Solve Using the Square Root Property 3(x+4)^2=21

$3 {(x + 4)}^{2} = 21$

Step 1

Divide each term in $3 {(x + 4)}^{2} = 21$ by $3$ and simplify.

Divide each term in $3 {(x + 4)}^{2} = 21$ by $3$ .

$\frac{3 {(x + 4)}^{2}}{3} = \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(x + 4)}^{2}}{3} = \frac{21}{3}$

Divide ${(x + 4)}^{2}$ by $1$ .

${(x + 4)}^{2} = \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

${(x + 4)}^{2} = 7$

Step 2

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

$x + 4 = \pm \sqrt{7}$

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.

$x + 4 = \sqrt{7}$

Subtract $4$ from both sides of the equation.

$x = \sqrt{7} - 4$

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

$x + 4 = - \sqrt{7}$

Subtract $4$ from both sides of the equation.

$x = - \sqrt{7} - 4$

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

$x = \sqrt{7} - 4, - \sqrt{7} - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7} - 4, - \sqrt{7} - 4$

Decimal Form:

$x = - 1.35424868 \dots, - 6.64575131 \dots$