Algebra Examples

${(18 - n)}^{\frac{1}{2}} = {(\frac{n}{8})}^{\frac{1}{2}}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$18 - n = \frac{n}{8}$

Step 2

Solve for $n$ .

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Step 2.1

Multiply both sides by $8$ .

$(18 - n) \cdot 8 = \frac{n}{8} \cdot 8$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Simplify $(18 - n) \cdot 8$ .

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Step 2.2.1.1.1

Apply the distributive property.

$18 \cdot 8 - n \cdot 8 = \frac{n}{8} \cdot 8$

Step 2.2.1.1.2

Simplify the expression.

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Step 2.2.1.1.2.1

Multiply $18$ by $8$ .

$144 - n \cdot 8 = \frac{n}{8} \cdot 8$

Step 2.2.1.1.2.2

Multiply $8$ by $- 1$ .

$144 - 8 n = \frac{n}{8} \cdot 8$

Step 2.2.1.1.2.3

Reorder $144$ and $- 8 n$ .

$- 8 n + 144 = \frac{n}{8} \cdot 8$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Cancel the common factor of $8$ .

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Step 2.2.2.1.1

Cancel the common factor.

$- 8 n + 144 = \frac{n}{8} \cdot 8$

Step 2.2.2.1.2

Rewrite the expression.

$- 8 n + 144 = n$

Step 2.3

Solve for $n$ .

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Step 2.3.1

Move all terms containing $n$ to the left side of the equation.

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Step 2.3.1.1

Subtract $n$ from both sides of the equation.

$- 8 n + 144 - n = 0$

Step 2.3.1.2

Subtract $n$ from $- 8 n$ .

$- 9 n + 144 = 0$

Step 2.3.2

Subtract $144$ from both sides of the equation.

$- 9 n = - 144$

Step 2.3.3

Divide each term in $- 9 n = - 144$ by $- 9$ and simplify.

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Step 2.3.3.1

Divide each term in $- 9 n = - 144$ by $- 9$ .

$\frac{- 9 n}{- 9} = \frac{- 144}{- 9}$

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Cancel the common factor of $- 9$ .

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Step 2.3.3.2.1.1

Cancel the common factor.

$\frac{- 9 n}{- 9} = \frac{- 144}{- 9}$

Step 2.3.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 144}{- 9}$

Step 2.3.3.3

Simplify the right side.

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Step 2.3.3.3.1

Divide $- 144$ by $- 9$ .

$n = 16$