Pre-Algebra Examples

$16 x^{2} - 49 = 0$

Step 1

Add $49$ to both sides of the equation.

$16 x^{2} = 49$

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $16$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Simplify the numerator.

Tap for more steps...

Step 4.2.1

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

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{16}}$

Step 4.2.2

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

$x = \pm \frac{7}{\sqrt{16}}$

Step 4.3

Simplify the denominator.

Tap for more steps...

Step 4.3.1

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

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

Step 4.3.2

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

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

Step 5

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

Tap for more steps...

Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

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

Step 5.2

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

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

Step 5.3

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

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