Solve Using the Square Root Property 4x^2-52=0

$4 x^{2} - 52 = 0$

Step 1

Add $52$ to both sides of the equation.

$4 x^{2} = 52$

Step 2

Divide each term in $4 x^{2} = 52$ by $4$ and simplify.

Divide each term in $4 x^{2} = 52$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{52}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{52}{4}$

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

$x^{2} = \frac{52}{4}$

Simplify the right side.

Divide $52$ by $4$ .

$x^{2} = 13$

Step 3

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

$x = \pm \sqrt{13}$

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.

$x = \sqrt{13}$

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

$x = - \sqrt{13}$

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

$x = \sqrt{13}, - \sqrt{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{13}, - \sqrt{13}$

Decimal Form:

$x = 3.60555127 \dots, - 3.60555127 \dots$