Trigonometry Examples

${(x + 3)}^{4} - 16 = 0$

Step 1

Add $16$ to both sides of the equation.

${(x + 3)}^{4} = 16$

Step 2

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

$x + 3 = \pm \sqrt[4]{16}$

Step 3

Simplify $\pm \sqrt[4]{16}$ .

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Step 3.1

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

$x + 3 = \pm \sqrt[4]{2^{4}}$

Step 3.2

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

$x + 3 = \pm 2$

Step 4

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

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Step 4.1

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

$x + 3 = 2$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$x = 2 - 3$

Step 4.2.2

Subtract $3$ from $2$ .

$x = - 1$

Step 4.3

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

$x + 3 = - 2$

Step 4.4

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

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Step 4.4.1

Subtract $3$ from both sides of the equation.

$x = - 2 - 3$

Step 4.4.2

Subtract $3$ from $- 2$ .

$x = - 5$

Step 4.5

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

$x = - 1, - 5$