Algebra Examples

$h = 62.5 \sqrt[3]{t} + 75.8$

Step 1

Rewrite the equation as $62.5 \sqrt[3]{t} + 75.8 = h$ .

$62.5 \sqrt[3]{t} + 75.8 = h$

Step 2

Subtract $75.8$ from both sides of the equation.

$62.5 \sqrt[3]{t} = h - 75.8$

Step 3

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

${(62.5 \sqrt[3]{t})}^{3} = {(h - 75.8)}^{3}$

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 $\sqrt[3]{t}$ as $t^{\frac{1}{3}}$ .

${(62.5 t^{\frac{1}{3}})}^{3} = {(h - 75.8)}^{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(62.5 t^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.1

Apply the product rule to $62.5 t^{\frac{1}{3}}$ .

${62.5}^{3} {(t^{\frac{1}{3}})}^{3} = {(h - 75.8)}^{3}$

Step 4.2.1.2

Raise $62.5$ to the power of $3$ .

$244140.625 {(t^{\frac{1}{3}})}^{3} = {(h - 75.8)}^{3}$

Step 4.2.1.3

Multiply the exponents in ${(t^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.3.1

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

$244140.625 t^{\frac{1}{3} \cdot 3} = {(h - 75.8)}^{3}$

Step 4.2.1.3.2

Cancel the common factor of $3$ .

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Step 4.2.1.3.2.1

Cancel the common factor.

$244140.625 t^{\frac{1}{3} \cdot 3} = {(h - 75.8)}^{3}$

Step 4.2.1.3.2.2

Rewrite the expression.

$244140.625 t^{1} = {(h - 75.8)}^{3}$

Step 4.2.1.4

Simplify.

$244140.625 t = {(h - 75.8)}^{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify ${(h - 75.8)}^{3}$ .

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Step 4.3.1.1

Use the Binomial Theorem.

$244140.625 t = h^{3} + 3 h^{2} \cdot - 75.8 + 3 h {(- 75.8)}^{2} + {(- 75.8)}^{3}$

Step 4.3.1.2

Simplify each term.

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Step 4.3.1.2.1

Multiply $- 75.8$ by $3$ .

$244140.625 t = h^{3} - 227.4 h^{2} + 3 h {(- 75.8)}^{2} + {(- 75.8)}^{3}$

Step 4.3.1.2.2

Raise $- 75.8$ to the power of $2$ .

$244140.625 t = h^{3} - 227.4 h^{2} + 3 h \cdot 5745.64 + {(- 75.8)}^{3}$

Step 4.3.1.2.3

Multiply $5745.64$ by $3$ .

$244140.625 t = h^{3} - 227.4 h^{2} + 17236.92 h + {(- 75.8)}^{3}$

Step 4.3.1.2.4

Raise $- 75.8$ to the power of $3$ .

$244140.625 t = h^{3} - 227.4 h^{2} + 17236.92 h - 435519.512$

Step 5

Divide each term in $244140.625 t = h^{3} - 227.4 h^{2} + 17236.92 h - 435519.512$ by $244140.625$ and simplify.

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Step 5.1

Divide each term in $244140.625 t = h^{3} - 227.4 h^{2} + 17236.92 h - 435519.512$ by $244140.625$ .

$\frac{244140.625 t}{244140.625} = \frac{h^{3}}{244140.625} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $244140.625$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{244140.625 t}{244140.625} = \frac{h^{3}}{244140.625} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{h^{3}}{244140.625} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Multiply by $1$ .

$t = \frac{1 h^{3}}{244140.625} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.2

Factor $244140.625$ out of $244140.625$ .

$t = \frac{1 h^{3}}{244140.625 (1)} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.3

Separate fractions.

$t = \frac{1}{244140.625} \cdot \frac{h^{3}}{1} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.4

Divide $1$ by $244140.625$ .

$t = 0.00000409 \frac{h^{3}}{1} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.5

Divide $h^{3}$ by $1$ .

$t = 0.00000409 h^{3} + \frac{- 227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.6

Move the negative in front of the fraction.

$t = 0.00000409 h^{3} - \frac{227.4 h^{2}}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.7

Factor $227.4$ out of $227.4 h^{2}$ .

$t = 0.00000409 h^{3} - \frac{227.4 (h^{2})}{244140.625} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.8

Factor $244140.625$ out of $244140.625$ .

$t = 0.00000409 h^{3} - \frac{227.4 (h^{2})}{244140.625 (1)} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.9

Separate fractions.

$t = 0.00000409 h^{3} - (\frac{227.4}{244140.625} \cdot \frac{h^{2}}{1}) + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.10

Divide $227.4$ by $244140.625$ .

$t = 0.00000409 h^{3} - (0.00093143 \frac{h^{2}}{1}) + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.11

Divide $h^{2}$ by $1$ .

$t = 0.00000409 h^{3} - (0.00093143 h^{2}) + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.12

Multiply $0.00093143$ by $- 1$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + \frac{17236.92 h}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.13

Factor $17236.92$ out of $17236.92 h$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + \frac{17236.92 (h)}{244140.625} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.14

Factor $244140.625$ out of $244140.625$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + \frac{17236.92 (h)}{244140.625 (1)} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.15

Separate fractions.

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + \frac{17236.92}{244140.625} \cdot \frac{h}{1} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.16

Divide $17236.92$ by $244140.625$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + 0.07060242 \frac{h}{1} + \frac{- 435519.512}{244140.625}$

Step 5.3.1.17

Divide $h$ by $1$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + 0.07060242 h + \frac{- 435519.512}{244140.625}$

Step 5.3.1.18

Divide $- 435519.512$ by $244140.625$ .

$t = 0.00000409 h^{3} - 0.00093143 h^{2} + 0.07060242 h - 1.78388792$