Algebra Examples

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

Step 1

Simplify $- 2 x + {(x + 3)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

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

Step 1.1.2

Expand $(x + 3) (x + 3)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

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

Step 1.1.2.2

Apply the distributive property.

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

Step 1.1.2.3

Apply the distributive property.

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

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

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

Step 1.1.3.1.2

Move $3$ to the left of $x$ .

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

Step 1.1.3.1.3

Multiply $3$ by $3$ .

$- 3 y + \sqrt{x} = - 2 x + x^{2} + 3 x + 3 x + 9$

Step 1.1.3.2

Add $3 x$ and $3 x$ .

$- 3 y + \sqrt{x} = - 2 x + x^{2} + 6 x + 9$

Step 1.2

Add $- 2 x$ and $6 x$ .

$- 3 y + \sqrt{x} = x^{2} + 4 x + 9$

Step 2

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

$- 3 y = x^{2} + 4 x + 9 - \sqrt{x}$

Step 3

Divide each term in $- 3 y = x^{2} + 4 x + 9 - \sqrt{x}$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y = x^{2} + 4 x + 9 - \sqrt{x}$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{x^{2}}{- 3} + \frac{4 x}{- 3} + \frac{9}{- 3} + \frac{- \sqrt{x}}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{x^{2}}{- 3} + \frac{4 x}{- 3} + \frac{9}{- 3} + \frac{- \sqrt{x}}{- 3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x^{2}}{- 3} + \frac{4 x}{- 3} + \frac{9}{- 3} + \frac{- \sqrt{x}}{- 3}$

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.

$y = - \frac{x^{2}}{3} + \frac{4 x}{- 3} + \frac{9}{- 3} + \frac{- \sqrt{x}}{- 3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{3} - \frac{4 x}{3} + \frac{9}{- 3} + \frac{- \sqrt{x}}{- 3}$

Step 3.3.1.3

Divide $9$ by $- 3$ .

$y = - \frac{x^{2}}{3} - \frac{4 x}{3} - 3 + \frac{- \sqrt{x}}{- 3}$

Step 3.3.1.4

Dividing two negative values results in a positive value.

$y = - \frac{x^{2}}{3} - \frac{4 x}{3} - 3 + \frac{\sqrt{x}}{3}$

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.

$f (x) = - \frac{x^{2}}{3} - \frac{4 x}{3} - 3 + \frac{\sqrt{x}}{3}$