Algebra Examples

$- 2 y + \sqrt[3]{x} = {(x - 6)}^{2}$

Step 1

Simplify ${(x - 6)}^{2}$ .

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Step 1.1

Rewrite.

$- 2 y + \sqrt[3]{x} = 0 + 0 + {(x - 6)}^{2}$

Step 1.2

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$- 2 y + \sqrt[3]{x} = (x - 6) (x - 6)$

Step 1.3

Expand $(x - 6) (x - 6)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$- 2 y + \sqrt[3]{x} = x (x - 6) - 6 (x - 6)$

Step 1.3.2

Apply the distributive property.

$- 2 y + \sqrt[3]{x} = x \cdot x + x \cdot - 6 - 6 (x - 6)$

Step 1.3.3

Apply the distributive property.

$- 2 y + \sqrt[3]{x} = x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $x$ by $x$ .

$- 2 y + \sqrt[3]{x} = x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6$

Step 1.4.1.2

Move $- 6$ to the left of $x$ .

$- 2 y + \sqrt[3]{x} = x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6$

Step 1.4.1.3

Multiply $- 6$ by $- 6$ .

$- 2 y + \sqrt[3]{x} = x^{2} - 6 x - 6 x + 36$

Step 1.4.2

Subtract $6 x$ from $- 6 x$ .

$- 2 y + \sqrt[3]{x} = x^{2} - 12 x + 36$

Step 2

Subtract $\sqrt[3]{x}$ from both sides of the equation.

$- 2 y = x^{2} - 12 x + 36 - \sqrt[3]{x}$

Step 3

Divide each term in $- 2 y = x^{2} - 12 x + 36 - \sqrt[3]{x}$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y = x^{2} - 12 x + 36 - \sqrt[3]{x}$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{x^{2}}{- 2} + \frac{- 12 x}{- 2} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{x^{2}}{- 2} + \frac{- 12 x}{- 2} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x^{2}}{- 2} + \frac{- 12 x}{- 2} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{2} + \frac{- 12 x}{- 2} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.2

Cancel the common factor of $- 12$ and $- 2$ .

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Step 3.3.1.2.1

Factor $- 2$ out of $- 12 x$ .

$y = - \frac{x^{2}}{2} + \frac{- 2 (6 x)}{- 2} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $- 2$ out of $- 2$ .

$y = - \frac{x^{2}}{2} + \frac{- 2 (6 x)}{- 2 (1)} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.2.2.2

Cancel the common factor.

$y = - \frac{x^{2}}{2} + \frac{- 2 (6 x)}{- 2 \cdot 1} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.2.2.3

Rewrite the expression.

$y = - \frac{x^{2}}{2} + \frac{6 x}{1} + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.2.2.4

Divide $6 x$ by $1$ .

$y = - \frac{x^{2}}{2} + 6 x + \frac{36}{- 2} + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.3

Divide $36$ by $- 2$ .

$y = - \frac{x^{2}}{2} + 6 x - 18 + \frac{- \sqrt[3]{x}}{- 2}$

Step 3.3.1.4

Dividing two negative values results in a positive value.

$y = - \frac{x^{2}}{2} + 6 x - 18 + \frac{\sqrt[3]{x}}{2}$

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - \frac{x^{2}}{2} + 6 x - 18 + \frac{\sqrt[3]{x}}{2}$