Find the Roots (Zeros) g(x)=4x^2-484

$g (x) = 4 x^{2} - 484$

Step 1

Set $4 x^{2} - 484$ equal to $0$ .

$4 x^{2} - 484 = 0$

Step 2

Solve for $x$ .

Add $484$ to both sides of the equation.

$4 x^{2} = 484$

Divide each term in $4 x^{2} = 484$ by $4$ and simplify.

Divide each term in $4 x^{2} = 484$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{484}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{484}{4}$

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

$x^{2} = \frac{484}{4}$

Simplify the right side.

Divide $484$ by $4$ .

$x^{2} = 121$

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

$x = \pm \sqrt{121}$

Simplify $\pm \sqrt{121}$ .

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

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

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

$x = \pm 11$

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.

$x = 11$

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

$x = - 11$

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

$x = 11, - 11$

Step 3