Solve Using the Square Root Property 9x^2=17

$9 x^{2} = 17$

Step 1

Divide each term in $9 x^{2} = 17$ by $9$ and simplify.

Divide each term in $9 x^{2} = 17$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{17}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{17}{9}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{17}{9}$

Step 2

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

$x = \pm \sqrt{\frac{17}{9}}$

Step 3

Simplify $\pm \sqrt{\frac{17}{9}}$ .

Rewrite $\sqrt{\frac{17}{9}}$ as $\frac{\sqrt{17}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{17}}{\sqrt{9}}$

Simplify the denominator.

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

$x = \pm \frac{\sqrt{17}}{\sqrt{3^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{\sqrt{17}}{3}$

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.

$x = \frac{\sqrt{17}}{3}$

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

$x = - \frac{\sqrt{17}}{3}$

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

$x = \frac{\sqrt{17}}{3}, - \frac{\sqrt{17}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{17}}{3}, - \frac{\sqrt{17}}{3}$

Decimal Form:

$x = 1.37436854 \dots, - 1.37436854 \dots$