Solve Using the Square Root Property 5x^2-11=234

$5 x^{2} - 11 = 234$

Step 1

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

Add $11$ to both sides of the equation.

$5 x^{2} = 234 + 11$

Add $234$ and $11$ .

$5 x^{2} = 245$

Step 2

Divide each term in $5 x^{2} = 245$ by $5$ and simplify.

Divide each term in $5 x^{2} = 245$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{245}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{245}{5}$

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

$x^{2} = \frac{245}{5}$

Simplify the right side.

Divide $245$ by $5$ .

$x^{2} = 49$

Step 3

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

$x = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

Rewrite $49$ as $7^{2}$ .

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

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

$x = \pm 7$

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.

$x = 7$

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

$x = - 7$

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

$x = 7, - 7$