Solve Using the Square Root Property (2x)^2-64=0

${(2 x)}^{2} - 64 = 0$

Step 1

Simplify each term.

Apply the product rule to $2 x$ .

$2^{2} x^{2} - 64 = 0$

Raise $2$ to the power of $2$ .

$4 x^{2} - 64 = 0$

Step 2

Add $64$ to both sides of the equation.

$4 x^{2} = 64$

Step 3

Divide each term in $4 x^{2} = 64$ by $4$ and simplify.

Divide each term in $4 x^{2} = 64$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{64}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{64}{4}$

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

$x^{2} = \frac{64}{4}$

Simplify the right side.

Divide $64$ by $4$ .

$x^{2} = 16$

Step 4

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

$x = \pm \sqrt{16}$

Step 5

Simplify $\pm \sqrt{16}$ .

Rewrite $16$ as $4^{2}$ .

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

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

$x = \pm 4$

Step 6

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.

$x = 4$

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

$x = - 4$

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

$x = 4, - 4$