Solve Using the Square Root Property x^2-45=0

$x^{2} - 45 = 0$

Step 1

Add $45$ to both sides of the equation.

$x^{2} = 45$

Step 2

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

$x = \pm \sqrt{45}$

Step 3

Simplify $\pm \sqrt{45}$ .

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$x = \pm \sqrt{9 (5)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 3 \sqrt{5}$

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

$x = - 3 \sqrt{5}$

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 6.70820393 \dots, - 6.70820393 \dots$