Finite Math Examples

$\sqrt{12 - x} = 4$

Step 1

Subtract $4$ from both sides of the equation.

$\sqrt{12 - x} - 4 = 0$

Step 2

Add $4$ to both sides of the equation.

$\sqrt{12 - x} = 4$

Step 3

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

${\sqrt{12 - x}}^{2} = 4^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{12 - x}$ as ${(12 - x)}^{\frac{1}{2}}$ .

${({(12 - x)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(12 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(12 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1.1

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

${(12 - x)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(12 - x)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(12 - x)}^{1} = 4^{2}$

Step 4.2.1.2

Simplify.

$12 - x = 4^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $4$ to the power of $2$ .

$12 - x = 16$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Subtract $12$ from both sides of the equation.

$- x = 16 - 12$

Step 5.1.2

Subtract $12$ from $16$ .

$- x = 4$

Step 5.2

Divide each term in $- x = 4$ by $- 1$ and simplify.

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Step 5.2.1

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $4$ by $- 1$ .

$x = - 4$