Algebra Examples

$16 = 8 \sqrt{100 - x}$

Step 1

Rewrite the equation as $8 \sqrt{100 - x} = 16$ .

$8 \sqrt{100 - x} = 16$

Step 2

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

${(8 \sqrt{100 - x})}^{2} = 16^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{100 - x}$ as ${(100 - x)}^{\frac{1}{2}}$ .

${(8 {(100 - x)}^{\frac{1}{2}})}^{2} = 16^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(8 {(100 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $8 {(100 - x)}^{\frac{1}{2}}$ .

$8^{2} {({(100 - x)}^{\frac{1}{2}})}^{2} = 16^{2}$

Step 3.2.1.2

Raise $8$ to the power of $2$ .

$64 {({(100 - x)}^{\frac{1}{2}})}^{2} = 16^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(100 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

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

$64 {(100 - x)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$64 {(100 - x)}^{\frac{1}{2} \cdot 2} = 16^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$64 {(100 - x)}^{1} = 16^{2}$

Step 3.2.1.4

Simplify.

$64 (100 - x) = 16^{2}$

Step 3.2.1.5

Apply the distributive property.

$64 \cdot 100 + 64 (- x) = 16^{2}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $64$ by $100$ .

$6400 + 64 (- x) = 16^{2}$

Step 3.2.1.6.2

Multiply $- 1$ by $64$ .

$6400 - 64 x = 16^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $16$ to the power of $2$ .

$6400 - 64 x = 256$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $6400$ from both sides of the equation.

$- 64 x = 256 - 6400$

Step 4.1.2

Subtract $6400$ from $256$ .

$- 64 x = - 6144$

Step 4.2

Divide each term in $- 64 x = - 6144$ by $- 64$ and simplify.

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Step 4.2.1

Divide each term in $- 64 x = - 6144$ by $- 64$ .

$\frac{- 64 x}{- 64} = \frac{- 6144}{- 64}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 64$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 64 x}{- 64} = \frac{- 6144}{- 64}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6144}{- 64}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 6144$ by $- 64$ .

$x = 96$