Trigonometry Examples

$4^{4} - 21 x^{2} + 80 = 0$

Step 1

Simplify $4^{4} - 21 x^{2} + 80$ .

Tap for more steps...

Step 1.1

Raise $4$ to the power of $4$ .

$256 - 21 x^{2} + 80 = 0$

Step 1.2

Add $256$ and $80$ .

$- 21 x^{2} + 336 = 0$

Step 2

Subtract $336$ from both sides of the equation.

$- 21 x^{2} = - 336$

Step 3

Divide each term in $- 21 x^{2} = - 336$ by $- 21$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- 21 x^{2} = - 336$ by $- 21$ .

$\frac{- 21 x^{2}}{- 21} = \frac{- 336}{- 21}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 21$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{- 21 x^{2}}{- 21} = \frac{- 336}{- 21}$

Step 3.2.1.2

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

$x^{2} = \frac{- 336}{- 21}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $- 336$ by $- 21$ .

$x^{2} = 16$

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 $\pm \sqrt{16}$ .

Tap for more steps...

Step 5.1

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

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

Step 5.2

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.

Tap for more steps...

Step 6.1

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

$x = 4$

Step 6.2

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

$x = - 4$

Step 6.3

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

$x = 4, - 4$