Solve Using the Square Root Property 5(x+3)^2=60

$5 {(x + 3)}^{2} = 60$

Step 1

Divide each term in $5 {(x + 3)}^{2} = 60$ by $5$ and simplify.

Divide each term in $5 {(x + 3)}^{2} = 60$ by $5$ .

$\frac{5 {(x + 3)}^{2}}{5} = \frac{60}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(x + 3)}^{2}}{5} = \frac{60}{5}$

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

${(x + 3)}^{2} = \frac{60}{5}$

Simplify the right side.

Divide $60$ by $5$ .

${(x + 3)}^{2} = 12$

Step 2

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

$x + 3 = \pm \sqrt{12}$

Step 3

Simplify $\pm \sqrt{12}$ .

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

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.

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

Subtract $3$ from both sides of the equation.

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

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

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

Subtract $3$ from both sides of the equation.

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.46410161 \dots, - 6.46410161 \dots$