Trigonometry Examples

$(x^{2} - 4) (x^{2} + 1)$

Step 1

Set $(x^{2} - 4) (x^{2} + 1)$ equal to $0$ .

$(x^{2} - 4) (x^{2} + 1) = 0$

Step 2

Solve for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} - 4 = 0$

$x^{2} + 1 = 0$

Step 2.2

Set $x^{2} - 4$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x^{2} - 4$ equal to $0$ .

$x^{2} - 4 = 0$

Step 2.2.2

Solve $x^{2} - 4 = 0$ for $x$ .

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Step 2.2.2.1

Add $4$ to both sides of the equation.

$x^{2} = 4$

Step 2.2.2.2

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

$x = \pm \sqrt{4}$

Step 2.2.2.3

Simplify $\pm \sqrt{4}$ .

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Step 2.2.2.3.1

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

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

Step 2.2.2.3.2

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

$x = \pm 2$

Step 2.2.2.4

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

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Step 2.2.2.4.1

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

$x = 2$

Step 2.2.2.4.2

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

$x = - 2$

Step 2.2.2.4.3

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

$x = 2, - 2$

Step 2.3

Set $x^{2} + 1$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x^{2} + 1$ equal to $0$ .

$x^{2} + 1 = 0$

Step 2.3.2

Solve $x^{2} + 1 = 0$ for $x$ .

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Step 2.3.2.1

Subtract $1$ from both sides of the equation.

$x^{2} = - 1$

Step 2.3.2.2

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

$x = \pm \sqrt{- 1}$

Step 2.3.2.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i$

Step 2.3.2.4

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

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Step 2.3.2.4.1

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

$x = i$

Step 2.3.2.4.2

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

$x = - i$

Step 2.3.2.4.3

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

$x = i, - i$

Step 2.4

The final solution is all the values that make $(x^{2} - 4) (x^{2} + 1) = 0$ true.

$x = 2, - 2, i, - i$

Step 3