Solve Using the Square Root Property 7x^2-6=57

$7 x^{2} - 6 = 57$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$7 x^{2} = 57 + 6$

Add $57$ and $6$ .

$7 x^{2} = 63$

Step 2

Divide each term in $7 x^{2} = 63$ by $7$ and simplify.

Divide each term in $7 x^{2} = 63$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{63}{7}$

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

$x^{2} = \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$x^{2} = 9$

Step 3

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

$x = \pm \sqrt{9}$

Step 4

Simplify $\pm \sqrt{9}$ .

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

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

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$