# Finite Math Examples

,

Step 1

Step 1.1

Subtract from both sides of the equation.

Step 1.2

Divide each term in by and simplify.

Step 1.2.1

Divide each term in by .

Step 1.2.2

Simplify the left side.

Step 1.2.2.1

Dividing two negative values results in a positive value.

Step 1.2.2.2

Divide by .

Step 1.2.3

Simplify the right side.

Step 1.2.3.1

Simplify each term.

Step 1.2.3.1.1

Divide by .

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

Step 1.2.3.1.3

Divide by .

Step 2

Step 2.1

Replace all occurrences of in with .

Step 2.2

Simplify the left side.

Step 2.2.1

Simplify each term.

Step 2.2.1.1

Apply the distributive property.

Step 2.2.1.2

Multiply by .

Step 3

Step 3.1

Add to both sides of the equation.

Step 3.2

Add and .

Step 3.3

Factor the left side of the equation.

Step 3.3.1

Factor out of .

Step 3.3.1.1

Reorder and .

Step 3.3.1.2

Factor out of .

Step 3.3.1.3

Factor out of .

Step 3.3.1.4

Rewrite as .

Step 3.3.1.5

Factor out of .

Step 3.3.1.6

Factor out of .

Step 3.3.2

Factor.

Step 3.3.2.1

Factor using the AC method.

Step 3.3.2.1.1

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Step 3.3.2.1.2

Write the factored form using these integers.

Step 3.3.2.2

Remove unnecessary parentheses.

Step 3.4

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 3.5

Set equal to and solve for .

Step 3.5.1

Set equal to .

Step 3.5.2

Add to both sides of the equation.

Step 3.6

Set equal to and solve for .

Step 3.6.1

Set equal to .

Step 3.6.2

Subtract from both sides of the equation.

Step 3.7

The final solution is all the values that make true.

Step 4

Step 4.1

Replace all occurrences of in with .

Step 4.2

Simplify the right side.

Step 4.2.1

Simplify .

Step 4.2.1.1

Raise to the power of .

Step 4.2.1.2

Add and .

Step 5

Step 5.1

Replace all occurrences of in with .

Step 5.2

Simplify the right side.

Step 5.2.1

Simplify .

Step 5.2.1.1

Raise to the power of .

Step 5.2.1.2

Add and .

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

Step 7

The result can be shown in multiple forms.

Point Form:

Equation Form:

Step 8