Algebra Examples

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

Step 1

Simplify $- 4 x + {(x - 3)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$y + \sqrt{x} = - 4 x + (x - 3) (x - 3)$

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.

$y + \sqrt{x} = - 4 x + x (x - 3) - 3 (x - 3)$

Step 1.1.2.2

Apply the distributive property.

$y + \sqrt{x} = - 4 x + x \cdot x + x \cdot - 3 - 3 (x - 3)$

Step 1.1.2.3

Apply the distributive property.

$y + \sqrt{x} = - 4 x + x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3$

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 $x$ .

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

Step 1.1.3.1.2

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

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

Step 1.1.3.1.3

Multiply $- 3$ by $- 3$ .

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

Step 1.1.3.2

Subtract $3 x$ from $- 3 x$ .

$y + \sqrt{x} = - 4 x + x^{2} - 6 x + 9$

Step 1.2

Subtract $6 x$ from $- 4 x$ .

$y + \sqrt{x} = x^{2} - 10 x + 9$

Step 2

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

$y = x^{2} - 10 x + 9 - \sqrt{x}$

Step 3

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.

$f (x) = x^{2} - 10 x + 9 - \sqrt{x}$