Finite Math Examples

$y = x^{2} \arccos (\frac{2}{x})$

Step 1

Set $x^{2} \arccos (\frac{2}{x})$ equal to $0$ .

$x^{2} \arccos (\frac{2}{x}) = 0$

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 $0$ .

$x^{2} = 0$

$\arccos (\frac{2}{x}) = 0$

Step 2.2

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

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Step 2.2.1

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

$x^{2} = 0$

Step 2.2.2

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

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Step 2.2.2.1

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

$x = \pm \sqrt{0}$

Step 2.2.2.2

Simplify $\pm \sqrt{0}$ .

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Step 2.2.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.2.2.2.2

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

$x = \pm 0$

Step 2.2.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.3

Set $\arccos (\frac{2}{x})$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $\arccos (\frac{2}{x})$ equal to $0$ .

$\arccos (\frac{2}{x}) = 0$

Step 2.3.2

Solve $\arccos (\frac{2}{x}) = 0$ for $x$ .

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Step 2.3.2.1

Take the inverse arccosine of both sides of the equation to extract $x$ from inside the arccosine.

$\frac{2}{x} = \cos (0)$

Step 2.3.2.2

Simplify the right side.

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Step 2.3.2.2.1

The exact value of $\cos (0)$ is $1$ .

$\frac{2}{x} = 1$

Step 2.3.2.3

Find the LCD of the terms in the equation.

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Step 2.3.2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 2.3.2.3.2

The LCM of one and any expression is the expression.

$x$

Step 2.3.2.4

Multiply each term in $\frac{2}{x} = 1$ by $x$ to eliminate the fractions.

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Step 2.3.2.4.1

Multiply each term in $\frac{2}{x} = 1$ by $x$ .

$\frac{2}{x} x = 1 x$

Step 2.3.2.4.2

Simplify the left side.

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Step 2.3.2.4.2.1

Cancel the common factor of $x$ .

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Step 2.3.2.4.2.1.1

Cancel the common factor.

$\frac{2}{x} x = 1 x$

Step 2.3.2.4.2.1.2

Rewrite the expression.

$2 = 1 x$

Step 2.3.2.4.3

Simplify the right side.

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Step 2.3.2.4.3.1

Multiply $x$ by $1$ .

$2 = x$

Step 2.3.2.5

Rewrite the equation as $x = 2$ .

$x = 2$

Step 2.4

The final solution is all the values that make $x^{2} \arccos (\frac{2}{x}) = 0$ true.

$x = 0, 2$

Step 2.5

Exclude the solutions that do not make $x^{2} \arccos (\frac{2}{x}) = 0$ true.

$x = 2$

Step 3