Finite Math Examples

$x = \frac{1}{16} \cdot {(y + 6)}^{2} + 12$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(y + 6)}^{2}$ as $(y + 6) (y + 6)$ .

$x = \frac{1}{16} \cdot ((y + 6) (y + 6)) + 12$

Step 1.2

Expand $(y + 6) (y + 6)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x = \frac{1}{16} \cdot (y (y + 6) + 6 (y + 6)) + 12$

Step 1.2.2

Apply the distributive property.

$x = \frac{1}{16} \cdot (y \cdot y + y \cdot 6 + 6 (y + 6)) + 12$

Step 1.2.3

Apply the distributive property.

$x = \frac{1}{16} \cdot (y \cdot y + y \cdot 6 + 6 y + 6 \cdot 6) + 12$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $y$ by $y$ .

$x = \frac{1}{16} \cdot (y^{2} + y \cdot 6 + 6 y + 6 \cdot 6) + 12$

Step 1.3.1.2

Move $6$ to the left of $y$ .

$x = \frac{1}{16} \cdot (y^{2} + 6 \cdot y + 6 y + 6 \cdot 6) + 12$

Step 1.3.1.3

Multiply $6$ by $6$ .

$x = \frac{1}{16} \cdot (y^{2} + 6 y + 6 y + 36) + 12$

Step 1.3.2

Add $6 y$ and $6 y$ .

$x = \frac{1}{16} \cdot (y^{2} + 12 y + 36) + 12$

Step 1.4

Apply the distributive property.

$x = \frac{1}{16} y^{2} + \frac{1}{16} (12 y) + \frac{1}{16} \cdot 36 + 12$

Step 1.5

Simplify.

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Step 1.5.1

Combine $\frac{1}{16}$ and $y^{2}$ .

$x = \frac{y^{2}}{16} + \frac{1}{16} (12 y) + \frac{1}{16} \cdot 36 + 12$

Step 1.5.2

Cancel the common factor of $4$ .

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Step 1.5.2.1

Factor $4$ out of $16$ .

$x = \frac{y^{2}}{16} + \frac{1}{4 (4)} (12 y) + \frac{1}{16} \cdot 36 + 12$

Step 1.5.2.2

Factor $4$ out of $12 y$ .

$x = \frac{y^{2}}{16} + \frac{1}{4 (4)} (4 (3 y)) + \frac{1}{16} \cdot 36 + 12$

Step 1.5.2.3

Cancel the common factor.

$x = \frac{y^{2}}{16} + \frac{1}{4 \cdot 4} (4 (3 y)) + \frac{1}{16} \cdot 36 + 12$

Step 1.5.2.4

Rewrite the expression.

$x = \frac{y^{2}}{16} + \frac{1}{4} (3 y) + \frac{1}{16} \cdot 36 + 12$

Step 1.5.3

Combine $3$ and $\frac{1}{4}$ .

$x = \frac{y^{2}}{16} + \frac{3}{4} y + \frac{1}{16} \cdot 36 + 12$

Step 1.5.4

Combine $\frac{3}{4}$ and $y$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{1}{16} \cdot 36 + 12$

Step 1.5.5

Cancel the common factor of $4$ .

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Step 1.5.5.1

Factor $4$ out of $16$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{1}{4 (4)} \cdot 36 + 12$

Step 1.5.5.2

Factor $4$ out of $36$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{1}{4 \cdot 4} \cdot (4 \cdot 9) + 12$

Step 1.5.5.3

Cancel the common factor.

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{1}{4 \cdot 4} \cdot (4 \cdot 9) + 12$

Step 1.5.5.4

Rewrite the expression.

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{1}{4} \cdot 9 + 12$

Step 1.5.6

Combine $\frac{1}{4}$ and $9$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{9}{4} + 12$

Step 2

To write $12$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{9}{4} + 12 \cdot \frac{4}{4}$

Step 3

Combine $12$ and $\frac{4}{4}$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{9}{4} + \frac{12 \cdot 4}{4}$

Step 4

Combine the numerators over the common denominator.

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{9 + 12 \cdot 4}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $12$ by $4$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{9 + 48}{4}$

Step 5.2

Add $9$ and $48$ .

$x = \frac{y^{2}}{16} + \frac{3 y}{4} + \frac{57}{4}$