Solve Using the Square Root Property 7(x+4)^2=35

$7 {(x + 4)}^{2} = 35$

Step 1

Divide each term in $7 {(x + 4)}^{2} = 35$ by $7$ and simplify.

Divide each term in $7 {(x + 4)}^{2} = 35$ by $7$ .

$\frac{7 {(x + 4)}^{2}}{7} = \frac{35}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 {(x + 4)}^{2}}{7} = \frac{35}{7}$

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

${(x + 4)}^{2} = \frac{35}{7}$

Simplify the right side.

Divide $35$ by $7$ .

${(x + 4)}^{2} = 5$

Step 2

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

$x + 4 = \pm \sqrt{5}$

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.

$x + 4 = \sqrt{5}$

Subtract $4$ from both sides of the equation.

$x = \sqrt{5} - 4$

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

$x + 4 = - \sqrt{5}$

Subtract $4$ from both sides of the equation.

$x = - \sqrt{5} - 4$

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

$x = \sqrt{5} - 4, - \sqrt{5} - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5} - 4, - \sqrt{5} - 4$

Decimal Form:

$x = - 1.76393202 \dots, - 6.23606797 \dots$