Solve Using the Square Root Property x^2-175=0

$x^{2} - 175 = 0$

Step 1

Add $175$ to both sides of the equation.

$x^{2} = 175$

Step 2

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

$x = \pm \sqrt{175}$

Step 3

Simplify $\pm \sqrt{175}$ .

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$x = \pm \sqrt{25 (7)}$

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

$x = \pm \sqrt{5^{2} \cdot 7}$

Pull terms out from under the radical.

$x = \pm 5 \sqrt{7}$

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.

$x = 5 \sqrt{7}$

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

$x = - 5 \sqrt{7}$

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

$x = 5 \sqrt{7}, - 5 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 5 \sqrt{7}, - 5 \sqrt{7}$

Decimal Form:

$x = 13.22875655 \dots, - 13.22875655 \dots$