Solve Using the Square Root Property 9x^2-18=7

$9 x^{2} - 18 = 7$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $18$ to both sides of the equation.

$9 x^{2} = 7 + 18$

Add $7$ and $18$ .

$9 x^{2} = 25$

Step 2

Divide each term in $9 x^{2} = 25$ by $9$ and simplify.

Divide each term in $9 x^{2} = 25$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{25}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{25}{9}$

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

$x^{2} = \frac{25}{9}$

Step 3

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

$x = \pm \sqrt{\frac{25}{9}}$

Step 4

Simplify $\pm \sqrt{\frac{25}{9}}$ .

Rewrite $\sqrt{\frac{25}{9}}$ as $\frac{\sqrt{25}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{9}}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{9}}$

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

$x = \pm \frac{5}{\sqrt{9}}$

Simplify the denominator.

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

$x = \pm \frac{5}{\sqrt{3^{2}}}$

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

$x = \pm \frac{5}{3}$

Step 5

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.

$x = \frac{5}{3}$

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

$x = - \frac{5}{3}$

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

$x = \frac{5}{3}, - \frac{5}{3}$