Solve Using the Square Root Property 5(x-9)^2=15

$5 {(x - 9)}^{2} = 15$

Step 1

Divide each term in $5 {(x - 9)}^{2} = 15$ by $5$ and simplify.

Divide each term in $5 {(x - 9)}^{2} = 15$ by $5$ .

$\frac{5 {(x - 9)}^{2}}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(x - 9)}^{2}}{5} = \frac{15}{5}$

Divide ${(x - 9)}^{2}$ by $1$ .

${(x - 9)}^{2} = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

${(x - 9)}^{2} = 3$

Step 2

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

$x - 9 = \pm \sqrt{3}$

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.

$x - 9 = \sqrt{3}$

Add $9$ to both sides of the equation.

$x = \sqrt{3} + 9$

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

$x - 9 = - \sqrt{3}$

Add $9$ to both sides of the equation.

$x = - \sqrt{3} + 9$

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

$x = \sqrt{3} + 9, - \sqrt{3} + 9$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3} + 9, - \sqrt{3} + 9$

Decimal Form:

$x = 10.73205080 \dots, 7.26794919 \dots$