Solve Using the Square Root Property x^2-75=0

$x^{2} - 75 = 0$

Step 1

Add $75$ to both sides of the equation.

$x^{2} = 75$

Step 2

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

$x = \pm \sqrt{75}$

Step 3

Simplify $\pm \sqrt{75}$ .

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$x = \pm \sqrt{25 (3)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 5 \sqrt{3}$

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

$x = - 5 \sqrt{3}$

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 8.66025403 \dots, - 8.66025403 \dots$