}^{2}}{3} = \frac{54}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x + 6)}^{2}}{3} = \frac{54}{3}$

Divide ${(x + 6)}^{2}$ by $1$ .

${(x + 6)}^{2} = \frac{54}{3}$

Simplify the right side.

Divide $54$ by $3$ .

${(x + 6)}^{2} = 18$

Step 2

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

$x + 6 = \pm \sqrt{18}$

Step 3

Simplify $\pm \sqrt{18}$ .

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$x + 6 = \pm \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$x + 6 = \pm \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$x + 6 = \pm 3 \sqrt{2}$

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.

$x + 6 = 3 \sqrt{2}$

Subtract $6$ from both sides of the equation.

$x = 3 \sqrt{2} - 6$

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

$x + 6 = - 3 \sqrt{2}$

Subtract $6$ from both sides of the equation.

$x = - 3 \sqrt{2} - 6$

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

$x = 3 \sqrt{2} - 6, - 3 \sqrt{2} - 6$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{2} - 6, - 3 \sqrt{2} - 6$

Decimal Form:

$x = - 1.75735931 \dots, - 10.24264068 \dots$