Solve Using the Square Root Property 4x^2-256=0

$4 x^{2} - 256 = 0$

Step 1

Add $256$ to both sides of the equation.

$4 x^{2} = 256$

Step 2

Divide each term in $4 x^{2} = 256$ by $4$ and simplify.

Divide each term in $4 x^{2} = 256$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{256}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{256}{4}$

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

$x^{2} = \frac{256}{4}$

Simplify the right side.

Divide $256$ by $4$ .

$x^{2} = 64$

Step 3

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

$x = \pm \sqrt{64}$

Step 4

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2}}$

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

$x = \pm 8$

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.

$x = 8$

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

$x = - 8$

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

$x = 8, - 8$