Algebra Examples

$2 = \sqrt{\frac{- h + 80}{16}}$

Step 1

Rewrite the equation as $\sqrt{\frac{- h + 80}{16}} = 2$ .

$\sqrt{\frac{- h + 80}{16}} = 2$

Step 2

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

${\sqrt{\frac{- h + 80}{16}}}^{2} = 2^{2}$

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 $\sqrt{\frac{- h + 80}{16}}$ as ${(\frac{- h + 80}{16})}^{\frac{1}{2}}$ .

${({(\frac{- h + 80}{16})}^{\frac{1}{2}})}^{2} = 2^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{- h + 80}{16})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{- h + 80}{16})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(\frac{- h + 80}{16})}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{- h + 80}{16})}^{\frac{1}{2} \cdot 2} = 2^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{- h + 80}{16})}^{1} = 2^{2}$

Step 3.2.1.2

Simplify.

$\frac{- h + 80}{16} = 2^{2}$

Step 3.2.1.3

Factor $- 1$ out of $- h$ .

$\frac{- (h) + 80}{16} = 2^{2}$

Step 3.2.1.4

Rewrite $80$ as $- 1 (- 80)$ .

$\frac{- (h) - 1 (- 80)}{16} = 2^{2}$

Step 3.2.1.5

Factor $- 1$ out of $- (h) - 1 (- 80)$ .

$\frac{- (h - 80)}{16} = 2^{2}$

Step 3.2.1.6

Simplify the expression.

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Step 3.2.1.6.1

Rewrite $- (h - 80)$ as $- 1 (h - 80)$ .

$\frac{- 1 (h - 80)}{16} = 2^{2}$

Step 3.2.1.6.2

Move the negative in front of the fraction.

$- \frac{h - 80}{16} = 2^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$- \frac{h - 80}{16} = 4$

Step 4

Solve for $h$ .

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Step 4.1

Multiply both sides of the equation by $- 16$ .

$- 16 (- \frac{h - 80}{16}) = - 16 \cdot 4$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Simplify $- 16 (- \frac{h - 80}{16})$ .

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Step 4.2.1.1.1

Cancel the common factor of $16$ .

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Step 4.2.1.1.1.1

Move the leading negative in $- \frac{h - 80}{16}$ into the numerator.

$- 16 \frac{- (h - 80)}{16} = - 16 \cdot 4$

Step 4.2.1.1.1.2

Factor $16$ out of $- 16$ .

$16 (- 1) \frac{- (h - 80)}{16} = - 16 \cdot 4$

Step 4.2.1.1.1.3

Cancel the common factor.

$16 \cdot - 1 \frac{- (h - 80)}{16} = - 16 \cdot 4$

Step 4.2.1.1.1.4

Rewrite the expression.

$- - (h - 80) = - 16 \cdot 4$

Step 4.2.1.1.2

Multiply.

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Step 4.2.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (h - 80) = - 16 \cdot 4$

Step 4.2.1.1.2.2

Multiply $h - 80$ by $1$ .

$h - 80 = - 16 \cdot 4$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Multiply $- 16$ by $4$ .

$h - 80 = - 64$

Step 4.3

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

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Step 4.3.1

Add $80$ to both sides of the equation.

$h = - 64 + 80$

Step 4.3.2

Add $- 64$ and $80$ .

$h = 16$