Finite Math Examples

$f (x) = \sqrt{84 - 6 x}$

Step 1

Set $\sqrt{84 - 6 x}$ equal to $0$ .

$\sqrt{84 - 6 x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{84 - 6 x}}^{2} = 0^{2}$

Step 2.2

Simplify each side of the equation.

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Step 2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{84 - 6 x}$ as ${(84 - 6 x)}^{\frac{1}{2}}$ .

${({(84 - 6 x)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Simplify ${({(84 - 6 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.1.1

Multiply the exponents in ${({(84 - 6 x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(84 - 6 x)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.2.1.1.2.1

Cancel the common factor.

${(84 - 6 x)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.1.1.2.2

Rewrite the expression.

${(84 - 6 x)}^{1} = 0^{2}$

Step 2.2.2.1.2

Simplify.

$84 - 6 x = 0^{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raising $0$ to any positive power yields $0$ .

$84 - 6 x = 0$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Subtract $84$ from both sides of the equation.

$- 6 x = - 84$

Step 2.3.2

Divide each term in $- 6 x = - 84$ by $- 6$ and simplify.

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Step 2.3.2.1

Divide each term in $- 6 x = - 84$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 84}{- 6}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Cancel the common factor of $- 6$ .

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Step 2.3.2.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 84}{- 6}$

Step 2.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 84}{- 6}$

Step 2.3.2.3

Simplify the right side.

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Step 2.3.2.3.1

Divide $- 84$ by $- 6$ .

$x = 14$

Step 3