Solve Using the Square Root Property 4x^2=121

$4 x^{2} = 121$

Step 1

Divide each term in $4 x^{2} = 121$ by $4$ and simplify.

Divide each term in $4 x^{2} = 121$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{121}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{121}{4}$

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

$x^{2} = \frac{121}{4}$

Step 2

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

$x = \pm \sqrt{\frac{121}{4}}$

Step 3

Simplify $\pm \sqrt{\frac{121}{4}}$ .

Rewrite $\sqrt{\frac{121}{4}}$ as $\frac{\sqrt{121}}{\sqrt{4}}$ .

$x = \pm \frac{\sqrt{121}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $121$ as $11^{2}$ .

$x = \pm \frac{\sqrt{11^{2}}}{\sqrt{4}}$

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

$x = \pm \frac{11}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$x = \pm \frac{11}{\sqrt{2^{2}}}$

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

$x = \pm \frac{11}{2}$

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.

$x = \frac{11}{2}$

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

$x = - \frac{11}{2}$

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

$x = \frac{11}{2}, - \frac{11}{2}$