Solve Using the Square Root Property 18-x^2=0

$18 - x^{2} = 0$

Step 1

Subtract $18$ from both sides of the equation.

$- x^{2} = - 18$

Step 2

Divide each term in $- x^{2} = - 18$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 18$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 18}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 18}{- 1}$

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

$x^{2} = \frac{- 18}{- 1}$

Simplify the right side.

Divide $- 18$ by $- 1$ .

$x^{2} = 18$

Step 3

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

$x = \pm \sqrt{18}$

Step 4

Simplify $\pm \sqrt{18}$ .

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$x = \pm \sqrt{9 (2)}$

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

$x = \pm \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{2}$

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.

$x = 3 \sqrt{2}$

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

$x = - 3 \sqrt{2}$

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

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$x = 4.24264068 \dots, - 4.24264068 \dots$