Solve Using the Square Root Property 7x^2=252

$7 x^{2} = 252$

Step 1

Divide each term in $7 x^{2} = 252$ by $7$ and simplify.

Divide each term in $7 x^{2} = 252$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{252}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{252}{7}$

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

$x^{2} = \frac{252}{7}$

Simplify the right side.

Divide $252$ by $7$ .

$x^{2} = 36$

Step 2

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

$x = \pm \sqrt{36}$

Step 3

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

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

$x = \pm 6$

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.

$x = 6$

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

$x = - 6$

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

$x = 6, - 6$