Solve Using the Square Root Property 49x^2-3=13

$49 x^{2} - 3 = 13$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$49 x^{2} = 13 + 3$

Add $13$ and $3$ .

$49 x^{2} = 16$

Step 2

Divide each term in $49 x^{2} = 16$ by $49$ and simplify.

Divide each term in $49 x^{2} = 16$ by $49$ .

$\frac{49 x^{2}}{49} = \frac{16}{49}$

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

$\frac{49 x^{2}}{49} = \frac{16}{49}$

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

$x^{2} = \frac{16}{49}$

Step 3

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

$x = \pm \sqrt{\frac{16}{49}}$

Step 4

Simplify $\pm \sqrt{\frac{16}{49}}$ .

Rewrite $\sqrt{\frac{16}{49}}$ as $\frac{\sqrt{16}}{\sqrt{49}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{49}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{49}}$

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

$x = \pm \frac{4}{\sqrt{49}}$

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{4}{\sqrt{7^{2}}}$

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

$x = \pm \frac{4}{7}$

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.

$x = \frac{4}{7}$

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

$x = - \frac{4}{7}$

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

$x = \frac{4}{7}, - \frac{4}{7}$